Year 6 Maths Worksheets 27g5a

Year 6 Worksheets 200 Maths Worksheets Ages 10 -11 years

Includes: Place, value and ordering Addition Subtraction Multiplication and Division Factors and Multiples Fractions and Decimals Ratio and Probability Shape, Angles Measuring, Time Money Handling Data Number Problems Answers Included

© C. Diamond – Not for resale

1

Contents 1. Place, value and ordering 2. Addition 3. Subtraction 4. Multiplication 5 Factors and Multiples 6. Division 7. Multiplication and Division 8. Fractions and Decimals 9. Ratio and Probability 10. Handling Data 11. Shape 12. Time 13. Measuring 14. Money 15. Number Problems Answers End

Page 3 16 31 40 66 74 90 95 124 131 145 167 172 179 185 202 252

2

Place, value and ordering 1 What is the place value of the blue digits? Draw a place value chart if it helps! Example: Tth Th H 45713 4 5 7 The 5 is 5000 1. 62871

800

T

U

1

3

2.

9240

3. 617450

4.

42601

5. 237380

6.

960193

7. 344169

8.

75328

Write these numbers out in words. 9. 57826

Fifty seven thousand, eight hundred and twenty six

10. 46310 11. 3290 12. 25891 Write these numbers in figures. 13. Seventeen thousand, one hundred and twenty 14. Fifty nine thousand, two hundred and six 3

Place, value and ordering 2 Read these decimal fractions. What does the blue digit represent? 1.

6·48

2.

3·78

3.

2·91

4.

5·14

5.

3.342

Eight hundredths

Write these numbers in order, smallest to largest. 6.

9·45

9·55

5·95

7·73

5·09

7.

1·68

1·86

1·62

1·87

1·61

8.

2·35

20·15

2·53

0·53

2·05

9.

1·17

1·117

1·07

1·007

1·71

4

Place, value and ordering 3 Write the missing hundredth on the number lines. 1. 1·2 1·21 1·22

1·34

2. 5·55

5·69

3. 4·0

Write the missing thousandths on the number lines. 4. 1·35 1·351

1·364

5. 4·03

4·044

6. 2·890

5

Place, value and ordering 4 For each set of numbers, underline the smallest number and a cross through the largest number. 1. 4·13

3·672

4·013

3·009

4·123

2. 15·75

16·01

15·07

16·13

16·103

3. 23·12

23·21

23·02

23·01

23·13

4. 124·60

123·9

124·06

123·09

124·006

5. 0·01

0·02

0·002

0·1

0·03

What is the value of 4 in each of these numbers? 6. 17435

7.

14879

8. 40121

9.

377·4

Here are four digit cards.

9

2

0

3

10. What is the smallest number you can make using all four cards? 11. What is the largest number you can make using all four cards? 12. Underline the largest number. Ninety five thousand, eight hundred and two

Ninety five thousand, six hundred and sixty- two

6

Place, value and ordering 5 1.

Put these prices in order starting with the smallest.

£12425 £14908 £

£ 2.

£

£11·05

£ 3.

4. 2·8 22.7 ·7

£

£14900

£

£

£12·75 £

£12·50

£11·06

£

£12·02

£

£

Put these masses in order starting with the heaviest.

9·06 kg kg

£12634

Put these prices in order starting with the highest.

£12·15 £

£13967 £12245

8·07kg

9·6kg

kg

7·08kg

kg

0·75kg kg

0·76kg kg

kg

Find and mark the position of the following numbers on the number line. 3·25

3·1

2·95 3·025 26 3.0

27 28 29 30 31 3·4

7

Place, value and ordering 6 Round these numbers to the nearest multiple of 10. 1. 45897

2. 2364

3. 5601

4. 90456

Round these numbers to the nearest multiple of 100. 5. 15756

6. 1387

7. 39004

8. 40318

Round these numbers to the nearest multiple of 1000. 9. 134894 11. 87417

10. 1399 12. 56328

Round these numbers to the nearest whole number. 13. 24·9

14. 16·4

15. 9·45

16. 11·09

17. 45·26

18. 23·55

19. 15·15

20. 0·56

8

Place, value and ordering 7 Round the numbers to the nearest multiple of 10 1. 67 456 2. 15 894 3. 62 129 4. 34 592 Round the numbers to the nearest multiple of 100 5. 47 635 6. 25 001 7. 12 890 8. 31 504 9. 83 251 Round the numbers to the nearest multiple of 1000 10. 77 462 11. 19 921 12. 99 978 13. 289 131 9

Place, value and ordering 8 Use the thermometer to help you work out these positive and negative temperatures questions.

___________________________________________________________________________________________________ - 20 -15 -10 -5 0 5 10 15 20

This thermometer shows

1.

The temperature is 8°C. It drops by 12 degrees. What is the temperature now?

2.

The temperature is -12°C. It rises by 7 degrees. What is the temperature now?

3.

At night, the temperature was -8°C, in the day it was 2°C. What was the difference between the temperatures?

4.

In Paris the temperature is -2°C and in Moscow it is -11°C. How much colder is Moscow than Paris?

5.

The temperature is -7°C. It rises by 17 degrees. What is the temperature now?

6.

The temperature in Oslo is -16°C. How much will the temperature need to rise to be -3°C?

10

Place, value and ordering 9 Order these positive and negative numbers from lowest to highest. 1. -4 -7 8 - 10 4 -2

2. 0

-3

-22

- 14

2

-9

3. - 22

-5

20

-13

15

-12

- 18

-28

-9

3

-19

4. -8

Work out these calculations. 5.

6-8=

6.

-9+4=

7.

-7+15=

8.

0-18=

9.

-11-8=

10. -13+17=

11

Place, value and ordering 10 Find the difference between these numbers. Use the number line to help you. - 10 - 9

-8

-7

A. 1.

-8, 2

3.

-6

-5

-4

-3

-2

-1

0

1

2

3

2.

4, -6

-9, -3

4.

1, -10

5.

-7, 4

6.

8, -7

7.

-10, 10

8.

-3, -6

9.

9, -8

10.

0, -9

10

4

5

6

7

8

9

Work out these calculations without using a number line. B. 1. -104 +12

2.

-123 - 47

3.

-80 - 23

4.

44 -123

5.

83 - 21

6. -147 - 24

7. -124+22

8. -163 - 65

9. -228+112

10. 452 -156

12

10

Place, value and ordering 11 A.

Work out these square numbers.

1. 4² = 16

2.

9² =

3. 7² =

4.

1² =

5. 12² =

6.

2² =

7. 5² =

8.

8² =

9. 10² =

10.

11² =

12.

13² =

11.

6² =

B.

Complete each of the following.

1.

4² + 6 =

2.

10² - 9

3. 12² + 11 =

4.

7² + 24 =

5.

4² + 2² =

6.

6² - 21 =

7. 11² - 3² =

8.

9² + 19 =

10.

4² + 5² =

9.

6² + 6² =

=

11. 12² - 5²

=

12.

8² + 7² =

13.

9² - 7²

=

14.

6² + 4² =

15. 13² - 9²

=

16.

7² + 9² = 13

Place, value and ordering 12 Work out the rule for each sequence below. Write the next 3 numbers in each sequence, then write the rule. 1.

100, 106, 112, The rule is add 6.

,

,

2.

445, 450, 455, , , The rule is _________________________________

3.

-53, -50, -47, , , The rule is _________________________________

4.

-24, -12, 0, , , The rule is _________________________________

5.

150, 125, 100, , , The rule is _________________________________

6.

-60, -36, -12, , , The rule is _________________________________

7.

36, 45, 54, , , The rule is _________________________________

8.

15, -5, -25, , , The rule is _________________________________

14

Place, value and ordering 13 Use the numbers from the cards to make general statements about odd and even numbers. Try at least three examples for each statement.

1.

20

7

3

2

28

17

11

5

8

16

9

15

4

10

The sum of 3 odd numbers is

3 + 5 + 9 = 17

7 + 17 + 11 = 35

odd 15 + 9 + 7 = 31

2.

The sum of 2 even numbers is

3.

The sum of an odd number and an even number is

4.

The difference between 2 even numbers is

15

Place, value and ordering 14 Use the numbers from the cards to make general statements about odd and even numbers. Try at least three examples for each statement.

2 4

9

1

12

22

7

10

5

15

3

6

11

8

1. The product of 3 odd numbers is

2. The product of 2 even numbers is

3. The product of 2 odd numbers is

4. The product of 1 even number and 1 odd number is

16

Addition 1 Partition the numbers into hundreds tens and units to help you add them. 1. 325 + 278 = 300 +200 = 500 20 + 70 = 90 5+ 8 = 13 = 603

2. 167 + 164=

3. 456 + 234 =

4. 645 + 357=

5. 552 + 268 =

6. 785 + 247=

Round the second number to the nearest multiple of 10 or 100 to help work out these calculations. 7. 156 + 69 = 156 + 70 = 226 226 - 1 = 225

9. 433 + 102 =

8.

456 + 89 =

10.

391 + 99 =

17

Addition 2 Add these numbers using the vertical method. 1. 3568 + 455 4023

2.

8501 + 178

3.

7494 + 267

4.

3464 + 389

5. 2784 + 246

6.

6891 + 567

7.

2879 + 352

8.

8936 + 957

9. 3046 + 3589

10.

8501 + 2673

11.

7494 + 4761

12.

3464 + 3678

13. 7649 + 8463

14.

6832 + 6945

15.

9452 + 7902

16.

3764 + 9673

17. 1388 38 239 + 2784 4449

18.

8501 3490 594 + 4891

19.

7494 96 2385 + 3570

20.

3464 2389 784 + 2754

22.

9502 23. 693 8462 + 794

6491 3479 2845 + 6743

24.

4462 593 6936 + 8931

1 1 1

1 2 2

21. 1449 247 5937 + 7461

18

Addition 3 Write these calculations vertically and then work out the answer. 1.

56987 + 6390

2.

98236 + 43367

3.

671782 + 87345

4.

378140 + 29893

5.

135899 + 89246

6.

783478 + 34729

7.

989367 + 35924

8.

45612 + 89249

19


23789 + 3897 + 345

2.

13762 + 2351 + 899

3.

7335 + 25978 + 8935

4.

67789 + 4589 + 136

5.

99672 + 7824 + 189

6.

6849 + 9856 + 92361

7.

3893 + 98026 + 5864

8.

89572 + 9994 + 989

20


6·98 + 34·78

2.

782·98 + 137·985

3.

67·981 + 257·452

4.

6712·12 + 95·246

5.

5036·89 + 467·907

6.

67·446 + 137·009

7.

904·136 + 984·341

8.

672·981 + 90·398

21


73·34 + 56·34 + 3·45

2.

93·034 + 12·78 + 8·9

3.

1·945 + 89·231 + 9·45

4.

304·52 + 4·89 + 3·87

5.

98·452 + 2·341 + 9·98

6.

34·002 + 9·009 + 3·61

7.

78·34 + 10·007 + 3·679 8.

902·12 + 0·135 + 9·59

22

Addition 7 Write in the missing numbers. 1.

2.

1590 + 1 1841 3.

3567 + 74 5312 4.

5728 + 3 6451 5.

3567 + 13 8480 6.

1 6· 3 5 + ·2 1 9· 6 1 7.

2 5 4· 7 + 7 4· 2 9· 5 8.

2 ·5 7 3 + ·8 2 3 ·4 1 5

1 9· 2 5 + 7 4· 9 3· 6 1

23

Addition 8 Add the 2 digit numbers together, then use the answer to work out the other calculations. 1.

3.

57 + 21

=

2.

78 + 65

=

570 + 210 =

780 + 650 =

5700 + 2100 =

7800 + 6500 =

0·57 + 0·21 =

0·78 + 0·65 =

5·70 + 2·10 =

7·80 + 6·50 =

0·057 + 0·021=

0·078+0·065 =

98 + 24

=

4.

56 + 75

=

980 + 240 =

560 + 750 =

9800 + 2400 =

5600 + 7500 =

0·98 + 0·24 =

0·56 + 0·75 =

9·80 + 2·40 =

5·60 + 7·50 =

0·098 + 0·024=

0·056+0·075 =

24

Addition 9 Work out these addition calculations. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.

5700 + 2500 6400 + 3400 5900 + 1800 6600 + 7200 1300 + 2900 2900 + 7800 5100 + 9900 9300 + 7800 6700 + 5800 5600 + 8900 4500 + 8600 5800 + 3700 9200 + 9600

= = = = = = = = = = = = =

What is the missing number in these calculations? 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24.

5600 + + 6800 + 1400 5900 + + 1300 + 4900 2200 + + 9500 9600 + + 3800 4800 +

= 7900 = 11700 = 5600 = 7500 = 8900 = 7800 = 8700 = 14200 = 22700 = 17800 = 6900

25

Addition 10 What is the missing number in these calculations? 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.

5·71 +

= 5·8 + 9·31 = 9·4 + 14·22 = 14·3 5·52 + = 5·6 + 11·67 = 11·7 + 4·33 = 4·4 2·27 + = 2·3 + 6·91 = 7 9·12 + = 9·3 + 2·03 = 3·1 4·36 + = 4·4


6·7 +

=7 + 5 ·3 = 6 + 14·2 = 15 5·55 + = 6 + 13·46 = 14 + 4·83 = 5 2·2 + = 3 + 6·91 = 7 9·12 + = 10 + 2·03 = 3 4·56 + = 5

26

Addition 11 Work out these decimal calculations. 1. 0·3 + 0·26

=

2. 0·5 + 0·42

=

3. 0·15 + 0·62

=

4. 0·22 + 0·16

=

5. 0·73 + 1·44

=

6. 1·19 + 1·25

=

7. 5·51 + 3·93

=

8. 8·19 + 0·09

=

9. 7·37 + 4·67

=

10. 0·951 + 0·921 = 11. 7·142 + 0·497 = 12. 1·081 + 1·065 = 13. 1·032 + 0·079 = 14. 8·187 + 3·973 =

27

Addition 12 1.

Circle the two numbers which add up to 500.

201 2.

325

256

254

175

150

250

195

100

155

350

125

150

450

255

375

Circle the three numbers which add up to 850.

225 5.

199


555 4.

425


225 3.

175

150

300

450

350

250

425

Circle the three numbers which add up to 600.

25

125

150

275

75

425

200

28

Addition 13 Use an empty number line to add up two numbers. Fill in the missing numbers. 1.

7624 + 3957 = 7624 + 7 + 50 + 900 + 3000 = +7 + 50

+900

7624 7631 7681

2.

+3000

8581

11581

1357 + 297 = 1357 + 7 + 90 + 200 = +

+ 90

+200

1357 1364

3.

5724 + 562 =

4.

7534 + 1582 =

29

Addition 14 Use an empty number line to add up two numbers. Fill in the missing numbers. 1.

9241 + 5176 = 9241 + 6 + 70 + 100 + 5000 =

+6 +70

+100

9241 9247 9317

2.

+5000

9417

14417

4276 + 247 = 4276 + 7 + 40 + 200 = +

+ 40

+

4276 4283

3.

3793 + 493 =

4.

5056 + 3873 =

30

Subtraction 1 Use complementary addition to find the difference between two numbers. Use an empty number line. Example: 604 – 74 = 6 + 20 + 500 + 4 = 530 +6 +20 +500 +4 74 80

100

1.

403 – 67 =

2.

309 – 94 =

3.

713 – 83 =

4.

521 – 78 =

600

604

31

Subtraction 2 Subtract these numbers using the vertical method. 4 181

1. 5697 - 749 4948

2. 5134 - 623

3. 7634 - 805

4. 4494 - 865

5. 2845 - 783

6. 6793 - 985

7. 2942 - 836

8. 8634 - 459

9. 3049 - 2457

10. 8467 - 6734

11. 1123 - 1034

12. 4678 - 2489

13. 7356 - 4378

14. 8469 - 7356

15. 8174 - 4286

16. 8312 - 4295

17. 56345 - 7891

18. 98534 - 7351

19. 16474 - 7891

20. 53464 - 34897

21. 89321 - 6712

22. 12567 - 7834

23. 23870 - 12671

24. 90501 - 67232

32

Subtraction 3 Write these calculations vertically and then work out the answer. 1.

9746 - 6358

2.

8995 - 8439

3.

67986 - 8399

4.

67780 - 29936

5.

155783 - 84196

6.

93489 - 82457

7.

903401 - 98922

8.

65690 - 39897

33

Subtraction 4 Write these calculations vertically and then work out the answer. 1.

156·980 - 134·981

2.

782·98 - 137·99

3.

679·81 - 259·45

4.

6712·12 - 98·986

5.

1036·895 - 368·908

6.

267·446 - 189·77

7.

901·182 - 784·347

8.

872·981 - 89·396

34

Subtraction 5 Write in the missing numbers. 1.

2.

3290 8 2752 3.

5324 - 37 1954 4.

6327 83 3644 5.

8619 23 3596 6.

2 2· 1 7 ·3 1 6· 7 8 7.

6 2 1· 6 - 2 7 5· 45 · 7 8.

6 ·3 7 2 - ·1 4 1 ·2 3 8

-

4 9· 1 6 2 4· 24·68

35

Subtraction 6 Subtract the 2- digit numbers from each other, then use the answer to work out the other calculations. 1.

3.

87 - 25

=

2.

74 - 35

=

870 - 250 =

740 - 350 =

8700 - 2500 =

7400 - 3500 =

0·87 - 0·25 =

0·74 - 0·35 =

8·70 - 2·50 =

7·40 - 3·50 =

0·087 - 0·025 =

0·074 - 0·035 =

92 - 37

=

4.

76 - 29

=

920 - 370 =

760 - 290 =

9200 - 3700 =

7600 - 2900 =

0·92 - 0·37 =

0·76 - 0·29 =

9·20 - 0·37 =

7·60 - 2·90 =

0·092 - 0·037 =

0·076 - 0·029 =

36

Subtraction 7 Work out these subtraction calculations. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.

8700 - 2600 = 6300 - 5400 = 5800 - 2700 = 8300 - 5800 = 7300 - 2900 = 2900 - 2200 = 9600 - 3700 = 9500 - 7700 = 6400 - 4900 = 11700 - 8700 = 12400 - 3800 = 22800 - 11700 = 19200 - 15600 =


9600 - 4700 - 1800 2400 - 1800 - 4300 8200 - 9500 7400 - 2800 9800 -

= = = = = = = = = = =

3400 2700 7600 1900 3700 6700 4700 9200 6700 3800 3900

37

Subtraction 8 Work out these decimal calculations. Sometimes it helps to change tenths to hundredths. 1. 1·3 - 0·6

=

2. 0·5 - 0·4

=

3. 0·75 - 0·6

=

4. 0·82 - 0·10 = 5. 0·77 - 0·34

=

6. 1·19 - 0·95 = 7. 5·5 - 0·43

=

8. 2·27 - 0·09

=

9. 6·37 - 4·69

=

10. 0·951 - 0·021 = 11. 7·282 - 0·297 = 12. 1·081 - 1·065 = 13. 1·067- 0·039 = 14. 8·163 - 3·952 = 38

Subtraction 9 1.

Circle the two numbers with a difference of 3. -8

2.

7 ·5

5 ·5

1 ·5

17·5

-4·5

-2·5

-5·5

3 ·5

2 ·5

-1·2

2 ·2

3 ·2

-5·2

8 ·5

1 ·2

Circle the two numbers with a difference of 0·5. 1·25

5.

-6

Circle the two numbers with a difference of 12. -8·8

4.

3 ·5

Circle the two numbers with a difference of 8. 11·5

3.

- 1 ·5

-2·5

-1·5

-2·5

0·25

3 ·5

-1·0

Circle the two numbers with a difference of 0·75. 1·75

- 1 ·5

1·25

-0 ·5

0·25

2 ·5

-0·2

39

Multiplication 1 Multiply these numbers by 10. 560

1. 56

2. 78

3. 236

4. 600

5. 3912

6. 52891

7. 13

8. 2689

Multiply these numbers by 100. 2400

9. 24

10. 14

11. 789

12. 400

13. 4510

14. 46813

15. 2296

16. 35891

Complete the multiplication calculations. 17. 80 ×

= 800

18. 37 × 100 =

19. 70 ×

= 700

20. 99 × 100 =

21.

x

× 10 = 500

23. 124 × 100 =

22. 171 ×

= 1710

24. 456 ×

= 4560

40

Multiplication 2 Work out these pairs of calculations. 1. 45 ×10 ×10 = 45 ×

=

2. 89 ×10 ×10 = 89 ×

=

4500

=

3. 24 ×10 ×10 ×10 = 24 × 4. 321 ×10 ×10 = 321 × 5. 90 ×10 ×10 ×10 = 90 × 6. 305 ×10 ×10 ×10 = 305 ×

= = = =

Decide whether to multiply by 10, 100 or 1000 to change the first number to the second. 7. 236

×10

2 360

8. 14

1 400

9. 27

270

10. 253

256 000

11. 98

9 800

12. 72

72 000

41

Multiplication 3 Look at the rule for multiplying by 50. Rule: To × 50 first × 100 then ÷ 2 Example 14 × 50 (14 × 100) ÷ 2 Multiply the numbers below by 50.

1400 ÷ 2 = 700

1. 11 2. 24 3. 29 4. 50 5. 36 Now look at the rule for multiplying by 25. Use the rule to multiply these numbers by 25. Rule: To × 25 first × 100 then ÷ 4 Example 18 × 25 (18 × 100) ÷ 4 1800 ÷ 4 = 450 Multiply the numbers below by 25. 6. 20 7. 16 8. 50 9. 34 10. 48 42

Multiplication 4 Use the 8 times table and doubling to help multiply by 16. Example 13 × 16 (13 × 8) × 2 104 × 2 = 208 Multiply the numbers below by 16. 1. 14 2. 22 3. 15 4. 32 5. 42 Use the 6 times table and doubling to help multiply by 24. Example 16 × 24 (16 × 6 ) × 2 × 2 Multiply the numbers below by 24.

(96 × 2) × 2 = 384

6. 6 7. 14 8. 15 9. 50 10. 42

43

Multiplication 5 Sweets come in different sized bags. Calculate how many sweets you have altogether when you buy more than one bag. Try to work out the answers in your head. 1.

26 Strawberry Chews per bag

2. 64 Chocolate Drops per bag

3.

48 Lemon Melts per bag

a.

Buy 7 bags

b.

Buy 4 bags

c.

Buy 9 bags

a.

Buy 3 bags

b.

Buy 5 bags

c.

Buy 8 bags

a.

Buy 4 bags

b.

Buy 7 bags

c.

Buy 9 bags

44

Multiplication 6 Partition each of these calculations to find the answer. Example 46 × 4 = (40 × 4) + (6 × 4) = 160 + 24 = 184

1.

37 × 3 =

2.

65 × 4 =

3.

43 × 7 =

4.

59 × 8 =

5.

76 × 9 =

6.

87 × 6 =

7.

58 × 7 =

8.

79 × 8 = 45

Multiplication 7 Partition each of these calculations to find the answer. Example 92 × 8 = (90 × 8) + (2 × 8) = 720 + 16 = 736

1.

65 × 6 =

2.

45 × 9 =

3.

72 × 7 =

4.

49 × 9 =

5.

67 × 8 =

6.

54 × 6 =

7.

98 × 7 =

8.

73 × 8 = 46

Multiplication 8 Find the missing number by multiplying mentally. 1.

64 ×

7

= 448

2. 134 ×

= 536

3. 115 ×

= 345

4. 144 ×

= 864

5. 132 ×

= 924

6.

87 ×

= 522

7.

29 ×

= 203

8.

63 ×

= 504

9.

5×

= 380

10.

4×

= 328

11.

3×

= 285

12.

8×

= 616

13.

9×

= 243

14.

11 ×

= 308

15.

4×

= 312 47

Multiplication 9 Multiply these numbers by 49. Multiply by 50 first then adjust. Example 17 × 49 = (17 × 50) – 17 = 850 -17 = 833 1.

6 × 49 =

2.

4 × 49 =

3. 15 × 49 =

4.

8 × 49 =

5. 26 × 49 =

6. 33 × 49 =

7. 49 × 49 =

8.

94 × 49 =

48

Multiplication 10 Multiply these numbers by 51. Multiply by 50 first then adjust. Example 14 × 51 = (14 × 50) + 14 = 700 -14 = 686 1.

5 × 51 =

2.

7 × 51 =

3.

9 × 51 =

4.

12 × 51 =

5. 24 × 51 =

6. 36 × 51 =

7. 78 × 51 =

8.

53 × 51 =

49

Multiplication 11 When we multiply large numbers, we can use the grid method. Fill in the gaps. Example 628 × 7 = 600 20 8 = 4396 7 4200 140 56 1. 465 × 5 = 4

400

60

5

=

748 × 6 = 6

700

40

8

=

2.

3. 734 × 3 =

=

876 × 9 =

=

978 × 8 =

=

4.

5.

50

Multiplication 12 When we multiply large numbers we can use the grid method. Fill in the gaps. Example 5674 × 6 = 5000 600 70 4 = 34044 6 30000 3600 420 24 1. 2461 × 4 = 2000 4

400

60

1

=

3255 × 5 = 3000 5

200

50

5

=

2.

3. 6328 × 3 =

=

1289 × 7 =

=

4196 × 8 =

=

4.

5.

51

Multiplication 13 When we multiply large numbers, we can use the grid method. Fill in the missing numbers. Example 2__83 × 5 = 2000 600 80 3 = 13415 5 10000 3000 400 15 1. 4__56 × 3 = 3

= 12768

37__8 × 6 = 6

= 22368

614__ × 7 = 7

= 43022

__578 × 9 =

= 41202

2.

3.

4. 9 5. 7__52 × 8 = 8

= 60416

52

Multiplication 14 Approximate the answer to each calculation. Fill in the gaps. Complete each multiplication. 1. 126×5

125 × 5 = 600

2. 756×4

126 × 5 500 (100 × 5) 100 ( 20 × 5) + 30 ( 6 × 5) (126 × 5) 3. 453×8

756 × 4 +

4.

691 × 6

453 × 8

691 × 6 ( ( ( (

+

) ) ) )

5. 728×9

( ( ( (

+

6.

) ) ) )

847 × 8

728 × 9 +

(700 × 4) ( 50 × 4) ( 6 × 4) (756 × 4)

847 × 8 ( ( ( (

) ) ) )

+

( ( ( (

) ) ) )

53

Multiplication 15 Approximate the answer to each calculation. Fill in the gaps. Complete each multiplication. 1. 1526× 5

1500 × 5 = 7500 2. 2715 × 3

1526 × 5 (1000 × 5) ( 500 × 5) ( 20 × 5) ( 6 × 5)

+

3. 3642 × 5

+

4. 7367 × 3

3642 × 5 ( ( ( (

+

) ) ) )

5. 4318× 7

+

+

7367 × 3 ( ( ( (

) ) ) )

6. 6967×8

4318 × 7 ( ( ( (

2715 × 3 (2000 × 3) ( 700 × 3) ( 10 × 3) ( 3 × 3)

) ) ) )

+

6967 × 8 ( ( ( (

) ) ) ) 54

Multiplication 16

Work out an approximate answer for each multiplication. Then calculate the answer using a standard method of multiplication. 1. 597×6 597 × 6 3582

600 × 6 =3600

2. 736×6 736 × 6

54

3. 268×6

4. 947× 8

268 × 6

947 × 8

5. 783×7

6. 937 × 7

783 × 7

937 × 6

55

Multiplication 17

Work out an approximate answer for each multiplication. Then calculate the answer using a standard method of multiplication. 1. 4895×6 4895 × 6 29370

5000 × 6=30000

2. 6309 × 4 6309 × 4

553

3. 1297×5 1297 × 5

4. 3437 × 6 3437 × 6

5. 4779×7

6. 9786 × 8

4779 × 7

9786 × 8

56

Multiplication 18 Answer these multiplication questions. Calculate an approximate answer first, and then use the standard method of recording. Show your working. 1.

There are 4726 paper clips in a box. How many paper clips are there in 4 boxes?

2.

The shop sells 2678 cakes each day. How many cakes are sold in 5 days?

3.

A bus travels 3679 km every week. How far does it travel in 6 weeks?

4.

A school cook buys 3478 carrots every week. How many carrots did she buy in 9 weeks?

57

Multiplication 19 To multiply decimals numbers. First work out an approximate answer then partition the number, multiply each part and add them up. Example 5·93 × 3 (6 × 3) = 18 5·00 × 3 = 15·00 0·90 × 3 = 2·70 0·03 × 3 = 0·09 17·79 1.

8·26 × 4

(

)=

8·00 × 4 = 0·20 × 4 = 0·06 × 4 = 3.

5·17 × 6

6·84 × 7 6·00 × 7 = 0.80 × 7 = 0.04 × 7 =

(

)=

(

)=

(

)=

4·00 × 5 = 0·80 × 5 = 0·06 × 5 = (

)=

5·00 × 6 = 0·10 × 6 = 0·07 × 6 = 5.

2. 4·81 × 5

4. 6·35 × 4 6·00 × 4 = 0·30 × 4 = 0·05 × 4 =

(

)=

6. 9·68 × 8 9.00 × 8 = 0.60 × 8 = 0.08 × 8 =

58

Multiplication 20 To multiply decimals numbers. First work out an approximate answer then partition the number, multiply each part and add them up. 1.

7·54 × 7

(8×7)= 56

7·00 ×7= 0·50 ×7= 0·04 ×7= 3.

2.

9·78 × 6

(

) =

9·00 × 6 = 0·70 × 6 = 0·08 × 6 =

6·05 × 8

(

)=

4.

5·73 × 9

(

) =

5. 12·24 × 3

(

)=

6. 24·72 × 4

(

)=

7. 16·82 × 5

(

)=

8. 23·06 × 6

(

)=

59

Multiplication 21 Write in the missing three-digit numbers.

1.

× 2 = 300

2.

× 2 = 354

3.

× 10 = 2000

4.

× 100 = 34000

5.

× 0·1 = 50

6.

× 1·5 = 300

7.

× 0·5 = 200

8.

× 0·2 = 120

60

Multiplication 22 When we multiply numbers by a 2 digit number we can use the grid method. Fill in the gaps. Example 785 × 16 = 7850 × 700 80 5 = + 4710 10 7000 800 50 12560 6 1.

4200

10

4000

5

700

6 = +

4760

60

694 × 24 = 20 4

90

4 = +

829 × 37 = ×

4.

70 350

× 600

3.

1

30

476 × 15 = × 400

2.

480

+ =

497 × 68 = ×

= +

61

Multiplication 23 When we multiply large numbers by a 2 digit number we can use the grid method. Fill in the gaps. Example 5536 × 17 = 55360 × 5000 500 30 6 = + 38752

1.

10

50000

5000

300

60

7

35000

3500

210

42

94112 1 1 1

3472 × 25 = ×

3000

20

60000

400

70 1400

2 = +

69440

40

5 2.

6193 × 32 = ×

6000

30

100

90

3 = +

2 3.

3831 × 53 = ×

4.

= +

8456 × 24 = ×

=

+

62

Multiplication 24 Complete each multiplication. Example 226 × 24 = 5424 2

× (

0

)

4

8

0

)

1

4

4

5

4

2

4

1

1

0

×

2

4

)

(

2

0

×

2

4

(

6

×

2

4

2.

746 × 43 =

42 8

0

345 × 35 =

6 4 2 0

2

1.

2

4

63

Multiplication 25 Complete each multiplication. 1.

262 × 42 = 2

× (

6

2

4

2

0

0

×

4

2

)

8

4

0

2 2 0

(

6

0

×

4

2

)

2

5

2

0

(

2(

×

4

2

)

4

8

4

2. 756 × 36 =

3.

534 × 65 =

64

Multiplication 26 Write in the missing numbers. You can use a calculator. 1.

2.

480 × 1 10080 3.

60 × 35 12600 4.

642 × 3 21828 5.

61 × 49 27489 6.

1 5· 3 × 1· 2 ·6 0 1 7.

1 2 6· 5 × 5· 6 9 5· 7 5 8.

2·56 × 4· 0 1 2 ·2 8 8

12 ·25 ×75·60 9 4 6 8· 9 0

65

Factors and Multiples 1 Find all the factors of these numbers.

1.

18

2.

40

3.

64

4.

20

5.

36

6.

48

7.

24

1, 2, 3, 6, 9, 18

Find three different ways to split these calculations using factors. Then write the answer to the calculation. 8. 12 × 15

12 × 3 × 5, 15 × 6 × 2, 15 × 3 × 4 = 180

9. 16 × 12 10. 24 × 18 11. 33 × 16 12. 27 × 18 13. 25 × 16 14. 24 × 25 66

Factors and Multiples 2 A prime number has only 2 factors, itself and 1. A composite number has more than 2 factors. 1 is neither a prime nor a composite number. Fill in this table of factors for the numbers up to 20

Number

Factors

Number of Factors

1

1

1

2

6

2

1

2

1

2

3

6

4

67

Factors and Multiples 3 Fill in this table of factors for the numbers from 21 to 45.

Number 21

1

Factors 1 3

7

21

Number of Factors 4

1

68

Factors and Multiples 4

Look at the tables of numbers from 1 to 45 on the previous two pages. 1.

2.

a.

Make a list of all the numbers you found with only two factors.

b.

What are these numbers called?

a.

Make list of all the numbers over 5 you found with three factors.

b.

What are these numbers called?

69

Factors and Multiples 5 Answer these questions about factors, prime numbers and composite numbers. 1.

Are square numbers prime numbers or composite numbers?

2.

Can you find pairs of numbers up to 99 where the digits are reversed and they are both prime numbers? ? 13, 31

3.

Explain why 845 could not be a prime number?

4.

Explain why 266 could not be a prime number?

5.

The sum of the digits in the number 21 are prime, 2+1 =3. Find 5 other numbers like this?

70

Factors and Multiples 6 Find 10 multiples of these pairs of numbers. Underline the common multiples.

1.

2.

2

2, 4, 6, 8, 10, 12, 14, 16, 18

3

3,6,9,12,15 18,21,24,27,30

5 4

3.

3 9

4.

5 7

5.

4 10

6.

6 9

71

Factors and Multiples 7 Find 10 multiples of these sets of 3 numbers. Underline the lowest common multiple. 6,12,18,24,30,36,42,48,54,60 1. 6

2.

3

3,6,9,12,15 18,21,24,27,30

5

5,10,15,20,25,30,35,40,45,50

3 6 8

3.

5 6 10

4.

4 6 9

5.

9 8 12 72

Factors and Multiples 8 Work out the answer to these multiplication problems. 1.

Write the first 6 multiples of 24.

2.

Write the lowest common multiple of 3, 10 and 15

3.

Find 3 common multiples of 7 and 6.

4.

What is the third common multiple of 8 and 12?

5.

Tom goes swimming every four days. Paul swims every Saturday. They meet at the swimming pool this Saturday, how long before they meet again?

6.

Jane is threading beads. She starts with a red bead and puts another red one every ninth bead. Her second bead is a silver bead. She uses a silver bead every fifteenth bead. How many beads will be threaded before they are together again?

73

Factors and Multiples 9 Work out the answer to these multiplication problems. 1.

Write the first 8 multiples of 13.

2.

Write the lowest common multiple of 4, 7 and 12.

3.

List 10 multiples of 5 between 300 and 600.

4.

a. Write the first 10 multiples of 25.

b. What do you notice about the multiples of 25?

5.

List the first 20 multiples of ll.

74

Division 1 Divide these numbers by 10. 1. 240

24

2. 3690

3. 130

4. 340

5. 4500

6. 46700

7. 1230

8. 78200

Divide these numbers by 100. 9. 6600

66

10. 400

11. 2300

12. 100

13. 6700

14. 92300

15. 2200

16. 54600

Complete the division calculations. 17. 80 ÷

=8

18.

19. 370 ÷

= 37

20. 5600 ÷ 100 =

21.

÷ 10 = 430

23. 1200 ÷ 100 =

900 ÷ 100 =

22. 130 ÷ 24. 98300 ÷

= 13 = = 983

75

Division 2 Work out these calculations. 1. 400 ÷ 10 ÷ 10 = 400 ÷

100

2. 4500 ÷ 10 ÷ 10 = 4500 ÷

=

4 =

3. 9000 ÷ 10 ÷ 10 ÷10 = 9000 ÷

=

4. 80000 ÷ 10 ÷10 = 80000 ÷ 5. 934 ÷ 10 ÷ 10 = 934 ÷ =

= =

6. 3215 ÷ 10 ÷10 ÷ 10 = 3215 ÷ 7. 456 ÷ 10 ÷10 ÷ 10 = 456 ÷

= =

Decide whether to divide by 10, 100 or 1000 to change the first number to the second. 8. 560 9. 14400

÷10

56 144

10. 2490

249

11. 17200

172

12. 98000

98

13. 1380

1·38

76

Division 3 Find all the factors of these numbers.

1.

32

2.

25

3.

48

4.

54

5.

60

1, 2, 4, 8, 16, 32

6. 100 7. 108

Find three different ways to split these calculations using factors. Then write the answer to the calculation. 8. 168 ÷ 12 9. 180 ÷ 15

(168÷3)÷4, (168÷6) ÷2,(84÷12)+(84÷12)=14 4

10. 60 ÷ 15 11. 120 ÷ 24 18 12. 800 ÷ 16 18 13. 108 ÷ 27 14. 390 ÷ 15

77

Division 4 Divisibility Tests A number is divisible by 2 if the last digit is 0,2,4,6 or 8. A number is divisible by 3 if the sum of its digits is divisible by 3. A number is divisible by 4 if the tens and units divide exactly by 4. A number is divisible by 5 if the last digit is 0 or 5. A number is divisible by 9 if the sum of its digits are divisible by 9. A number is divisible by 10 if the last digit is 0. Use the divisibility tests and approximation to decide if the division calculations below are true or false. Mark with a √ or x. 1. 468 ÷ 9 = 52 √

2. 560 ÷ 10 = 56

3. 154 ÷ 2 = 77

4. 326 ÷ 4 = 88

5. 264 ÷ 3 = 88

6. 92 ÷ 4 = 23

7. 232 ÷ 5 = 46

8. 369 ÷ 9 = 41

9. 171 ÷ 2 = 86

10. 405 ÷ 9 = 35

11. 176 ÷ 2 = 88

12. 240 ÷ 5 = 48

13. 465 ÷ 5 = 91

14. 148 ÷ 4 = 37

15. 189 ÷ 3 = 69

16. 324 ÷ 9 = 36 78

Division 5 Approximate the answer first. Choose a standard method of recording to work out the answer to each calculation. Record any remainder as a mixed number. Example 227 ÷ 8 ~ 240 ÷ 8 = 30 3

28 8 8 227 160 (20 × 8) 67 64 (8 × 8) 3

1. 246 ÷ 4 ~ 240 ÷ 4 = 60 61 24 4 246 240 ( × 4) 6 4 (1× ) 2 1 Answer 61 2 3. 294÷ 6

Answer

~ ~

3

Answer 28 8

2. 566 ÷ 5 ~

Answer 4. 451 ÷ 7

~

Answer 79

Division 6 Approximate the answer first. Choose a standard method of recording to work out the answer to each calculation. Record any remainder as a mixed number. 1. 149 ÷ 7 ~ 140 ÷ 7 = 20 21 27 7 149 140 (20 × 7) 9 7 ( 1 × 7) 2 2 Answer 21 7

2. 325 ÷ 6 ~

3. 230 ÷ 6 ~

4. 259 ÷ 5

Answer 5. 748 ÷ 9 ~

Answer

Answer ~

Answer 6. 685 ÷ 7 ~

Answer 80

Division 7 Approximate the answer first. Choose a standard method of recording to work out the answer to each calculation. Record any remainder as a decimal number. to line the decimal points up under each other. Example 28·3 ÷ 4 ~ 28 ÷ 4 = 7 7·075 Answer 7·075 4 28·3 28·0 (7 × 4) 0·30 0·28 (0.07 × 4) 0·02 (0.005 × 4) 1. 46·2 ÷ 7 ~ 42 ÷ 7 = 6

2. 11·75 ÷ 5 ~

7 46·2 42·0 (6 × 7) 4·2 ( 0·7 × 7 ) Answer 3. 25·9 ÷ 2 ~ ~

Answer

Answer 4. 18·9 ÷ 9 ~

Answer 81

Division 8 Approximate the answer first. Choose a standard method of recording to work out the answer to each calculation. Record any remainder as a decimal number. to line the decimal points up under each other. 1. 84·6 ÷ 9 ~ 81 ÷ 9 =9

2. 32·5 ÷ 5

~

9 84·6 81·0 (9 × 9) 3·6 (0.4 × 9) Answer 3. 47·4 ÷ 5 ~

Answer 5. 28·2 ÷ 6 ~

Answer

Answer 4. 24·72 ÷ 2 ~

Answer 6. 60·8 ÷ 8 ~

Answer 82

Division 9 Answer these problems on divisibility tests. 1.

A number is divisible by 2 if the last digit divides exactly by 2. Underline the numbers that are divisible by 2?

2156 123 470 140 678 467 998 1002 771 43 2.

A number is divisible by 4 if the last 2 digits divide exactly by 4. Underline the numbers that are divisible by 4?

12 66 94 104 236 126 282 398 448 732 512 3.

A number is divisible by 25 if the last 2 digits are 00 25, 50 or 75. Underline the numbers that are divisible by 25.

1025 1660 3450 36 775 240 900 3335 11175 45 6700 385 67450 24200 6590 1100 750 6648 175 4.

A number is divisible by 8 if half of it is divisible by 4 or the last 3 digits are divisible by 8. Underline the numbers that are divisible by 8.

6800 216 4256 444 816 612 2680 3156 796

83

Division 10 Use your knowledge of the divisibility tests of 2, 4, 8 and 25 to answer these problems. 1.

The year 2000 was a leap year. They occur every four years. a. Will the year 2024 be a leap year? b. Will the year 2078 be a leap year? c. Will the year 2036 be leap year?

2.

Cookies come in packets of eight. If Salford Junior school wants to buy 864 cookies. Can they buy the exact number of packets of biscuits? How do you know?

3.

A box of chocolates has 25 chocolates. Could 3500 chocolates fit exactly into boxes? How do you know?

4.

There are four cups of water in litre. Could 1786 cups of water be made into whole litres? How do you know?

84

Division 11 Answer these problems on divisibility tests. 1.

A number is divisible by 5 if the last digit is 0 or 5. Underline the numbers that are divisible by 5.

6500 219 4250 445 805 610 2681 3156 790 2.

A number is divisible by 3 if the sum of its digits is divisible by 3. Underline the numbers that are divisible by 3?

68 99 123 672 560 742 919 678 145 252 2106 178 471 142 6765 465 981 1002 771 43 3.

A number is divisible by 6 if it is even and also divisible by 3. Underline the numbers that are divisible by 6.

69 72 94 1242 236 99 282 398 448 732 512 4.

A number is divisible by 9 if the sum of its digits are divisible by 9. Underline the numbers that are divisible by 9.

68 900 609 504 112 799 75 810 702 333

85

Division 12 Use the tests of divisibility to write 6 numbers: 1. divisible by 2 between 300 and 400 2. divisible by 5 between 1500 and 2000 3. divisible by 3 between 600 and 700 4. divisible by 6 between 900 and 1200 5. divisible by 4 between 2000 and 2100 6. divisible by 9 between 1500 and 2000 7. divisible by 8 between 1600 and 2000 8. divisible by 10 between 400 and 800 9. divisible by 9 between 1000 and 1400 10. divisible by 8 between 700 and 1000

86

Division 13 1.

Circle the two numbers with a remainder of 2 when divided by 6. 36

2.

30

74

66

27

89

76

52

18

53

47

48

59

42

71

93


5.

38


4.

58


3.

46

37

79

40

28

15

24


30

22

72

42

62

92

87

Division 14 Write in the missing three-digit numbers.

1.

÷ 2 = 75

2.

÷ 3 = 122

3.

÷ 10 = 27

4.

÷ 5 = 25

5.

÷ 100 = 4·25

6.

÷ 50 = 8

7.

÷ 100 = 7·62

8.

÷ 25 = 20

88

Division 15 Approximate the answer first. Choose a standard method of recording to work out the answer to each calculation. 1. 437 ÷19 ~ ~

2. 648÷ 24

19 437

24 648

Answer 3. 459 ÷17 ~ ~

Answer 5. 522 ÷29 ~ ~

Answer

~ ~

Answer 4. 5

4. 546÷14

~

Answer 6. 663÷13 ~

Answer 89

Multiplication and Division 1 London Express Bus Service 1 person 2 people A group of 4

Worthing £10 £8 each £6 each

Brighton £12 £11each £7 each

Dover £14 £12 each £9 each

Here is the guide to prices the London Express Bus Services use in Southern England. Use it to help you to answer these questions. 1.

What is the total cost for a family of four to travel to Worthing?

2.

Three people took a bus ride it cost them £34. Where did they travel to?

3.

Four people travelled separately to Dover. How much would each person save if they travelled as a family?

4.

Six people travel to Worthing. What is the cheapest price they pay?

5.

Nine people travel to Brighton. What is the cheapest price they pay?

6.

Seven people travel together to Brighton. The driver gave them £8 change. How much money did they give him?

90

Multiplication and Division 2 How many different answers can you get from these calculations? (Use brackets and calculate the numbers inside the brackets first!) Example 6 × 5 + 4 ÷ 2 = (6 × 5) + 4 ÷ 2 = 30+4 ÷ 2 = 17 = 6 × (5 + 4) ÷ 2 = 9 × 6 ÷ 2 = 27 = 6 × 5 + (4 ÷ 2) = 2 + 30 = 32 1.

4+8×7+6=

2.

64 ÷ 8 × 4 × 3 =

3.

100 ÷ 5 × 5 +4 =

4.

56 ÷ 4 × 2 × 7 =

5.

3+7×5+6=

91

Multiplication and Division 3 Use brackets to make each answer an even number. Example: 30 ÷ 6 + 5 × 3 = (30 ÷ 6) + (5 × 3) = 5 + 15 = 20 1.

56 – 24 ÷ 8 =

2. 48 + 15 ÷ 3 + 7 = 3. 13 × 4 × 2 - 20 = 4.

56 ÷ 8 + 6 =

5. 47–11 × 12 ÷ 3 = 6.

7×7+9×3 =

Use brackets to make answers totalling 100. 7. 13 + 7 × 14 – 9 = 8. 14 + 6 × 9 + 32 = 9. 26 + 24 × 16÷8 = 10. 28 × 2 – 31 × 4 = 11. 56 ÷ 2 + 8 × 9 = 12. 5 × 12 × 4 – 28 = 92

Multiplication and Division 4 It has been agreed by mathematicians that if a sum has a bracket as part of it then the part inside the brackes will be calculated first. Then if there is any division this is calculated next followed by multiplication, addition and finally subtraction. This is known as BODMAS. Brackets Of Division, Multiplication, Addition, Subtraction

Use BODMAS to answer these questions. 1.

15 +19 – 7 =

2.

5+8×3=

3.

(14 + 7) – 15 =

4.

6 + 6 ÷3 =

5.

11 + 5 × 6 =

7.

12 + (7 × 7) =

9.

72 – (8 × 5) =

6. (24 – 9) + (19 – 8) = 8.

60 – (3 × 9) =

10. (11 × 5) + (7 × 6) =

11. (8 × 8) – (6 × 9) =

12.

9 + 32 ÷ 8 =

13.

45 ÷ (3 × 3) =

14.

130 – 25 × 3 =

15.

150 + (20 × 4) =

16. (36 ÷ 3) + (24 ÷ 4) =

17. 2000 – (12 × 4) =

18.

97 – (36 ÷ 2) =

19. (38 ÷2) + 42 ÷ 2 =

20.

420 – 12 × 11=

93

Multiplication and Division 5 Write in the missing three-digit numbers.

1.

÷ 2 = 450

2.

× 2 = 700

3.

÷ 10 = 39

4.

× 10 = 1000

5.

÷ 100 = 7·55

6.

× 1·5 = 375

7.

× 0·5 = 250

8.

÷ 100 = 2·01

94

Fractions and Decimals 1 Change these improper fractions to mixed numbers.

A 1.

11 8

=

2.

13 = 6

3.

22 9

=

4.

8 5

5.

17 = 8

6.

137 = 100

7.

20 = 19

8.

29 = 4

183

=

Change each mixed number to an improper fraction. B 7 15 1. 2 100 = 2. 212 =

3

4.

485

8

6.

15 3100 =

3. 410 =

5. 2 9 =

=

95

Fractions and Decimals 2 What is the relationship between these fractions? Use the diagrams to help you. 1 1 1. 2 6 1 2

2.

3.

4.

1 2

1 3

1 6

1 2

1 12

1

is three times as big as 6

1 8

96

Fractions and Decimals 3 What is the relationship between these fractions? Use the diagrams to help you. 1 1 1. 2 4

2.

3.

4.

1 4

1 5

11 24

1 12

1 10

1 16

97

Fractions and Decimals 4 Part of each shape below had been shaded. Work out which part has been shaded and circle the fraction on the number line below. 1.

0 2.7

⅛ ¼

⅜

½ 3.0⅝25 ¾ 26

⅞27 28 1 29 30 31

0 2.7

⅛ ¼

⅜

½ 3.0⅝25 ¾ 26

⅞27 28 1 29 30 31

⅛ ¼

⅜

½ 3.0⅝25 ¾ 26

⅞27 28 1 29 30 31

3.

0 2.7

98

Fractions and Decimals 5 Answer these fraction questions. 1.

Which of these fractions are less than 1? 1 6

2.

5 2

12 9

3 4

8 7

Which of these fractions are less than 2? 9 6

3.

2 5

12 5

5 2

18 10

9 4

11 7

Which of these fractions are more than 1? 3 2

2 7

8 9

9 8

3 10

10 7

99

Fractions and Decimals 6 Divide the numerator and the denominator by two to simplify the fractions. 1.

2 8

=

3. 14 20

=

5. 12 = 100

1 4

2. 6 8

=

4. 10 = 18 6.

6 = 10

Divide the numerator and denominator by three to simplify the fractions. 7.

3 6

=

8.

9.

9 15

=

10.

3 = 18

=

12.

9 = 24

11. 6 21

3 9

=

100

Fractions and Decimals 7 Multiply the numerator and the denominator by two to find an equivalent fraction. 1.

7 9

=

2.

5 9

=

3.

3 4

=

4.

4 5

=

5. 5 6

=

6.

7 10

=

14 18

Reduce the fractions to their simplest form. 7.

3 9

=

9. 30 = 100 11. 21 49

=

8.

6 16

=

10. 45 = 100 12.

14 = 36

101

Fractions and Decimals 8 Order these fractions. First, convert them to equivalent fractions. 1.

3 4

6 10

2 5

2.

1 2

5 6

2 3

3.

1 3

1 6

2 9

4.

1 4

1 2

1 3

5.

3 4

7 8

1 2

6.

2 5

7 10

2 3

7.

7 18

2 9

1 3

8.

4 7

3 4

1 2

9.

5 8

6 24

2 3

15 12 8 20 20 20

=

2 6 3 5 10 4

102

Fractions and Decimals 9 Add these fractions together. You will need to convert the fractions to the same denominator before you can add them. 1.

1 + 4

1 3

=

2.

1 4 +

1 5

=

3.

1 + 2

1 3

=

4.

1 9 +

2 3

=

5.

5 + 12

1 4

=

6.

7 10 +

1 5

=

7.

9 + 20

2 5

=

8.

5 18 +

2 3

=

3 12

+

4= 12

=

7 12

103

Fractions and Decimals 10 Add these fractions together. You will need to convert the fractions to the same denominator before you can add them. + 19 24 24

1.

5 6

2.

2 7 + 5 10

=

3.

2 + 3

3 4

=

4.

6 + 7

5 14

=

5.

7 + 12

3 4

=

6.

9 + 15

2 3

=

7.

9 + 10

4 5

=

8.

17 + 20

3 10

=

=

20 24

+

19 = 24

15 24

= 1

104

Fractions and Decimals 11 Subtract the second fraction. You will need to convert the fractions to the same denominator before you can subtract them. 1.

3 5

-

3 10

2.

1 2 -

1 4

=

3.

2 3

1 6

=

4.

3 4 -

1 2

=

5.

9 10

3 5

=

6.

5 12

-

1 3

=

7.

7 10

3 5

=

8.

3 4

2 3

=

-

=

6 10

-

3 10=

=

3 10

105

Fractions and Decimals 12 Subtract the second fraction. You will need to convert the fractions to the same denominator before you can subtract them. 2 3

=

4 5 -

3 10

=

3.

2 3

1 4

=

4.

7 8 -

1 4

=

5.

11 12

3 4

=

6.

13 15

-

2 5

=

7.

9 10

3 5

=

8.

19 20 -

3 4

=

1.

5 6

2.

-

5 6

-

4 = 6

=

1 6

106

Fractions and Decimals 13 Subtract the second fraction. You will need to convert the fractions to the same denominator before you can subtract them. 1.

3 14

-

2 3

=

2. 15

-

1 10

=

3.

2 13

-

1 6=

=

4.

7 28

-

3 4

=

1

3

5. 4 4

6.

7 515

7

7. 110

8.

19 124

3

- 28

=

4 35

=

-

-

9 20

=

-

7 8

=

21 12

-

8 12

=

1 1112

107

Fractions and Decimals 14 To multiply fractions: 1. Multiply the top numbers (the numerators) 2. Multiply the bottom numbers (the denominators) 3. Simplify the fractions. 1 4

Example

×

2 3

=

1×2 4×3

2 12

=

1 6

=

Multiply these fractions. 1.

1 2

3.

1 4

×

5.

4 5

×

×

1 3

=

2.

1 4

=

4.

1 3

=

6.

×

1 4

=

2 3

×

1 2 =

=

5 6

×

1 5

=

1 2

To divide a fraction by a whole number: 1. Multiply the denominator by the whole number. 2. Simplify the fraction if needed. Example

2 3

÷ 4 =

1 ×22 3×4

=

=

2 12 =

1 6

Divide these fractions by the whole number. 1.

1 5

÷ 3 =

2.

2 3

÷ 6 =

3.

1 4

÷ 5 =

4.

3 4

÷ 3 =

5.

1 6

÷ 3 =

6.

3 5

÷ 6 =

108

Fractions and Decimals 15 Find the fractions of these numbers and quantities. Example 3 of 60 = 45 4

1.

1 of £102 = 3

2.

2 of 126 = 3

3.

2 of 35 5

4.

¼ of 60 =15 (60÷4 = 15) ¾ of 60 = 45 (15×3 = 45)

1 of 102 = 34 (102÷3 = 34) 3

=

7 of 200 = 10

0 5.

4 of 81km = 9

6.

3 of 230 = 10

0 109

Fractions and Decimals 16 Find the fractions of these numbers and quantities

1.

1 8 of £48 =

2.

3 4 of 96

=

3 3. 10 of 200cm =

43 4. 100 of 3000g =

5.

2 3 of 621 =

6.

7 100 of 400ml =

7.

3 5 of 950km 110

Fractions and Decimals 17 Write these fractions as decimals. 1. 15

= 1·5

2.

9 10

=

25 10

=

4.

35 10

=

5. 30

=

6.

75 100

=

=

8.

158 = 100

=

10.

340 = 100

11. 350 =

12.

750 = 1000

10

3.

100

7. 95 100

9.

7 100

1000

13. 1245 = 1000

14.

568 = 1000

111

Fractions and Decimals 18 Write these fractions as decimals. Use a calculator to work them out if you need to. Write answers to two decimal places. Example 2 5

1. 1

= 1÷5 = 0·20

0·2 × 2 = 0·40

=

2.

1 4

=

=

4.

1 5

=

=

6.

1 3

=

1 = 100

2

3. 1 10

5. 3 4

7.

1 6

=

8.

9.

1 8

=

10.

5 6

=

11. 7

=

12.

4 5

=

8

112

Fractions and Decimals 19 Write these decimals as fractions. 1.

0·80 =

2. 0·15 =

3.

0·46 =

4. 2·58

5. 0·257=

6.

=

1·634 =

Underline the decimal that is equal to the fraction. 7. 146 100

1·46 0·146 10·146 14·60

8. 24 100

2·40 0·24 0·024

9. 129 1000

1·29 0·129 10·29 0·0129

10. 937 1000

9·37 93·7 0·937 0·0937

11. 1256 1000

0·1256 1·256 10·1256 0·01256

12.

7·8

78 1000

0·78

0·078

20·40

0·0078

113

Fractions and Decimals 20 A.

Add these decimals.

1.

0·7 + 0·9 =

3.

1·5 + 0·6 =

4. 1·4 + 1·7 =

5.

0·8 + 0·4 =

6. 2·6 + 0·4 =

7.

1·9 + 0·8 =

8. 1·8 + 1·6 =

9.

6·4 + 3·5 =

B.

Add these decimals.

1·6

2. 0·4 + 0·3 =

10.

3·4 + 4·9 =

1. 0·17 + 0·92 = 1·09

2.

1·45 + 0·31 =

3. 1·42 + 1·43 =

4.

2·34 + 1·77 =

5. 0·82 + 0·46 =

6. 12·61 + 0·43 =

7. 1·97 + 2·87 =

8.

1·93 + 1·88 =

9. 4·49 + 4·59 =

10.

0·47 + 4·96 =

11. 2·15 1·67 + 3·11

12. 6·34 2·45 + 3·47

13. 2·17 7·23 + 3·18

14. 9·57 3·46 + 12·35

114


Subtract these decimals.

1.

0·8 - 0·6 =

3.

0·2

2.

0·9 - 0·3 =

3·5 - 0·4 =

4.

10·8 - 6·5 =

5.

7·5 - 1·6 =

6.

2·3 - 1·4 =

7.

5·9 - 3·8 =

8.

6·8 - 4·9 =

9.

6·4 - 3·8 =

10.

3·4 - 2·7 =

B.

Subtract these decimals.

1. 3·13 - 0·72 =

2·41

2. 4·44 - 1·55 =

3. 9·02 - 1·04 =

4. 2·56 - 1·47 =

5. 3·46 - 2·58 =

6. 14·61 - 7·43 =

7. 8·67 - 2·86 =

8. 1·78 - 1·53 =

9. 9·41 - 4·39 =

10. 8·47 - 6·96 =

11. 2·15 -1·67

12. 6·34 -3·46

13. 4·17 -3·89

14. 9·34 -6·58

115

Fractions and Decimals 22 Order these decimals from smallest to largest. 1. 2·13

2·78

2·96

2·15

2·75

2·28

2. 6·24

6·2

6·61

6·23

6·5

6·09

3. 38·01

38·12

38·02

38·34

38·30

38·13

4. 1·04

1·40

1·44

1·14

1·004

1·041

5. 0.17

0·017

0·111

0·001

0·710

0·701

116


Multiply these tenths by a single digit.

1.

0·6 × 3 =

3.

1·8

2.

0·7 × 5 =

3·7 × 2 =

4.

4·8 × 3 =

5.

6·5 × 6 =

6.

5·4 × 4 =

7.

3·1 × 8 =

8.

5·8 × 6 =

9.

3·4 × 9 =

10.

7·8 × 8 =

B.

Multiply these hundredth by a single digit.

1.

3·53 × 4 =

3.

14.12

2.

1·25 × 7 =

6·32 × 3 =

4.

5·16 × 4 =

5.

5·18 × 2 =

6.

6·34 × 3 =

7.

7·34 × 5 =

8.

3·72 × 4 =

9.

6·07 × 6 =

10.

7·74 × 8 =

11. 3·24 × 5

12. 9·78 × 7

13. 8·69 × 9

14. 6·06 × 8

117


Divide these tenths by a single digit.

1.

16·6 ÷ 4 =

3.

4·15

2.

21·5 ÷ 5 =

12·8 ÷ 2 =

4.

13·6 ÷ 4 =

5.

17·7 ÷ 3 =

6.

16·1 ÷ 7 =

7.

20·8 ÷ 8 =

8.

38·7 ÷ 9 =

9.

13·5 ÷ 9 =

10.

25·2 ÷ 7 =

B.

Divide these hundredth by a single digit.

1.

54·06 ÷ 3 =

3.

30·60 ÷ 5 =

4. 18·72 ÷ 6 =

5.

32·34 ÷ 7 =

6. 28·84 ÷ 4 =

7.

17·82 ÷ 6 =

8.

9·52 ÷ 7 =

9.

15·21 ÷ 9 =

10.

3·04 ÷ 8 =

11. 3 17·04

18·02

12. 4 17·96

2.

9·36 ÷ 4 =

13. 6 14·28 14. 7 3·22

118

Fractions and Decimals 25 Write the equivalent fractions for these percentages. 1. 24% =

2. 30% =

3. 10% =

4. 90% =

5. 75% =

6. 25% =

Order the fractions and decimals from smallest to largest. 7.

2 10

8. 60%

12%

3 4

9. 0·35

40%

10. 99%

0·89

1 4

0·4

59%

0·54

1 3

50%

9 10

0·98

35%

7 8

4 6

17 20

What is the missing percentage? 11. 50% 50%

12. 75%

13. 64%

14. 12%

119

Fractions and Decimals 26 Find the percentages of these amounts. Use the answer to the first percentage to help you work out the second. Example 50% of £28 = £28 ÷2 = £14.

25% of £28 = £14÷2=£7

1. 50% of £300=

25% of £300=

2. 50% of £68 =

25% of £68 =

3. 50% of £90 =

25% of £90 =

4. 10% of £70 =

40% of £70 =

5. 10% of £700=

40% of £700=

6. 10% of £26 =

40% of £26 =

7. 5% of £55 =

25% of £55 =

8. 25% of £80 =

12½% of £80=

9. 25% of £28 =

12½% of £28=

10. 10% of £66 =

60% of £66 =

11. 10% of £54 =

60% of £54 =

12. 10% of £78 =

90% of £78 =

120

Fractions and Decimals 27 Match the amounts that are the same. 17 1 100

2·17

20 % 1·17

0·2

0·35

2

0·96

17 100

24 25

117 %

217 % 1 5

78%

0·05 0·9 7 20

96% 9 10

5%

1 20

0·78

39 50

90% 35% 121

Fractions and Decimals 28 Work out these percentage problems. Show your work. 1.

There are 50 children in the park.

a.

50% of the children are under 5. How many children is that?

b.

10% of the children are playing on the climbing frame. How many children is that?

c.

15 children are wearing boots what percentage is that?

2.

There are 48 people working at the supermarket.

a.

25% work on the tills. How many people is this?

b.

36 of the workers are female. What percentage of the workers are male?

c.

12·5% of the workers are on the early shift. How many people is this?

122

Fractions and Decimals 29 Answer these percentage problems. 1.

There are 32 children in a class. They did a survey of favourite fruit. 25% like apples best. How many children is this?

2.

James got 16 spellings right out of 20. What percentage did he get right?

3.

Estimate the percentage of The rectangle that is coloured yellow?

4.

Melissa’s Dad gives her the choice between getting 20% of £55 or

2 5

of £30.

You can use a calculator to work out which is more and by how much?

123

Ratio and Probability 1 A.

Work out the ratio of red to yellow squares.

Example

The ratio is 1 red square to every 3

yellow squares.

1.

The ratio is

red squares to every

yellow squares.

red squares to every

yellow squares.

2.

The ratio is B.

Look at the patterns above. Work out the proportion of the squares which are red.

Example 1 in every 4

squares are red.

1.

in every

squares are red,

2.

in every

squares are red. 124

Ratio and Probability 2 Answer these problems involving ratio and proportion. 1.

Jill has a bag of 16 sweets. She has 1 orange sweet for every 3 red sweets. 1

a. What is the ratio of red to orange sweets? b. What proportion of sweets are red?

: 3

in

c. How many orange sweets are there? 2.

A cake recipe needs 1 egg to make 6 cakes. Tom wants to make 24 cakes.

a. What is the ratio of eggs to cakes?

:

b. How many eggs are there? 3. At the zoo, school parties must have a ratio of 1 adult to every 5 children. The school takes 60 children. a.

How many adults must go on the trip?

b.

What proportion of adults are on the trip

4.

Class 6b has 36 children. The ratio of boys to girls is 2:1.

a.

How many boys are in class 6b?

b.

What proportion of the class are girls?

in

in 125

Ratio and Probability 3 Answer these ratio and proportion problems. 1. +

=

Pink paint is mixed in a ratio 1:6 red to white. If 1·75 litres red is used, then how much white is used?

2.

:

a. The ratio yellow to green? b. The proportion yellow to green?

1 in every

c. The fraction green? d. The area of the yellow rectangle is the green rectangles. 3.

the size of

:

a. The ratio blue to pink?

b. The proportion pink to blue?

1 in every

c. The fraction pink? d. The area of the pink rectangle is blue rectangles.

the size of the

126

Ratio and Probability 4 Work out the probability that these events will happen. Example What is the probability you will pick a heart from a set of Jacks from a pack of cards? 1 out of 4 = ¼ = 0·25 The probability is 0·25. 1.

What is the probability that you will toss heads on a coin?

2.

What is the probability Jim will pick a blue ball from this bag of balls?

3.

What is the probability Jim will pick a red ball?

4.

What is the probability Jim will pick a yellow ball?

5.

What is the probability Jim will pick a round ball?

127

Ratio and Probability 5 Use the words and phrases below in the sentences to show the probability of an event happening. likely

equal chance

biased

impossible

Fifty-fifty chance certain

random

good chance

unlikely 1.

If I drop a coin there is an ______________ it will land heads up.

2.

It is ____________ there will be a Tuesday this week.

3.

There is a _________________ that I will see a cat.

4.

It is _________________ that there will be 32 days this month.

5.

If a 5 year old runs against a 10 year old a ___________ result should occur.

6.

If I choose a card from a pack the result should be _________________.

7.

There is a __________________________ that a card picked from a pack of 52 cards will be red.

8.

It is ______________ I will go to the moon. 128

Ratio and Probability 6 Answer these probability problems. Give the answer as a fraction. 1.

A bag of sweets has 6 red and 3 orange sweets.

What is the probability that a random sweet taken from the bag is orange?

2.

The School keeps its balls in boxes. Each box has 10 tennis balls, 4 footballs and 6 basketballs. Mrs Jones asks Tina to fetch a ball. What is the chance Tina will bring a football?

129

Ratio and Probability 7 Match the probability of an event occurring on the line, when rolling an ordinary 1-6 die. A die will roll an even number.

0 impossible A die roll a one or two.

A die roll a number.

A die roll a zero.

A die will roll a six

0·5

1

evens

certain A die will roll a number greater than three.

A die will roll a seven

A die will not roll a 4.

Match the probability of an event occurring on the line, when choosing one of these cards without looking. 0

1

2

A 6 will be picked.

0 0·1 impossible A ten will be picked.

3

4

5

A number from 5 to 9 will be picked

0 ·2

0·3 0·4

6

7

An odd number will be picked

0·5 0·6 evens

A 6,7, or 8 will be picked.

8

9 A 2 or 3 will be picked.

0 ·7 0 ·8

A 2 will not be picked.

0 ·9

1 certain

A number above 3 will be picked.

130

Handling Data 1 A.

Calculate the mode (the most frequent) of these numbers.

1.

1, 1, 1, 2, 3

2.

20, 21, 22, 22, 23, 24

3.

100, 101, 102, 100, 103

4.

3, 3, 3, 4, 4, 4, 4, 5, 6, 6, 7

5.

2, 8, 4, 7, 8, 4, 3, 2, 1, 7, 8

6.

5, 6, 5 7, 5, 6, 7, 6, 5, 7

B.

Calculate the range (the difference between the highest and lowest) of these numbers.

1.

6, 3, 9, 8, 5

2.

21, 24, 15, 7, 8, 10

3.

3, 3, 7, 7, 8, 9, 10

4.

44, 36, 24, 55, 33

5.

135, 295, 340, 75, 455, 165

6.

66, 44, 22, 55, 77, 44, 55

7.

202, 203, 204, 206, 207

1

9-3=6

131

Handling Data 2 A.

Find the median (middle) number from an odd numbered list. Order them first from smallest to largest.

1.

5, 4, 8, 3, 4, 7, 6

2.

7, 8, 2, 5, 9, 1, 6

3.

2, 5, 9, 7, 1, 7, 8

4.

2, 14, 6, 11, 8, 12, 15

5.

24, 67, 35

6.

9, 0, 2, 5, 0, 4, 0

B.

Find the median number from an even numbered list. (halfway between the middle two numbers)

1.

12, 14, 18, 20

2.

1, 2, 6, 6, 4, 8

3.

14, 16, 12, 22

4.

1, 1, 3, 5, 9, 11

5.

1, 1, 7, 7, 9, 9

6.

34, 44, 56, 68, 73, 89

3,4,4,5,6,7,8 = 5

14 + 18 = 32 ÷ 2 = 16

132

Handling Data 3 A.

Find the mean (sum of all the numbers divided by the number of items) number.

1.

6, 4, 9, 7, 8, 2

2.

7, 8, 2, 3, 9, 1

3.

2, 5, 3, 7, 1, 1, 9

4.

20, 14, 6, 11, 8, 1

5.

6, 6, 2, 4, 7, 3, 7

6.

99, 66, 33

7.

4, 0, 2, 3, 0, 4, 1

B.

Find the mean of these prices.

1.

£1·20, £1·40, £1·90

2.

10p, 22p, 64p, 4p

3.

£1·50, £2·40, £1·80

4.

£230, £256, £114

5.

£2·24, £4·35, £3·01

6.

17p, 11p, 19p, 13p

6+4+9+7+8+2 = 36÷6=6

£1·20 + £1·40 + £1·90 = £4·50 ÷3 = £1·50

133

Handling Data 4 Here are the results for class B’s History test. Number of Marks Number of Children

1 2

2 1

3 3

4 6

5 10

6 4

7 4

8 2

Draw a bar chart of the results of class B’s History Test. 12 10 8

Number of children

6 4 2 0

1

2

3

4

5

6

7

8

Score in History Test

Use the bar chart to answer these questions. 1.

How many children took the History test?

2.

What is the mode score?

3.

What does the shortest bar tell you ?

134

Handling Data 5 Sarah collects data about vehicles going past her school. She draws a table and bar chart showing her results. Vehicles 16 14 12 Number

10

Of Vehicles

8 6 4 2 0 Lorry

Bike

Car Motorbike Type of Vehicles

Bus

1.

Write in four pieces of information missing from the table. Type of Vehicle Number of Vehicles Lorry Bike 0 Car 4 2 2.

Which is the mode vehicle?

3.

How many vehicles did Sarah record? 135

Handling Data 6 Here is a line graph to show the level of water in a paddling pool.

14

×

12

×

×

10

×

Level of water (cm)

×

8

×

6 4 2 0

×

10

20

30

40 50 Time in minutes

60

×

70

Use the graph to answer these questions. 1.

What was the highest level of water in the pool?

2.

Estimate how long the water was over 10cm?

3.

After 40 minutes the children left the pool. How long were they out of the pool for?

4.

If the pool started filling at 2pm. What time was it completely empty again?

136

80

Handling Data 7 Transport to Valley Junior School

walk

car

200 pupils bike

bus

Transport to Star Primary

walk

360 pupils

car bike bus

1.

Estimate how many children at each school walk to school. a. At Valley Junior pupils walk b.

At Star Primary

pupils walk

2.

Do more children travel by bus to Star Primary School or Valley Junior School? Give a reason for your answer. ______________________________________________ ______________________________________________ ______________________________________________ 137

Handling Data 8 Look at the pie charts and answer the questions Class G's Favourite Fruit

36 pupils apple banana grapes strawberry

1.

Estimate how many children in class G like apples.

2.

Estimate how many children in class G like bananas

3.

Estimate the the total number of children who like apples and grapes.

4.

Estimate the difference between the number of children who like apples and strawberries.

138

Handling Data 9 Here is a line graph for the 4 times table.

48

×

44

×

40

× ×

36 32

×

28

×

24

×

20

×

16

×

12

×

8

×

4

×

0 0

1

2

3

4

5

6

7

8

9

10

11

12

Use the graph to answer these questions. a. 3·5 × 4

=

c. 2½ × 4

=

d. 7·5 × 4 =

e. 12 × 4

=

f. 5½ × 4 =

g. 11·5 × 4

=

h. 6·5 × 4 =

14

b. 8 × 4 =

139

Handling Data 10 Mark in the missing parts of this line graph for the 6 times table.

12

×

6

×

0

1

2

3

4

5

6

7

8

9

10

11

12


=

c. 8½ × 6

=

d. 4·5 × 6 =

e. 45 ÷ 6

=

f. 10½ × 6 =

g. 1·5 × 6

=

h. 6·5 × 6 =

15

b. 39 ÷ 6 =

140

Handling Data 11 Draw a line graph for the 8 times table.


=

b. 44 ÷ 8 =

c. 7½ × 8

=

d. 9·5 × 8 =

e. 92 ÷ 8

=

f. 12½ × 8 =

g. 5·5 × 8

=

h. 96 ÷ 8 =

141

Handling Data 12 Here is a time and distance graph for a car journey from Newton to Farl and back again.

70 60 50 Distance from Farl in kilometres

× ×

40 30

×

×

20 10 0

×

10

20

30


60

70


How far was the car from Farl after 15 minutes?

2.

How far was the car from Farl after 55 minutes?

3.

How long did the car stay in Newton?

4.

How far was the car from Farl after an hour?

5.

How long did the car take to arrive back in Farl?

142

×

80

Handling Data 13 Draw a time and distance graph for a bus journey from Jute to Saxon and back again. Time in minutes 0 15 20 30 35 45 65

Distance from Jute in Kilometres 0 15 20 30 30 20 0

70 60 50 Distance from Jute in kilometres 40 30 20 10 0

10

20

30


60

70


How far was the bus from Jute after 20 minutes?

2.


3.


4.

How far was the bus from Jute after 1 minute?

143

80

Handling Data 14 This graph converts between gallons and litres. 140 120 100

Litres (l)

80 60 40 20 0

2

4

6

8

10

12

14

16

18

20

22

24

26

28

30

Gallons

Convert these to litres. 1.

9 gallons

2.

18 gallons

3.

11 gallons

4.

29 gallons

Convert these to gallons. 5.

40 litres

6.

90 litres

7.

140 litres

8.

70 litres

Complete this table of values. Gallons 0 2 4 6 8 10

Litres(l) 0 9

144

32

32

Shape 1 G

E

DD

A

F B

C

Answer these questions about the shape above. AB and

1.

Name 2 parallel edges.

2.

Name 2 perpendicular edges.

3.

Edge DE is parallel to edge

4.

Edge AB is perpendicular to edges

G.

H.

Answer these questions about the shapes above. 5.

How many pairs of parallel faces does shape G. have?

6.

What is the total number of edges on the shapes. G.

H. 145

Shape 2 Tick the shapes which are nets of a closed cube. 1.

2.

× 3.

4.

5.

6.

7.

8.

146

Shape 3 A parallelogram has its opposite sides equal and parallel. Draw 4 different parallelograms using the grid below.

.

A rhombus is a parallelogram which has equal sides. Draw 4 different rhombi using the grid below.

147

Shape 4 A trapezium has one pair of opposite parallel sides Draw 4 different trapezia using the grid below.

.

A kite has two pairs of adjacent sides of equal length. Draw 4 different kites using the dots below.

148

Shape 5 Look at these quadrilaterals. Draw in the diagonals; tick the shape if the diagonals intersect at right angles. Write the name of each shape.

149

Shape 6 1.

Look at these shapes and put the right letter in the statements below.

a

b

c

d

e

1.

Which shape has reflective symmetry?

2.

Which shape has 2 pairs of parallel lines?

3.

Which shape is an irregular hexagon?

4.

Which shape has angles adding up to 180º?

5.

Which shape is an irregular pentagon?

6.

Draw a reflection of the shapes in the mirror line.

Mirror line 150

Shape 7 1.

Draw a reflection of the shapes in the mirror line

Mirror line 2.

Shade in two more squares to make the design symmetrical about the mirror line.

Mirror line

151

Shape 8 6 5 4 3 2 A

B 1

-8

-7

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

7

8

7

8

-1 D

C -2

List the vertices and co-ordinates of the rectangle above. A (-4, 2)

B( , )

C(

, ) D(

, )

Plot and these points up in order on the graph below. A (-5, 2) B( 5, 3 ) C( 2, -2) D( -5, -2) 5 4 3 2 1

-8

-7

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

-1 -2 -3 -4

1

152

Shape 9 6 5 4 3

A

2 1

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

14

15

Plot these points on the grid to make shape B. ( 6, 3) (10, 3) (10, 5) (6, 5) Shape A has been translated ___to the right, then ___up. 6 5 4

C

3 2 1 1 0

1

2

3

4

5

6

7

8

9

10

11

12

13

Plot these points on the grid to make shape D. ( 3, 1) (7, 1) (5, 5) Shape C has been translated __ places to the left, then ___down. 153

Shape 10 Look at the pairs of congruent right angle triangles.

. .A . . . . . . . . . . . . . .

. . . . . . . . .D . . . . . . .

. . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . .

. B . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . .

. . . . . . . . . . . .E . . . .

. . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . .

. . . .C . . . . . . . . . . . .

. . . . . . . . . . . . . . .F .

. . . . . . . . . . . . . . . .

Name the shape in each overlap of two congruent right-angled triangles. Write in which of the arrangements a triangle is translated and or rotated. A

square, rotated and translated

B

C

D

E

F

154

Shape 11 Rotate the triangles ABC through 90º about the vertex A. Repeat the rotations 3 more times. 4 B 3 2 1

-8

-7

-6

-5

-4

-3

-2

-1

A 0

C 1

2

3

4

5

6

7

8

4

5

6

7

8

-1 -2 -3 -4

Write the co-ordinates of C for each rotation. ( , ) ( , ) ( , ) 4 B

3 2 1

-8

-7

-6

-5

-4

-3

-2

-1

A 0

C 1

2

3

-1 -2 -3 -4

Write the co-ordinates of B for each rotation. ( , ) ( , ) ( , ) 155

Shape 12 Measure and record the marked angles. 1.

2. b

a

3.

4. d

c

Measure and add the angles for each triangle. 5.

6.

+

+

=

+

+

=

156

Shape 13 Write these angles in the correct column in the chart below. 1. 5. 9.

27º 180º 11º

acute

2. 89º 6. 90º 10. 190º right

3. 7. 11. obtuse

105º 310º 125º

4. 8. 12.

straight

270º 145º 256º reflex 270º

Draw and label angles of these sizes. 13. 90º

15. 43º

Right angle

14. 108º

16.

157º

157

Shape 14 Calculate the size of each missing angle. 1.

2. 270º 44º

90º

3.

4.

78º

5.

131º

6.

222º

162º

158

Shape 15 Measure and record the sizes of angles ABC 1. A

B

B A

C

C

Measure, then check by working out, the marked angles on these triangles. 2.

3.

D

H

E

E

F D

I

F

G

G

H

I

159

Shape 16 Use the formula Perimeter = 2 × (length + breadth) to work out the perimeter of the rectangles below. 1. 7cm 2. 16 cm

5cm

4 cm

2 × (7+5) cm 2 × 12cm = 24 cm 3.

23cm

4.

19 cm 12 cm

28cm

These shapes are made by overlapping congruent squares or rectangles. Work out the perimeter of each green 5m shape. 6. 6m 7. 2.5m 5m 2m 3m 4m 5m 3m 2.5m 4m 5m

160

Shape 17 Find the area of each of the shaded shapes in cm²

A

B

C

A.

B.

C.

Work out the area of these shapes. Multiply the length by breadth. D. E. 21cm 28cm 7cm cmm

9cm mm

m

F.

D. 21 × 7 =

cm²

E. 39cm 39cm mmm

3cm mm

F. 161

Shape 18 Work out the area of these shapes. Add or subtract the area of separate rectangles. 1. 2. 20cm

4cm 10cm 5cm

30cm 9cm

21cm

8cm

(10cm × 17cm) + (4cm × 5cm) = 170cm² + 20cm² = cm²

(20cm × 30cm) - (9cm × 8cm) = 600cm² - 72cm² = cm² 3.

4.

15cm

3cm

3cm 3cm

11cm

5cm

9cm

10cm

4cm 4cm 3cm

4cm

162

Shape 19 Work out the area of these shapes. 1. 2. 11cm 5cm 6cm 15cm

5cm 5cm

17cm

7cm

25cm

5cm

Work out the shaded area of these shapes. 3.

4. 26cm

20cm 4cm 5cm

15cm

20cm m 6cm

163

16cm

Shape 20 Find the area of each of the shaded right angle triangles in cm². Multiply the length and breadth then divide by 2. B A

C

A. (4×3) ÷ 2 = 6cm²

B.

C.

D.

D

Work out the area of these triangles. E. F. 10 cm

8cm

4cm cmm

15cm

m

E F 164

Shape 21 Find the area of each of the shaded pentagons in cm². Draw lines to divide the pentagons into rectangles and triangles.

B

A

A

B

Draw two different right angled triangles with an area of 12cm².

165

Shape 22 Here is a rectangular block. (not drawn to scale) 5 5cm 40cm 1. How many blocks can fit into shape A?

A

blocks

40 cm

55cm What is the area of shape A in cm² cm² 2. How many blocks can fit into shape B?

25cm

B 120 cm What is the area of shape B in cm²

cm² 166

Time 1 Look at the timetables and answer the questions below. 1.

Swimming lessons Group Beginners Intermediate Advanced

Start time 15:40 16:05 16:35

Finish time 16:05 16:35 17:10

a. b.

How long is the advanced swimming lesson? How long is it from the start of the beginners lesson to the end of the advanced lesson?

c.

If the swimming teacher needs 20 minutes to sort out the swimming pool after the lessons have finished. Her journey home takes 15 minutes. What time does the swimming teacher arrive home?

2.

Film Times Film

Mr and Mrs Jones The Monsters Space Adventure

Screen 1 13:30 15:45 17:20

Screen 2 17:15 13:55 15:30

a.

James finishes school at 15:30 and takes 30 minutes to travel to the cinema. Which film can he not watch at the cinema?

b.

How long is “Mr and Mrs Jones”?

167

Time 2 1.

Here is a clock.

How many minutes until this clock shows 5:25? ______

2.

minutes

Here is another clock.

21:26 What time did the clock show 45 minutes ago?

3.

One of the clocks below is 12 minutes fast. The other is 6 minutes slow.

20:02 What is the correct time?

168

Time 3 The sign shows the opening times for the cake shop.

Monday – Friday Saturday Sunday

Morning 9:00 – 12.30 8:30 – 13.00 10:00 – 13.00

Afternoon 14:00 – 16:00 14:00 – 18:30

Answer the questions about shop opening times. 1.

How long was the shop open on Thursday afternoon?

2.

How long was the shop shut for lunch on Monday?

3.

How long is is the shop closed from Sunday to Monday?

4.

Is the shop open longer on Saturday or on weekdays?

5.

How many hours a week is the shop open?

169

Time 4 Answer these time questions. 1.

Sue goes to the cinema to watch a film at 16:25. The film is 2 hours 40 minutes long. She has a 15 minute walk home from the cinema. Will she be home from the cinema by 7:00 pm?

Show your working here.

2.

Here are the instructions for cooking a fruit cake. Cook for 25 minutes per 250 g plus 30 minutes. If the cake mix weighs 750g. How long will the cake take to cook? Show your working here.

3.

Here is a clock

a.

How many minutes until this clock shows 4:05?

b.

What time did the clock show 50 minutes ago?

170

Time 5 Answer the questions about world time.

. LA

L

. NY

.T

.

B

.R

.

.P

C

.

S

-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3+4 +5 +6 +7+8 +9+10+11+12

Time Zones B Bangkok LA Los Angeles T Tokyo

Key C Cape Town NY New York P Perth

L London R Rio de Janeiro S Sidney

1. It is 12 noon in London. In which city is the time 7pm? Bangkok 2. It is 12 noon in London. In which city is the time 9am? 3. It is 12 noon in London. In which city is the time 4am?

4. What is the time difference between New York and Sidney? 5. What is the time difference between Cape Town and Perth?

171

Measuring 1 Convert these units of length. 1.

0·167km into metres.

2.


3.


4.

7823m into kilometres.

5.

5834m into kilometres.

6.

56mm into centimetres.

7.

23mm into centimetres.

8.

1·6m into centimetres.

9.

2·7m into centimetres.

10. 8·5m into kilometres. 11. 1·95m into millimetres. 12. 3·38m into millimetres. 13. 0·456m into millimetres. 14. 64cm into kilometres. 15. 894cm into kilometres. 172

Measuring 2 44

40

36

32

d

24 c

kilometers b

16

a

8

0 0

5

10

15

20

miles

Use the conversion table to find these equivalent distances. a.

8 km =

c.

20 km =

5 miles

b. 16km = d. 30km =

Find the equivalent distance. e.

17 miles =

g.

15 miles =

27 km

f.

24 miles =

h.

3 miles = 173

Measuring 3 Answer these length problems. 1.

Jane is 97cm tall Paul is 1·29m tall What is the difference between their heights in metres?

2.

A family journey includes a 30·8km car drive followed by a 10·7km bike ride then a 600m walk. How far do they travel?

3.

A snail travelled 456mm in 10 minutes, a tortoise travelled 6 times as far. Find the length of the tortoise’s journey in centimetre.

4.

How many 65cm pieces of string can be cut from a 20 metre ball of string?

5.

How much string will be left over in the previous question?

6.

A ladder is 5m high,the rungs are at 30cm intervals. Sally climbs up 9 rungs. What is her height from the ground?

7.

How far has Sally still to climb to reach the top of the ladder?

174

Measuring 4

6·088 kg 7·346 kg

5·613 kg

4·869 kg

A

B

C

D

Write the weight of each parcel as kilograms and grams then as grams only. A

7 kg 346g =

C

g

B D

Write the number of grams represented by the digit 6 in each of the parcels. A

6 grams

C

B D

Round each weight to the nearest tenth of a kilogram. A C

7·3kg

B D

Find the difference in weight between parcels: A and C B and D

175

Measuring 5 1 pound (lb) = 16 ounces 1 pound = 454grams 700

600

500

400

300 grams 200

100

0 2

0

4

6

8

10

12

14

16

18

20

22

24

ounces

Use the conversion table to work out these answers. Round the figures to the nearest ounce or 10 grams. a.

7 oz =

g

b.

1 lb =

c.

10 oz =

g

d. 4 oz

=

g

e.

100g =

oz

f. 150g

=

oz

g.

500g =

oz

h. 325g =

oz

g

176

Measuring 6 The librarian is moving books to a new shelf. She has: 30 encyclopaedias weighing 700g each. 42 paperbacks weighing 120g each. 11 hard backs weighing 230g each. 10 hard backs weighing 190g each. 17 hard backs weighing 350g each. If she can only carry 5kg at a time, work out these problems you can use a calculator but show your working. 1.

How many journeys must she make with the encyclopaedias?

2.

How many paperbacks can she carry at a time?

3.

What is the total weight of all the hardback books?

4.

She has a rest when she has moved 30kg of books. How many more journeys must she make?

177

Measuring 7

1 Tonne

A cubic metre of water weighs 1 Tonne. 1 Tonne = 1000kg. 1.

How many tonnes of water are in a in a tank 2 metres by 2 metres by 2 metres? 2m × 2m × 2m = 8m³ = 8 tonnes

2.

How many tonnes of water are in a tank 6 metres by 2 metres by 2 metres?

3.

How many tonnes of water are in a swimming pool 10 metres by 5 metres by 1 metre?

4.

How many cubic kg of water are in a tank 4 metres by 2 metres by 1 metre?

5.

How many cubic kg of water are in a pool measuring 6 metres by 8 metres by 2 metres?

178

Money 1 To convert pounds (£) into other currencies, multiply the number of pounds by the exchange rate. Example 250·0 Australia ($) rate = 1·6 × 1·6 Change £250 = 250 × 1·6 = 150·0 + 250·0 Answer $400 400·0 1.

India (rupees) rate = 65 Change £370 Answer ____________ rupees 2.

Japan (yen) rate = 150·2 Change £100 Answer_____________yen 3.

(euro) rate = 1·19 Change £300 Answer______________euro 4.

Switzerland (franc) rate = 2·55 Change £150 Answer______________franc 5.

USA($) 1·38 Change £450 Answer $______________ 179

Money 2 To convert pounds (£) into other currencies, multiply the number of pounds by the exchange rate. You can use a calculator to help you. Give answers to the nearest whole unit of currency. 1.

Italy (euro) rate = 1·19 Change £487 Answer ____________ euros 2.

USA ($) rate = 1·38 Change £634 Answer $_____________ 3.

Malaysia (ringgit) rate = 5·79 Change £935 Answer______________ringgit 4.

Mexico (peso) rate = 12·92 Change £784 Answer______________peso 5.

Norway (krone) rate 13·46 Change £104 Answer ______________krone 6.

Canada($) rate 2·27 Change £209 Answer $_______________ 180

Money 3 Tourist Rate (May)

Tourist Rate (July)

Australia ($)

1·69

Australia ($)

1·79

Denmark (Krone)

12·67

Denmark (Krone)

12·90

India (rupees)

50·34

India (rupees)

51·26

Japan (yen)

157·78

South Africa (rand) 157.78 Thailand (baht)

Japan (yen)

10·36

157·77

South Africa (rand) 157.78 Thailand (baht)

54·01

11·02 53·78

Above are the tourist exchange rates for six countries at different times of the year. Work out if the exchange rate has increased ( ) or decreased ( ) between April and September. Work out the difference between exchanging £100 in May or July. Write how much it has increased ( ) or( ) decreased. Decide when the better time to travel to each country would be based on this information. Fill in the table below. Country

Australia

Exchange rate May

1

1·69

1

Exchange rate July

1

1·79

or

0·10

Difference between changing £100 in May or July

1

$10

1

Best time to travel May

1

1

181

Money 4 Tourist Rate Canada ($)

2·65

Hong Kong ($)

12·03

Israel (shekel)

6·87

Mexico (peso)

14·29

Norway (krone)

13·46

Switzerland (franc)

2·55

Above are the tourist exchange rates for six countries. To convert other currencies into pounds, divide the amount by the exchange rate. Work out the cost in English pounds of the items below. Round each currency rate to the nearest whole number. 1.

Mexico 45 peso

2.

Israel 144 shekel

3.

Norway 132 krone

4.

Canada $ 93

5.

Hong Kong $152

6.

Switzerland 14 francs

7.

Mexico 100 peso

8,

Canada $ 122

45 ÷ 14 = £3·00

182

Money 5 Use the information on the hotel price list to answer the questions.

Double Single Suite

The Grand Hotel Prices per night week £126 £540 £ 74 £336 £168 £931

1.

What is the difference in price between a week in a double room and a week in a Suite?

2.

How much would it cost to stay in a double room for 3 nights?

3.

What is the difference in price between staying in a single room for 4 days or for a week?

4.

Work out the cost per night for a week in a suite?

5.

Half board (breakfast and dinner) costs 25% of the cost per night for a single room. How much does half board cost?

183

Money 6 Answer these money questions. 1.

Sandra saves 5p coins she saves 105 of them. How much money has Sandra saved?

2.

John has saved £8·80 in 20p coins. How many coins has he saved?

3.

James works 36 hours every week. James is paid £7·25 for every hour. You can use a calculator to answer these questions. a.

How much does James get paid every week?

James has earned over £900 so far this year. b.

What is the fewest number of hours he has worked to earn £900?

184

Number Problems 1 Answer these number problems. 1.

Fill in the numbers 1-20 in this Venn diagram. factors of 18

2.

Fill in the numbers below in this Venn diagram. 12

4 25 11 square numbers

3.

multiples of 3

9

16

49

36 5

7

odd numbers

Fill in the numbers 1-30 in this Venn diagram. square numbers

multiples of 2

185

Number Problems 2 Fill in the missing numbers on these addition magic squares. 1.

23

28

21

2.

17

71 59

24

5

47

27

Total =

Total =

These magic squares are made by multiplying instead of adding. When the numbers on any side or diagonal are multiplied they make the same total. Fill in the missing numbers. 3. 4. 36

16

3

32

8

12

64

16

48

Total = 5.

4

Total = 6.

28

2

14 4

Total =

12 6

7

1

3

Total = 186

Number Problems 3 Fill in the missing numbers on these multiplication pyramids. 1. 2.

92610 735

126

35 5

21 7

6 3

2

3.

2

5

2

4

6

3

9

2

7

6

3

5

4.

5

6

4

5

3

6

6.

8

5

9

187

Number Problems 4 Fill in the missing numbers in these number sentences. 1.

24 ÷

× 2 × 2 = 12

2.

(25 -

) ×3 × 4 = 120

3.

8×

+ (5 × 2) = 26

4.

40 ÷

+ 6 + 2 = 16

5. 6.

(7 × 6) 54 ÷ (

7. 8.

= 31

× 9) × 8 = 24

(15 × 3) (

= 28

÷ 3) + (4 × 8) = 65

Use these symbols to make the number sentences below true. + - × ÷ ( ) 9.

30

6

7

3 = 36

10.

8

3

5

7 = 26

11.

(27

12.

9) 7

(7 5

4) = 31 6 = 72

13.

9

5

(4

14.

(12

6)

7

3) = 33 6=8 188

Number Problems 5 Work out the answers to these problems. 1.

A box of pens holds 64 pens. a. A school needs 230 pens. How many boxes must they buy?

b. A shop has 12 boxes of pens. How many pens is that altogether?

2.

In the bookshop sale hardback books cost £7·55 and paperback books cost £4·82. a. Steven bought a hardback and 3 paperback books. How much did he spend?

b. Beth bought two hardback books. She paid with a £20 note. How much change did she get?

c. Mary bought 10 hardback books and was given a discount of 10%. How much did she pay?

189


A bag of marbles holds 94 marbles. They come in boxes of ten bags. a. How many marbles are in a box?

b. If I have 18 800 marbles. How many boxes do I have? c. If I buy 100 boxes. How many marbles do I have? 2.

Cakes are sold in packs of eight. The packs come in boxes. Each box contains 20 packs. a. How many cakes does a box hold? b. If a shop has 5 boxes, how many packs do they have?

c. If a pack costs 87p, how much does a box cost?

190


A bottle of mineral water holds 360 ml. In a week Jack drinks 10·08 litres of mineral water. a. How many bottles does Jack drink in a week? b. If a bottle of mineral water costs 55p. How much does Jack spend on water in a week? c. If I buy 6 bottles of water a day. How many bottles do I buy in two weeks?

2.

Lollies are sold in packs of twelve. a. A pack costs £2·04. How much does each lolly cost? b. If Sam buys 10 packs of lollies. How much will that cost?

c. If Joe buys 4 lollies. How much does he spend?

191


A mechanic charges £36 per hour. Car parts cost £48·75. a. The mechanic gives an estimate of £300·75 to fix a car. How many hours does he think he will spend fixing the car?

b. One week he earns £1260 for his work. How many hours did he work? c. If the mechanic works for 21 hours and uses £246 of car parts. How much will it cost?

2.

The teacher is sorting out the sports equipment. The cupboard contains 1200 balls. a. 25% of the balls are soft foam. How many balls is that?

b. If 42% of the balls are large. How many is that?

192


Buns come in packs of 4 or 8. A pack of 4 costs 65p, a pack of 8 costs £1·12. a. A group of 4 children bought a pack of 8 and shared them. How much did they each pay?

b. Terry buys 2 packs of 4 buns and Simon buys 1 pack of 8 buns. How much more does Terry pay? c. Star Playgroup buys 10 packs of 8 buns. How much do they pay?

2.

a. Mrs Jones buys 4 pears. She pays with a £5 note. She gets £3·20 change. How much is one pear?

b. Ralph buys 10 pears. How much do they cost?

c. I have £2·70. How many pears can I buy?

193

Number Problems 10 1.

Joy lives 145 metres from the post office. If she travelled 870 metres travelling to and from the post office. How many times did she visit the post office? Show your working.

2.

Five children time themselves in a skipping race.

Name Time in seconds a.

Paul 25·8

Tariq 22·4

Sofia 21·7

Glen 26·4

Jade 23·2

Who finished the race first?

b.

How many seconds faster was Tariq than Glen?

194

Number Problems 11 1.

Philip describes a number. “The number I am thinking of is an odd number. It is a multiple of 9, is less than 50 and contains consecutive numbers.”

2.

Jayne describes a number. “The number I am thinking of is a square number. It is a multiple of 12. It is less than 80.”

3.

Tom describes a number. “The number I am thinking of is a multiple of 8. It is more than 40 and less than 90. It contains consecutive numbers.”

4.

Winnie describes a number. “The number is an odd number. It is more than 40 but less than 60. It is a multiple of 7.”

195

Number Problems 12 Answer these number problems 1.

a.

Write the prime numbers in the following list. 5

b.

7

a.

21

15

11

23 13

= = 20

Write the square numbers in the following list. 4

b.

10

Use two of the prime numbers to complete the following calculation. +

2.

4

8

9

10

12

15

16

18

25

Use two of the square numbers to complete the following calculation. -

= = 7

196

Number Problems 13 Answer these number problems 1.

a.

Write the factors of 64 in the following list.

64

9

b.

Use two of the factors of 64 to complete the following calculation.

2

16 ×

2.

a.

12 4

1

21

16

8

23 32

= =

Write the factors of 360 in the following list.

1 2 3 4 5 6 7 8 9 10 12 15 18 20 22 24 25 30 35 36 40 45 60 72 90 120 144 150 180 360

b.

Use two of the factors of 360 to complete the following calculation. -

= = 78

197

Number Problems 14 Here is a thermometer. 1. ____________________________________________________________________ - 20

-15

-10

-5

0

5

10

15

20

25

30

35

a.

At 3 pm the temperature is 8ºC. At 9pm the temperature is 15 degrees lower. What is the temperature at 9 pm? ºC

b.

At 2 am the temperature is - 14ºC. At 10am the temperature is 17º higher. What is the temperature at 10 am?

2.

ºC

Class 6 has been recording the temperature at 9 am for 5 days. Here are their results.

Monday

-2ºC

Tuesday - 5ºC

Wednesday Thursday Friday 2ºC - 6ºC -4ºC

a. What is the mean temperature for that week? ºC

b. What is the temperature range for that week? ºC

198

Number Problems 15 Use the numbers 1-9 to make these statements correct. For each number sentence a different letter indicates a different number. 1. a + a + a = 12

a=

2. b × b × b = 1

b=

4

3. c + c + c + c = 20 c = 4. 4 × d = 28

d=

5. e + e + e = 45

e=

6. g × g × g = 8

g=

7. 30 - h - h - h = 12 h = 8. i + i + i = j + j

i=

9. k + k + k = 96

k=

10. l × l × l = 27

l=

11. m × m = 72 – m

m=

j=

12. n + n + n + n = 56 n = 13. o × o + o = 42

o=

14. p × 2 = 34

p= 199

Number Problems 16 Use the numbers 1-9 to make these statements correct. For each number sentence a letter indicates a number. 1. 4a = 12

a =

2. 9b = 18

b =

3. 3c + 2 =14

c =

4. d + 5 = 12

d =

5. 7e = 35

e =

6. 2f + 6 = 3f + 3

f =

7. 2g– 9 = g – 3

g =

8. 2h + 2 = h +11

h =

Use different numbers between 1 and 9 for each letter in these equations. You may find more than one answer. 9.

2j + k = 5

j=

k=

, j=

k=

10.

3m – n = 5

m=

n=

, m=

n=

11.

p + 3r = 16

p=

r=

12.

3s ÷ t = 2

s=

t=

200

Number Problems 17 Write whether the following statements are true or false. Show your working. 1.

(32 × 120) ˃ 4120

2.

(1265 + 3987) ˂ 5346

3.

(45 × 34) ˃ 1224

4.

(12 × 349) ˃ 5502

5.

(9435 - 3355) ˂ 7250

6.

(4560 ÷ 30 ˃ 125

7.

(3270 ÷ 12) ˂ 235

201

Number Problems 18 Put the missing sign in these calculations. Use

+ - ÷ × ˂ ˃ =

1. 125

5 = 25

2. 5 × 300

1600

3. 12

36 = 432

4. 35

55 = - 20

5. 950

50 = 19

6. 72 × 36 7. 99

2592

3 = 33

8. -49

29 = -20

9. 2480 ÷ 5

490

10. 1035

26 = 1061

11. 6 × 3

11 = 198

12. 5·5

0·25 = 22

13. 7·75

12·5 = -4·75

14. 2·5

1·5 = 3·75 202

Year 6 Answers Place, value and ordering 1 page 3 1. 8. 10. 11. 12. 13.

800 2. 40 3. 7000 4. 600 5. 200000 6. 60000 70000 9. Fifty seven thousand, eight hundred and twenty six Forty six thousand, three hundred and ten Three thousand, two hundred and ninety Twenty five thousand, eight hundred and ninety one 17120 14. 59206

7. 4000

Place, value and ordering 2 page 4 1. 5. 7. 9.

Eight hundredths 2. Seven tenths 3. Nine tenths 4. Four hundredths Two thousandths 6. 5·09 5·95 7·73 9·45 9·55 1·61 1·62 1·68 1·86 1·87 8. 0·53 2·05 2·35 2·53 20·15 1·007 1·07 1·117 1·17 1·71

Place, value and ordering 3 page 5 1. 2. 3. 4.

1·2 1·21 1·22 1·23 5·55 5·56 5·57 5·58 4·0 4·01 4·02 4·03 1·35 1·351 1·352 1·361 1·362 1·363 5. 4·03 4·031 4·032 4·041 4·042 4·043 6. 2·890 2·891 2·892 2·901 2·902 2·903

1·24 1·25 1·26 1·27 5·59 5·60 5·61 5·62 4·04 4·05 4·06 4·07 1·353 1·354 1·355 1·364 4·033 4·034 4·035 4·044 2·893 2·894 2·895 2·904

1·28 1·29 1·3 1·31 1·32 1·33 1·34 5·63 5·64 5·65 5·66 5·67 5·68 5·69 4·08 4.09 4·10 4·11 4·12 4·13 4·14 1·356 1·357 1·358 1·359 1·360 4·036 4·037 4·038 4·039 4·040 2·896 2·897 2·898 2·899 2·900

Place, value and ordering 4 page 6 1. 4.

4·13 124·60

3·009 123·09

2. 5.

15·07 16·13 3. 0·002 0·1

6.

400

7.

4000

10.

0239

11.

9320

8.

23·21 23·01

9.

4/10 377

12. Ninety five thousand, eight hundred and two

Ninety five thousand, six hundred and sixty- two

203

Place, value and ordering 5 page 7 1. 2. 3.

£12245 £12·75 9·6kg 2·7 2.7

£12425 £12·50 9·06kg

£12634 £12·15 8·07kg

2·8

2·95

£13967 £12·02 7·08kg

£14900 £11·06 0·76kg

£14908 £11·05 0·75kg

3·0 25 263·1 27 28 3·29 25 3.0 30 31

3·4

Place, value and ordering 6 page 8 1. 5. 9. 13. 17.

45900 15800 135000 25 45

2. 6. 10. 14. 18.

2360 1400 1000 16 24

3. 5600 7. 39000 11. 87000 15. 9 19. 15

4. 8. 12. 16. 20.

90460 40300 56000 11 1

Place, value and ordering 7 page 9 1. 67 460 6. 25 000 11. 20 000

2. 15 890 3. 62 130 7. 12 900 8. 31 500 12. 100 000 13. 289 000

4. 34 590 9. 83 300

5. 47 600 10. 77 000

Place, value and ordering 8 page 10 1. -4◦C

2. -5◦C

3. 10◦C

4. -9◦C

5.

10◦C

6.

13◦C

Place, value and ordering 9 page 11 1. -10 3. -22 5. -2

-7 -4 -13 -12 6. -5

-2 4 8 -5 15 20 7. 8

2. -22 -14 -9 -3 0 2 4. -28 -19 -18 -9 -8 3 9. -19 10. 4

8. -18

Place, value and ordering 10 page 12 A 1. 10 2. 10 3. 6 4. 11 5. 11 6. 15 7. 20 8. 3 9. 17 10. 9 B 1. -92 2. -170 3. -103 4. -79 5. 62 6. -171 7. -102 8. -22 9. -116 10. 296 Place, value and ordering 11 page 13 A 1. 16 7. 25 B 1. 22 7. 112 13. 32

2. 81 8. 64

3. 49 9. 100

2. 91 8. 100 14. 50

3. 155 9. 72 15. 88

4. 1 10. 121

5. 144 11. 36

6. 4 12. 169

4. 10. 16.

5. 20 11. 119

6. 15 12. 113

73 41 130

204

Place, value and ordering 12 page 14 1. 118, 124, 130 The rule is add 6 3. -44, -41, -38 The rule is subtract 3 5. 75, 50, 25 The rule is subtract 25 7. 63, 72, 81 The rule is add 9

2. 4. 6. 8.

460, 465, 470 The rule is add 5 -12, -24, -36 The rule is subtract 12 12, 36, 60 The rule is add 24 -45, -65, -85 The rule is subtract 20

Place, value and ordering 13 page 15 1. The sum of odd numbers is odd. Examples include: 3 + 5 + 9 = 17 7+ 17 + 11 = 35 15 + 9 + 7 = 31 2. The sum of 2 even numbers is even. Examples include: 20 + 2 = 22 28 + 8 = 36 10 + 4 = 14 3. The sum of an odd number and and even number is odd. Exampes include: 20 + 7 = 27 3 + 2 = 5 28 + 11 = 39 4. The difference between two even numbers is even. Examples include: 20 – 2 =18 28 – 8 = 20 16 – 4 = 12 Place, value and ordering 14 page 16 1. The product of 3 odd numbers is odd. Examples include: 9 × 1 × 7 = 63 7 × 5 × 3 =105 3 × 11 × 7 = 231 2. The product of 2 even numbers is even. Examples include: 9 × 12 = 108 8 × 6 = 48 4 × 6 = 24 3. The product of 2 odd numbers is odd. Examples include: 9 × 7 = 63 11 × 7 = 77 5 × 5 = 15 4. The product of 1 even number and 1 odd number is even. Examples include: 2 × 9 = 18 12 × 7 = 84 10 × 5 = 50 Addition 1 page 17 1. 325 + 278 = 300 +200 = 500 20 + 70 = 90 5+ 8 = 13 = 603

2. 167 + 164 = 100 + 100 = 200 60 + 60 = 120 7 + 4 =11 = 331

3. 456 + 234 = 400 +200 = 600 50 + 30 = 80 6+ 4 = 10 = 690

4. 645 + 357 = 600 + 300 = 900 40 + 50 = 90 5 + 7 = 12 = 1002

5. 552 + 268 = 500 +200 = 700 50 + 60 = 110 2+ 8 = 10 = 820

6. 785 + 247 = 700 + 200 = 900 80 + 40 = 120 5 + 7 = 12 = 1032

7. 156 + 69 = 156 +70 = 156 + 70 = 226 -1= 225

8. 456 + 89 = 456 + 90 = 546 = 546 – 1 = 545

9. 433 + 102 = 433 + 100 = 533 + 2 = 535

10. 391 + 99 = 391 + 100 491 - 1= 490

205

Addition 2 page 18 1. 3568 + 455 4023

2. 8501 + 178 8679

111

7. 2879 + 352 3231 1 1 1

13. 7649 + 8463 16112

3. 7494 + 267 7761 11

8. 8936 + 957 9893 1 1

14. 6832 +6945 13777

1 1 1

11

9. 3406 + 3589 6995 1

4. 3464 + 389 3853

5. 2784 6. 6891 + 246 + 567 3030 7458

1 1

10. 8501 + 2673 11174

111

11. 7494 12. 3464 +4761 + 3678 12255 7142

11

15. 9452 +7902 17354

16. 3764 +7902 11666

1

1 1

1 11

20. 3464 2389 784 + 2754 9381

131

222

21. 1449 247 5937 +7461 15094 2 12

22. 9502 693 8462 + 794 19451 2 21

111

17. 1388 18. 8501 38 3490 239 594 + 2784 + 4891 4449 17476 122

19. 7494 96 2385 + 3570 13545

11

22

23.

6491 24. 4462 3479 593 2845 6936 + 6743 + 8931 19558 20922 1 2 1

2 21

Addition 3 page 19 1. 63377 6. 818207

2. 141603 3. 759127 7. 1025 291 8. 134 861

4. 408033

5. 225145

4. 72514

5. 107685

Addition 4 page 20 1. 28031 6. 109066

2. 17012 7. 107783

3. 42248 8. 100555

Addition 5 page 21 1. 41·76 6. 204·445

2. 920·965 3. 325·433 7. 1888·477 8. 763·379

4. 6807·366 5. 5504·797

Addition 6 page 22 1. 133·13 6. 46·621

2. 114·714 7. 92·026

3. 100·626 8. 911·845

4. 313·28

5. 110·773

206

Addition 7 page 23 1.

2. 1590 + 251 1841

+

5.

3. 3567 1745 5312

6. 1 6 ·3 5 + 3 ·2 6 1 9·6 1

+

4. 5728 + 723 6451

7. 2 5 4· 7 7 4· 2 3 2 1·5

3567 +4913 84 8 0 8.

2·5 7 3 + 0·8 4 2 3·4 1 5

1 9· 2 5 + 7 4· 3 6 9 3· 6 1

Addition 8 page 24 1.

3.

57 + 21 = 78 570 + 210 = 780 5700 + 2100 = 7800 0·57 + 0·21 = 0·78 5·70 + 2·10 = 7·80 0·057 + 0·021= 0·078 98 + 24 = 122 980 + 240 = 1220 9800 + 2400 = 12200 0·98 + 0·24 = 1·22 9·80 + 2·40 = 12·20 0·098+ 0·024 = 0·122

2.

78 + 65 = 780 + 650 = 7800 + 6500 = 0·78 + 0·65 = 7·80 + 6·50 = 0·078+0·065 = 4. 56 + 75 = 560 + 750 = 5600 + 7500 = 0·56 + 0·75 = 5·60 + 7·50 = 0·056+0·075 =

143 1430 14 300 1·43 14·30 0·143 131 1310 13100 1·31 13·10 0·131

Addition 9 page 25 1. 7. 13. 19.

8200 15000 18800 2900

2. 8. 14. 20.

9800 17100 2300 6500

3. 9 15. 21.

7700 12500 4900 4700

4. 10. 16. 22.

13800 14500 4200 13100

5. 11. 17. 23.

4200 13100 1600 14000

6. 12. 18. 24

10700 9500 7600 2100

3. 9. 15. 21.

0·08 0·18 0·45 0·97

4. 10. 16. 22.

0·08 1·07 0·54 0·44

5. 0·03 11. 0·04 17. 0·17

6. 0·07 12. 0·3 18. 0·8

5. 2·17 11. 7·639

6. 2·44 12. 2·146

Addition 10 page 26 1. 7. 13. 19.

0·09 0·03 0·7 0·09

2. 8. 14. 20.

0·09 0·09 0·8 0·88

Addition 11 page 27 1. 0·56 7. 9·44 13. 1·111

2. 0·92 8. 8·28 14. 12·16

3. 0·77 9. 12·04

4. 0·38 10. 1·872

207

Addition 12 page 28 1. 175 325 4. 150 250 425

2. 250 100 5. 125 275 200

3.

350

450

Addition 13 page 29 1. 7624 + 3957 = 7624 + 7 + 50 + 900 + 3000 = 11581 +7

+50

7624 7631

+ 900

7681

+3000

8581

11581

2. 1357 + 297 = 1357 + 7 + 90 + 200 = 1654 +7

1357

+90

+ 200

1364

1454

1654

3. 5724 + 562 = 5724 + 2 + 60 + 500 = 6286 +2

+60

5724 5726

+ 500

5786

6 286

4. 7534 + 1582 = 7534 + 2 80 + 500 + 1000 = 9116 + 2 +80

7534 7536

+ 500

7616

+1000

8116

9116

208

Addition 14 page 30 1. 9241 + 5176 = 9241 + 6 + 70 + 100 + 5000 = 14417 + 6 +70 + 100 +5000

9241 9247

9317

9417

14417

2. 4276 + 247 = 4276 + 7 + 40 + 200 = 4523 +7 +40 + 200

4276 4283

4323

4523

3. 3793 + 493 = 3793 + 90 + 400 = 4286 + 3 +90 + 400

3793 3796

3886

4286

4. 5056 + 3873 = 5056 + 3 + 70 + 800 + 3000 = 8929 + 3 +70 + 800 +3000

5056 5059

5129

5929

8929

Subtraction 1 page 31 1. 403-67= 3+30+300+3= 336 +3 +30 + 300

67 70 100 2. 309-94= 6+200+9= 215 +6 + 200

94

100

+3

400

403 +9

300

309

3. 713-83= 7+10+600+13= 630 +7 +10 + 600

+13

83 90 100 4. 521-78= 2+20+400+21=443 +2 +20 + 400

700

78

500

80

100

713 +21

521

209

Subtraction 2 page 32 41 8 1

41

1. 5697 - 749 4948

6121

2. 5134 - 623 4511 1 5 21

31

7. 2942 - 836 2106

8. 8634 - 459 8175

2 101

14. 8469 -7356 1113

1 15 31

19. 16474 - 7891 8583

15. -

8374 4286 4088

16. 8312 - 4295 4017

1 1 4 21351

8111

20. 53464 -34897 18567

1 5 61

11. 1123 12. 4678 - 1034 - 2489 89 2189 1 71421

4 151 2 1

17. 56345 18. 98534 - 7891 - 34697 48454 63837

11 1

21. 89321 - 6712 82609

6. 6793 - 985 5808

1 011

10. 8467 - 6734 1733

1 7 2 61

5181

5. 2845 - 783 2062

7 1

9. 3049 - 2457 592

1

71

4. 4494 - 865 3629

9 21 1

6 2 41

13. 7356 - 4378 2978

3 1 81

3. 7634 - 805 6829

9 8 1 411

716 1

22. 12567 - 7834 4733

23. 23870 24. 90501 - 12671 - 67232 11199 23269

Subtraction 3 page 33 1. 3388 7. 804479

2. 556 8. 25793

3. 59587

4. 37844

5. 71587

3. 420·36 8. 783·585

4. 6613·134

6. 11032

Subtraction 4 page 34 1. 21·999 6. 77·676

2. 644·99 7. 116·835

5. 667·987

Subtraction 5 page 35 1.

2. 3290 538 2752

6.

3. 5324 - 3370 1954

7. -

621· 6 275· 9 345· 7

4.

6327 - 2683 3644

5. 8 6 19 -5023 3596

22·17 5·39 16·78

8. 6· 3 7 2 - 5· 1 3 4 1·2 3 8

49·16 -24·48 24·68

210

Subtraction 6 page 36 1. 87 - 25

= 62

2. 74 - 35 = 39

3.

92-37 = 55

4. 76-29= 47

870 - 250 = 620

740 -350 =390

920-370 = 550

760-290=470

8700 - 2500 = 6200

7400 -3500 =3900

9200-3700=5500

7600-2900=4700

0·87 - 0·25 = 0·62

0·74 -0·35 =0·39

0·92-0·37=0·55

0·76-0·29=0·47

8·70 - 2·50 = 6·2

7·4 -3·5 =3·9

9·2- 3·7=5·5

0·087 - 0·025=0·062 0·074 - 0·035=0·039

7·6-2·9=4·7

0·092-0·37=0·055 0·076-0·029=0·047

Subtraction 7 page 37 1. 4. 7. 10. 13. 16. 19. 22.

8700 - 6000 = 6100 8300 - 5800 = 2500 9600 - 3700 = 5900 11700 - 8700 = 3000 19200 - 15600 = 3600 9400 – 1800 = 7600 11000 – 4300 = 6700 7400 – 700 = 6700

2. 6300 -5400 = 900 5. 7300 - 2900 = 4400 8. 9500 - 7700 = 1800 11. 12400 - 3800 = 8600 14. 9600 – 6200 = 3400 17. 2400 – 500 = 1900 20. 8200 – 3500 = 4700 23. 6600 – 2800 = 3800

3. 6. 9. 12. 15. 18. 21. 24.

5800 - 2700 = 3100 2900 -2200 = 700 6400 – 4900 = 1500 22800 – 11700 =11100 7400 – 4700 = 2700 5500 – 1800 = 3700 18700 – 9500 = 9200 9800 – 5900 = 3900

Subtraction 8 page 38 1. 0·7 7. 5·07 13. 1·028

2. 0·1 8. 2·18 14. 4·211

3. 0·15 9. 1·68

4. 0·72 10. 0·93

5. 0·43 11. 6·985

6. 0·24 12. 0·016

Subtraction 9 page 39 1. -1·5, 1·5 5. 1·75, 2·5

2. 3·5, -4·5 `

3. -8·8, 3·2

4. -1·5, -1·0

Multiplication 1 page 40 1. 7. 13. 19.

560 130 451000 10

2. 78 3. 2360 8. 26890 9. 2400 14. 4681300 15. 229600 20. 9900 21. 50

4. 10. 16. 22.

6000 5. 39120 1400 11. 78900 3589100 17. 10 10 23. 12400

6. 12. 18. 24.

528910 40000 3700 10

Multiplication 2 page 41 1. 5. 9.

100, 4500 2. 100, 8900 1000, 90000 6. 1000, 305000 ×10 10. × 1000

3. 1000, 24000 7. × 10 11. × 100

4. 100, 32100 8. × 100 12. × 1000 211

Multiplication 3 page 42 1. 550 6. 500

2. 1200 7. 400

3. 1450 8. 1250

4. 2500 9. 850

5. 1800 10. 1200

3. 240 8. 360

4. 512 9. 1200

5. 672 10. 1008

c. 234 c. 432

2. a. 192

b. 320

Multiplication 4 page 43 1. 224 6. 144

2. 352 7. 336

Multiplication 5 page 44 1. 3.

a. 182 a. 192

b. 104 b. 336

c. 512


(30 × 3) + (7 × 3) = 90 + 21 = 111 (40 × 7) + (3 × 7) = 280 + 21 = 301 (70 × 9) + (6 × 9) = 630 + 54 = 684 (50 × 7) + (8 × 7) = 350 + 56 = 406

2. 4. 6. 8.

(60 ×4) +(5×4) = 240 + 20 = 260 (50 ×8) +(9×8) = 400 + 72 = 472 (80 ×6) +(7×6) = 480 + 42 = 522 (70 ×8) +(9×8) = 560 + 72 = 632

2. 4. 6. 8.

(40 ×9) +(5×9) = 360 + 45 = 405 (40 ×9) +(9×9) = 360 + 81 = 441 (50 ×6) +(4×6) = 300 + 24 = 324 (70 ×8) +(3×8) = 560 + 24 = 584


(60 × 6) + (5 × 6) = 360 + 30 = 390 (70 × 7) + (2 × 7) = 490 + 14 = 504 (60 × 8) + (7 × 8) = 480 + 56 = 536 (90 × 7) + (8 × 7) = 630 + 56 = 686

Multiplication 8 page 47 1. 7. 13.

7 7 27

2. 4 8. 8 14. 28

3. 3 9. 76 15. 78

4. 6 10. 82

5. 11.

7 95

6. 12.

6 77


6 × 49 = (6 × 50) - 6 = 300 - 6 = 294 15 × 49 = (15 × 50)-15 = 750-15 = 735 26 × 49 = (26 × 50)-26 = 1300-26 =1274 49×49 = (49×50) -49 = 2500-49 =2401

2. 4 × 49 = (4 × 50)-4 = 200-4 = 196 4. 8 × 49 = (8×50)-8 = 400-8 =392 6. 33×49 = (33×50)-33 =1650-33 = 1617 8. 94 ×49= (94×50)-94 = 4700-94 =4606


5 × 51= (5 × 50) + 5 = 250 + 5 = 255 2. 7 × 51 = (7 × 50) + 7= 350 + 7 = 357 9 × 51= (9 × 50) + 9 = 450 + 9 = 459 4. 12 ×51=(12×50) +12 =600 +12 = 612 24×51=(24 × 50)+24=1200 + 24 =1224 6. 36×51= (36×50)+36=1800+36 =1836 78×51= (78×50)+78 =3900 +78 =3978 8. 53×51= (53×50)+53= 2650+53 = 2703

212

Multiplication 11 page 50

1.

465 × 5 =

400 5

2.

748 × 6 =

2100

876 × 9 =

978 × 8 =

240

30 90

= 2325

25

8

4

= 2202

12

70

6

7200

630

54

7200

= 4488

48

800

900 8

5

40

700

9 5.

4200

734 × 3 = 3

4.

300

700 6

3.

2000

60

70

= 7884

8

560

=7824

64

Multiplication 12 page 51 1.

2461 × 4 =

2000 4

2.

3255 × 5 = 5

3.

6328 × 3 = 3

4.

1289 × 7 =

4196 × 8 =

240

1000

250

25

6000

300

20

8

7000

32000

900

200 1400

100 800

60

= 9844

4

15000

18000

50

1

200

4000 8

1600

60

3000

1000 7

5.

8000

400

5

= 16275

= 18984

24

80

9

560

63

90

6

720

48

= 9023

= 33568

213


4256 × 3 =

4000 3

2.

3728 × 6 =

6146 × 7 = 7

4.

4578 × 9 = 9

5.

50

6

600

150

18

700

20

8

18000

4200

120

48

6000

100

40

6

12000

3000 6

3.

200

7552 × 8 =

42000

700

280

42

4000

500

70

8

36000

4500

630

72

7000 8

56000

500 4000

50 400

2

= 12768

= 22368

= 43022

= 41202

=

60416

16

214

Multiplication 14 page 53 1. 126×5 126 5 500 100 + 30 630

125 × 5 = 600

2. 756 × 4

756 4 2800 200 + 24 3024

×

3. 453x5 453 × 8 3200 400 + 24 3624 5. 728×9 728 × 9 6300 180 + 72 6552

750 ×4 = 3000

×

(100×5) ( 20 ×5) ( 6 ×5) (126×5) 450 × 5 = 2250

4. 691 × 6

(700×4) ( 50×4) ( 6×4) (756×4)

700 × 6 = 4200 691 6 3600 540 + 6 4146 ×

(400×8) ( 50 ×8) ( 3 ×8) (453×8) 720 10 = 7200

(700 ×9) ( 20 ×9) ( 8 ×5) (728×5)

6. 847 × 8

(600×6) ( 90×6) ( 1×6) (691×6)

850 × 8 = 3400 847 × 4 6400 320 + 56 6776

(800×8) ( 40×8) ( 7×8) (847×8)

215

Multiplication 15 page 54 1. 1526 × 5 1526 5 5000 2500 + 100 30 7630

1500 × 5 = 7500

2. 2715 × 3

2715 × 3 6000 2100 + 30 15 8145

×

3. 3642 × 5 3642 × 5 15000 3000 + 200 10 18210 5. 4318 × 7 4318 × 7 28000 2100 + 70 56 30226

2700 × 3 = 8100

(1000 ×5) ( 500 ×5) ( 20 ×5) ( 6 ×5)

3500 × 5 = 17500

4. 7367 × 3

(2000×3 ) ( 700×3 ) ( 10×3 ) ( 3×5 ) (2715×3)

7300 × 3 = 22000

7367 × 3 21000 (7000 ×3 ) 900 ( 300 ×3 ) + 180 ( 60 ×3 ) 21 ( 7 ×3) 22101 (7367 ×3)

(3000 ×5) ( 600 ×5) ( 40 ×5) ( 2 ×5)

4000 × 7 = 28000

6. 6967 × 8

7000 × 8 = 56000

6967 × 8 48000 7200 + 480 56 55736

(4000 ×7) ( 300 ×7) ( 10 ×7) ( 8 ×7)

(6000 ×8) ( 900 ×8) ( 60 ×8) ( 7 ×8) (6967 ×8)


597 × 6 3582 54

2.

736 × 6 4416 23

3.

268 × 6 1608 44

4.

947 × 8 7576 35

5. 783 × 7 5481 52

6. 937 × 6 5622 24

Multiplication 17 page 56 1. 4895 × 6 29370 5 53

2. 6309 × 4 25236 1 3

3. 1297 × 5 6485 143

4. 3437 × 6 20622 224

5. 4779 × 7 33453 556

6. 9786 × 8 78288 664

216

Multiplication 18 page 57 1. 18904

2. 13390

3. 22074

4. 31302


8·26 × 4 (8 ×4)= 32 8·00 × 4 = 32·00 0·20 × 4 = 0·80 0·06 × 4 = 0·24 33·04

2. 4·81 × 5 (5×5)=25 4·00 ×5 = 20·00 0·80 × 5 = 4·0 0·01 × 5 = 0·05 24·05

3.

5·17 × 6 (5×6)= 30 5·00 ×6 = 30·00 0·10 × 6 = 0·60 0·07 ×6 = 0·42 31·02

4. 6·35 × 4 (6×4)=24 6·00 × 4 = 24·00 0·30 × 4 = 1·20 0·05 × 4 = 0·20 25·40

5.

6·84 × 7 (7×7)=49 6·00 × 7 = 42·00 0·80 × 7 = 05·60 0·04 × 7 = 00·28 47·88

6. 9·68 × 8 (10×8)=80 9·00 × 8 = 72·00 0·60 × 8 = 4·80 0·08 × 8 = 0·64 77·44


7·54 ×7 (8 × 7 )=56 7·00 × 7 = 49·00 0·50 × 7 = 03·50 0·04 × 7 = 00·28 52·78

2.

9·78 × 6 (10×6) = 60 9·00 × 6 = 54·00 0·70 × 6 = 4·20 0·08 × 6 = 0·48 58·68

3

6·05 × 8 (6 × 8 )= 48 6·00 × 8 = 48·00 0·05 × 8 = 00·40 48·40

4.

5.

12·24 × 3 (12 ×3)=36 12·00 × 3 = 36·00 0·20 × 3 = 00·60 0·04 × 3 = 00·12 36·72

6.

5·73 × 9 (6 × 8) = 48 5·00 × 9 = 45·00 0·70 × 9 = 06·30 0·03 × 9 = 0·27 51·57 24·72 × 4 (25×4) = 100 24·00 × 4 = 96·00 00·70 × 4 = 02·80 00·02 × 4 = 00·08 98·88

7.

16·82 × 5 (17 ×5)=85 16·00 × 5 = 80·00 00·80 × 5 = 4·00 00·02 × 5 = 0·10 84.10

8.

23·06 × 6 (236)=138 23·00 × 6 = 138·00 00·06 × 6 = 00·36 138·36

217


2. 177

3. 200

4. 340

5. 500

6. 450

7. 400

8. 600


476 × 15 = × 105 0 5

2.

20 0 4

6

4000 2000

700 350

60 30

600

90

4

12000 2400

1800 360

80 16

800

20

9

=

+

24000 5600

305 0 7

600 140

=

+

=

+

270 63

60 0 8

400

90

7

24000 3200

5400 720

420 56

13880 2776 16656 11

24870 5803 30673 11

497 × 68 = ×

4760 2380 7140 11

829 × 37 = ×

4.

70

694 × 24 = ×

3.

400

=

+

29820 3976 33796 11

218


3472 × 25 = × 20 0 5

2.

60000 15000

6000

180000 00 12000

30 02

70

2

8000 2000

1400 350

40 10

100

90

3

3000 200

2700 180

90 6

800

30

1

40000 2400

1500 90

50 3

400

50

6

8000 1600

1000 200

120 24

=

+

69440 17360 86800 1

=

+

1

185790 12386 11 198176 11

3831 × 53 = × 3000

150000 009000

50 3 4.

400

6193 × 32 = ×

3.

3000

=

+

1 11

8456 × 24 = × 20 0 4

8000

160000 00 32000

191550 11493 11 203043

=

+

169120 33824 11 202944 11

219

Multiplication 24 page 63 1. 345 × 35 = 12075 3 × (

5

)

×

3 5 3

5

)

×

3

5

)

3

0

0

×

(

4

0

(

5

`

1

4

5

3

5

0

5

0

0

1

4

0

0

1

7

5

0

7

5

7

4

6

4

3

1

2

1

11

2. 746 × 43 = 32078

× (

7

0

0

(

4 (

4

3

)

0

× 5 ×

4

3

)

6

×

4

3

)

3

3

0

1

0

0

1

7

2

0

2

5

8

0

7

8

2 1

220


262 × 42 = 11004 2

0

0

×

4

2

)

8

4

0

(

6

0

×

4

2

)

2

5

2

0

(

2

×

4

2

)

8

4

0

4

5

6

3

1

0

1

1

756 × 36 = 27216 7

5

2

0

6 2 0

1

8

0

0

2

1

6

2

1

6

5

3

4

6

× (

4

2

1

2.

2 2 2 0

× (

6

7

0

0

×

3

6

)

(

5

0

×

3

6

)

(

6

×

3

6

)

2

2

7 1

3.

534 × 65 = 34710

2

5

0

5 2 0

1

9

5

0

2

6

0

4

7

1

0

1

1

× (

5

0

0

×

6

5

)

(

3

0

×

6

5

)

(

4

×

6

5

)

3

3


2. 3

3. 4

4. 5

5. 7

6. 5

7. 8

8. 5

221

Factors and Multiples 1 page 66 1. 18

1,2,3,6,9,18

2. 40

1, 2,4,5,8,10,20,40

4. 20

1,2,4,5,10,20

5. 36

1,2, 3,4, 6, 9,12, 18

6. 48

1,2,4,6,812,16,24,48 7. 24

3. 64

1,2,4,8, 16,32 64

1,2,4,6,8,12,24

Answers include: 8. 12 × 15 9. 16 × 12 10. 24 × 18

12 × 3 5, 15 × 6 × 2, 15 × 3 × 4 = 180 16 × 3 × 4, 16 × 2 × 6, 12 × 4 × 4 = 192 6 × 4 × 9 × 2, 12 × 2 × 9 × 2, 6 × 4 × 3 × 6 = 432

11.33 × 16

33 × 4 × 4, 33 × 8 × 2, 16 × 11 × 3 = 528

12. 27 × 18

27 × 9 × 2, 27 × 3 × 6, 18 × 3 × 9 = 486

13. 25 × 16

25 × 4 × 4, 25 × 2 × 8, 16 × 5 × 5 = 400

14. 24 × 25

24 × 5 × 5, 25 × 8 × 3, 25 × 6 × 4 = 600

222

Factors and Multiples 2 page 67

Number

Factors

Number of Factors

1

1

1

2

1

2

2

3

1

3

2

4

1

2

5

1

5

6

1

2 3

7

1

7

8

1 2

9

1

10

4

3 2 6

4

9

2

4 8

4

3

9

3

1

2

5

11

1

11

12

1

2 3 4 6

13

1

13

14

1

2

15

1 3

5

15

4

16

1 2

4

8 16

5

17

1

17

18

1

2

19

1

20

1

10

4 2 12

6 2

7

14

4

2 3 6

9

18

6

19 2

2 4

5

10

20

6

223

Factors and Multiples 3 page 68

Number

Factors 7

Number of Factors

21

1

3

21

4

22

1

2 11 22

4

23

1

23

2

24

1 2

25

1

5

26

1

2 13

27

1

3

28

1 2

29

1

30

1 2 3 5

31

1

31

32

1

2

33

1

3 11

34

1

2

35

1

5

7

35

36

1 2

3

4 6

37

1

37

38

1

2

19

38

4

39

1

3 13

39

4

40

1

2

5

41

1

41

42

1

2

43

1

43

44

1

2

45

1

3 5

3 4

6 8

12

24

8

25

3 26

4

9 27

4

4 7

14

28

6

29

2 6

10

15

30

8 2

4

8

16

32

6

33

17

4

34

4 4

9 12 18 36

9 2

4

8

10

20

40

8 2

3

6

7

14

21

42

8 2

4 11 22 9

15

44 45

6 6

224

Factors and Multiples 4 page 69 1.

a. 2 3 5 7

2.

9

25

11 13 17 19 23 29 31 37 41 43 3.

b. Prime numbers

Odd Square numbers

Factors and Multiples 5 page 70 1. Composite numbers

2. 13 31 17 71

19 91 37 73

3. 845 ends in 5 so it is divisible by 5 a prime number is only divisible by 1 or itself. 4. 266 is an even number a prime number is always odd. 5. Examples such as 23 12 14 16 25 Factors and Multiples 6 page 71 1. 2

2, 4, 6, 8, 10, 12, 14, 16, 18, 20

3

3, 6, 9, 12, 15, 18, 21, 24, 27, 30

2. 5

5,10,15,20,25,30,35,40,45,50

4

4, 8,12,16,20,24,28,32,36,40

3 3

3, 6, 9, 12, 15, 18, 21, 24, 27, 30 9

9, 18, 27, 36, 45, 54, 63, 72,81, 90

4. 5

5,10,15,20,25,30,35,40,45,50

7, 14,21,28,35, 42, 49,56, 63, 70

5. 4 6. 6

7

4, 8,12,16,20,24,28,32,36,40 10 6,12,18,24,30,36,42,48,54,60

10,20,30,40,50,60,70,80,90,100

9

9, 18, 27, 36, 45, 54, 63, 72,81, 90

Factors and Multiples 7 page 72 1. 6

6, 12,18,24,30,36,42,48,54,60

2. 3

3,6,9,12,15,18,21,24,27,30

3

3,6,9,12,15,18,21,24,27,30

6

6,12,18,24,30,36,42,48,54,60

5

5,10,15,20,25,30,35,40,45,50

8

8,16,24,32,40,48,56,64,72,80

3. 5

5,10,15,20.25,30,35,40,45,50

4

4,8,12,16,20,24,28,32,36,40

6

6,12,18,24,30,36,42,48,54,60,

6

6,12,18,24,30,36,42,48,54,60

10

10,20,30,40,50,60,70,80,90,100

9

9,18,27,36,45,54,63,72,81,90

5. 9 8 12

4.

9,18,27,36,45,54,63,72,81, , 8,16,24,32,40,48,56,64,72,80 12,24,36,48,60,72,84,96,108,120

225

Factors and Multiples 8 page 73 1. 24, 48, 72, 96, 120, 144

2. 30

3. . 42, 84, 126 4. 72

5.

28 days

6. 90 beads

Factors and Multiples 9 page 74 1.

13, 26, 39, 52, 65, 78, 91, 104

3.

Answers include 305, 310, 315, 320, 325, 330, 335, 340, 345, 350

4.

a. 25, 50, 75, 100, 125, 150, 175, 200, 225, 250 b. They all end in 25, 50, 75 or 00 11,22,33,44,55,66,77,88,99,110,121,132,143,154,165,176,187,198, 209, 220, 231,242,253,264,275

5.

2.

84

Division 1 page 75 1. 7. 13. 19.

24 123 67 10

2. 8. 14. 20.

369 7820 923 56

3. 9. 15. 21.

13 66 22 4300

4. 10. 16. 22.

34 4 546 10

5. 11. 17. 23.

450 23 10 12

6. 12. 18. 24.

4670 1 9 100

Division 2 page 76 1. 100, 4 2. 100, 45 3. 1000, 9 4. 100, 800 5. 100, 9.34 6. 1000 3.215 7. 1000, 0.456 8. ÷10 9. ÷100 10. ÷10 11. ÷100 12. ÷1000 13. ÷1000 Division 3 page 77 1. 32

1,2,4,8,16,32

2. 25

1, 2,5,25

4. 54

1, 2,3,6,9,27,54

5. 60

1,2,3,4,5,6,10,12,15,30,60

6. 100

1,2,4,5,10,25,50,100 7. 108

3. 48

1,2,3,4,8,16,24,48

1, 2, 3,4,6,9,12,18,27,54,108

Answers include: 8. 168 ÷ 12 9. 180 ÷ 15 10. 60 ÷ 15 11. 120 ÷ 24 12. 800 ÷ 16 13. 108 ÷ 27 14. 390 ÷ 15

(168÷3)÷4, (168÷6) ÷2,(84÷12)+(84÷12)=14 (180÷3)÷5, (180÷5) ÷3, (90÷15)+(90÷15)= 12 (60÷3)÷5, (60÷5) ÷3, (30÷15)+(30÷15)= 4 (120÷6)÷4, (120÷12) ÷2, (120÷8) ÷3= 5 (800÷8)÷2, (800÷4) ÷4, (400÷16)+(400÷16)= 50 (108÷3)÷9, (108÷9) ÷3, (54÷27)+(54÷27)= 4 (180÷3)÷5, (180÷5) ÷3, (90÷15)+(90÷15)= 12

226

Division 4 page 78 1. 9.

√ ×

2. √ 3. √ 4. × 10. × 11. √ 12. √

5. √ 13. ×

6. √ 14. √

7. × 15. ×

8. √ 16. √

Division 5 page 79

~ 240 ÷ 4 = 60

1. 246 ÷ 4

~

2. 566÷5

2

113 15 5 566 550 ( 110 × 5) 16 15 ( 3 × 5 ) 1

61 4 246 240 (60 × 4) 6 4 ( 1 ×× 4) 2

4

1

1

Answer 61 2 3.

550 ÷ 5 = 110

Answer 113 5

~

294 ÷5

290 ÷ 5 = 58 4.

451÷7

~420 ÷ 7 = 60

4

3

58 5 5 294 290 ( 58 ×5 ) 4

64 7 7 451 420 ( 60 ×7) 31 28 ( 4 × 7 ) 3

4

3

Answer 58 5

Answer 64 7

Division 6 page 80 1. 149 ÷ 7

~ ~~

2

140 ÷ 7 = 20

Answer 21 7

300 ÷ 6 = 50

Answer 54 6

180 ÷ 6 = 30

Answer 38 3

250 ÷ 5 = 50

Answer 51 45

5. 748 ÷ 9

720 ÷ 9 = 80

Answer 83 9

6..

630 ÷ 7 = 90

2. 325 ÷ 6 3. 230 ÷ 6 4. 259 ÷ 5

~ ~~

~ ~ 685 ÷ 7 ~

1

1

1

6

Answer 97 7

227

Division 7 page 81 46·2 ~ 42 ÷ 7 = 6 6·6 7 46·2 42 (6 × 7) 4·2 ( 0·6 ×7) Answer 6·6 1.

25·9 ÷2 ~ 24 ÷ 2 = 12 12·95 2 25·9 24 ( 12 × 2) 1·9 1·8 ( 0·9 × 2 ) 0· 10 (0·05 × 2) Answer 12·95 3.

2.

4.

11·75 ÷ 5 ~ 10 ÷ 5 =2 2·35 5 11·75 10 (2 × 5) 1·75 1·5 (0·3 × 5) 0·25 (0·05 × 5) Answer 2·35 18·9 ÷ 9 ~ 2 2·1 9 189 18 ( 2×9) 0·9 (0·1 × 9)

Answer 2·1

Division 8 page 82 84·6 ÷ 9 ~ 9 9·4 9 84·6 81·0 ( 9 × 9) 3·6 (0·4 ×9) Answer 9·4 1.

47·4 ÷ 5 ~ 45 ÷ 5 = 9 9·48 5 47·4 45·0 ( 9 × 5) 2·4 2·0 ( 0·4 × 5 ) 0·40 (0·08 × 5) Answer 9·48 3.

28·2 ÷ 6 ~ 24÷6= 4 4·7 6 28·2 24 ( 4 × 6) 4·2 ( 0·7 ×6) Answer 4·7 5.

2.

4.

32·5 ÷ 5 6·5 5 32·5 30 2·5 Answer 6·5

~ ~ 30 ÷ 5 =6 ( 6 × 5) (0·5 × 5)

24·72 ÷ 2 ~ 24 ÷ 2 =12 12·36 2 24·72 24 ( 12 × 2 ) 0·72 (0·36 × 2)

Answer 12·36 6.

60·8 ÷ 8 7·6 8 60·80 56 4·8 Answer 7·6

~ 56 ÷ 8 = 7 ( 7 × 8) (0·6 × 8)

228

Division 9 page 83 1. 2156 123 470 140 678 467 998 1002 771 43 2. 12 66 94 104 236 126 282 398 448 732 512 3. 1025 1660 3450 36 775 240 900 3335 11175 45 6700 385 67 450 24 200 6590 1100 750 6648 175 4. 6800 216 4256 444 816 612 2680 3156 796 Division 10 page 84 1. 2. 3. 4.

a. yes b. no c. yes yes Half of 864 is 432 which is divisible by 4. yes 3500 ends in 00 so it is divisible by 25. no 86 is not divisible by 4.

Division 11 page 85 1. 6500 219 4250 445 805 610 2681 3156 790 2. 68 99 123 672 560 742 919 678 145 252 2106 178 471 142 6765 465 981 1002 771 43 3. 69 72 94 1242 236 99 282 398 448 732 512 4. 68 900 609 504 112 799 75 810 702 333 Division 12 page 86 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

Answers include 302, 304, 306, 308, 312,314 Answers include 1505, 1510, 1515,1520, 1525 Answers include 603, 606, 609, 612, 615,618 Answers include 906, 912, 918, 924, 930,936 Answers include 2004,2008,2012,2016, 2024 Answers include 1503,1512,1521,1530, 1539 Answers include 1608,1616,1624,1632, 1640 Answers include 410, 420, 430, 440, 450,460 Answers include 1008, 1017, 1026, 1035,1044 Answers include 704, 712, 720, 728, 736,744

398 1995 699 1194 2096 1998 1992 790 1395 996

Division 13 page 87 1.

38 74

2. 89

53

3. 48

93

4. 79 40

5. 36 92

Division 14 page 88 1. 150 7. 762

2. 366 8. 500

3. 270

4. 125

5. 425

6. 400

Division 15 page 89 1. 437 ÷ 19 2. 648 ÷ 24

~ ~

440 ÷ 20 = 22 Answer 23 650 ÷ 25 = 26 Answer 27

229

3. 4. 5. 6.

459 ÷ 17 546 ÷ 14 522 ÷ 29 663 ÷ 13

~ ~~ ~ ~

459 ÷ 17 = 30 540 ÷ 15 = 36 510 ÷ 30 = 17 660 ÷ 10 = 66

Answer 27 Answer 39 Answer 18 Answer 51

Multiplication and Division 1 page 90 1. £24

2. Brighton

3. £20

4. £40

5. £68

£70

Multiplication and Division 2 page 91 1.

2.

4 + 8 7 + 6 = (4 + 8) × 7 + 6 = 12 × 7 + 6 = 90 =4 +( 8 × 7) + 6 = 56 + 4 + 6 = 66 =4 + 8 × (7 + 6) = 13 × 8 + 4 = 108 =(4 + 8) × (7 + 6) = 12 × 13 = 156 64 ÷ 8 × 4 × 3 =(64 ÷ 8) × 4 × 3 = 8 × 4 × 3 = 96 =64 ÷ (8 × 4) × 3 = 64 ÷32 ×3 = 6 100 ÷ 5 × 5 +4 =(100 ÷ 5) × 5 + 4 = 20 × 5 + 4 = 104 =100 ÷ (5 × 5) + 4 = 100 ÷ 25 + 4 = 8 =(100 ÷ 5) × (5 + 4) = 20 × 9 = 180 56 ÷ 4 × 2 × 7 =(56 ÷ 4) × 2 × 7 = 14 × 2 × 7 = 196 =56 ÷ (4 × 2) × 7 = 56 ÷ 8 ×7 = 49 =56 ÷ (4 × 2 × 7) = 56 ÷ 56 = 1 3 + 7 5 + 6 =(3 + 7 ) × 5 + 6 = 10 × 5 + 6 = 56 =3 + (7 × 5) + 6 = 35 + 3 + 6 = 44 =3 + 7 × (5 + 6) = 11 × 7 + 3 = 80 =(3 + 7) × (5 + 6 )= 10 × 11 = 110

3.

4.

5.

Multiplication and Division 3 page 92

56 – 24 ÷ 8 = (56 – 24) ÷ 8 = 32 ÷ 8 = 4 48 + 15 ÷ 3 + 7 =48 + (15 ÷ 3) + 7 = 48 + 5 + 7 = 60 13 × 4 × 2 - 20 =(13 × 4) × 2 - 20 = 52 × 2 -20 = 84 56 ÷ 8 + 6 = 56 ÷ (8 + 6) = 56 ÷ 14 = 4 47 - 11 × 12 ÷ 3 =(47 – 11) × 12 ÷ 3 = 36 × 12 ÷ 3 = 144 7 × 7 + 9 × 3 = (7 × 7) + ( 9 × 3) = 49 + 27 = 76 13 + 7 × 14 -9 = (13 + 7) × (14 -9) = 20 × 5 = 100 14 + 6 × 9 + 32 =14 + (6 × 9) + 32 = 54 + 32 +14 = 100 26 + 24 × 16÷8 =(26 + 24) × (16÷8) = 50 × 2 = 100 28 × 2 – 31 × 4 = (28 × 2) – 31 × 4 =( 56 -31) × 4 =100 56 ÷ 2 + 8 × 9 =(56 ÷2) + ( 8 × 9) = 28 + 72 =100 5 × 12 × 4-28 =5 × (12 × 4) – 28 = (48 -28) ×5 = 100

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.

Multiplication and Division 4 page 93 1. 27 10. 97 19. 40

2. 29 3. 6 11. 10 12. 13 20. 288

4. 13.

8 5

5. 41 14. 55

6. 26 7. 61 8. 33 9. 32 15. 230 16. 18 17. 1952 18. 79

230

Multiplication and Division 5 page 94 1. 900 7. 500

2. 350 8. 201

3. 390

4. 100

5. 755

6. 250

Fractions and Decimals 1 page 95 A 1. 1

1

3 8

4

2. 2 6

1

3

3. 2 9

4. 1 5

5. 2

1 8

37

6. 1100

1

7. 1 19

8. 7 4

B 1.

2.

215 100

31 12

43 10

3.

4.

37 8

315 100

5.

26 9

3.

1 2

is six times

3.

1 5

is twice

6.

Fractions and Decimals 2 page 96 1.

1 2

is three times

1 6

4.

1 2

is four times

1 8

2.

1 6

1 3

is twice

1 4

is three times

1 12


1 2

is twice

4.

1 4

is four times

1 4

2.

1 12

1 10

1 16


½

2.

3.

¼

⅜


2 5

1 6

3 4

9 6

2.

18 10

11 7

3 2

3.

9 8

10 7


5 9

5.

6 50

6.

3 5

3 5

10.

1 6

11.

2 7

12.

3 8

14 20

1.

1 4

2.

3 4

3.

7 10

7.

1 2

8.

1 3

9.


14 18

2.

10 18

3.

6 8

4.

8 10

5.

10 12

6.

7.

1 3

8.

3 8

9.

3 10

10.

9 20

11.

3 7

12.

7 18

231


15 12 8 20 20 20

=

3.

6 3 4 18 18 18

=

5.

6 8

7 8

2 6 3 5 10 4

2.

1 2 6 9

1 3

4.

4 8

=

1 3 7 2 4 8

6.

7.

7 4 6 18 18 18

=

2 9

8.

9.

15 6 16 24 24 24

=

6 5 2 24 8 3

1 7 3 18

3 5 6 6

4 6

=

1 2

2 5 3 6

3 6 4 12 12 12

=

1 4

1 1 3 2

=

2 5

2 7 3 10

=

1 2

4 3 7 4

12 21 20 30 30 30 16 21 14 28 28 28

Fractions and Decimals 9 page 103 1. 3 + 4 = 7 12 12 12

2.

5 + 4= 9 20 20 20

3.

3 +2 = 5 6 6 6

4. 1 + 9 7. 9 + 20

5.

5 + 3= 8 12 12 12 5 + 12 = 17 18 18 18

6.

7 +2 = 9 10 10 10

6= 9 8= 20

7 9 17 20

8.


20 24

+

4.

12 14

+

5 14

=

1

3 14

7.

9 10

+

8 10

=

1

7 10

19 24

=

15 24

1

2.

4 10

+

5.

7 12

+

8.

17 20

+

7 10 9 12

6 20

=

1

1 10

3.

8 12

+

=

1 12

4

6.

9 15

+

=

1 20

9 12

10 15

=

1

= 1

5 12

4 15

3

Fractions and Decimals 11 page 105 1. 6 - 3 = 3 10 10 10

2. 2 - 1 = 1 4 4 4

3. 4 - 1 = 3 = 1 6 6 6 2

5. 9 - 6 = 3 6. 5 - 4 = 1 7. 7 - 6 = 1 10 10 10 12 12 12 10 10 10

4.

8.

3 - 2 = 1 4 4 4 9 - 8 =1 12 12 12

232

Fractions and Decimals 12 page 106 1. 5 - 4 = 1 6 6 6

2.

8 - 3= 5 1 10 10 10 or 2

3.

8 -3 = 5 12 12 12

4. 7 - 2 = 5 8 8 8

5.

11 - 9 = 2 1 12 12 12 or 6

6.

13 - 6 = 7 15 15 15

7. 9 - 6 = 4 2 8. 10 10 10 or 5

19 - 15 = 4 1 20 20 20 or 5

Fractions and decimals 13 page 107 2

1. 112 6.

10

115

1

2.

110

7.

1 20

5

1

3.

12

8.

22 24

4.

1

28

3

5.

28

6.

1 6

6.

1 10

Fractions and decimals 14 page 10 1 6 1 15

1. 1.

2.

1 8

2.

1 9

1 3. 16 61 3. 20

4. 4.

1 3 1 4

5. 5.

4 15 1 18

Fractions and decimals 15 page 109 1. £34

2. 84

3. 14

4. 140

5. 36km

6. 69

Fractions and decimals 16 page 110 1. £6

2. 72

3. 60cm

4. 1290g

5. 414

6. 28ml

7. 570k

Fractions and Decimals 17 page 111 1. 1·5 7. 0·95 13. 1·250

2. 8. 14.

0 ·9 1·58 0·568

3. 9.

2·5 0·07

4. 10.

3 ·5 3·40

5. 0·3 11. 0·350

6. 0·75 12. 0·750

Fractions and Decimals 18 page 112 1. 0·50 2. 0·25 3. 0·10 4. 0·20 9. 0·13 10. 0·83 11. 0·88 12. 0·80

5. 0·75

6. 0·33

7. 0·17

8. 0·01


8 10

2.

15 100

3.

46 100

7.

1·46

8.

0·24

9.

0·129

4.

258 100

10. 0·937

5. 11.

257 1000

1·256

6.

1634 1000

12. 0·078

233

Fractions and decimals 20 page 114 A. 1. 1·6 2. 0·7 3. 2·1 7. 2·7 8. 3·4 9. 9·9 B 1. 1·09 2. 1·76 3. 2·85 7. 4·84 8. 3·81 9. 9·08 13. 12·58 14. 25·38

4. 10.

3 ·1 8 ·3

5.

1·2

4. 10.

4·11 5·43

5. 11.

1·28 6·93

5.

5·9

6.

3 ·0

6. 13·04 12. 12·26

Fractions and decimals 21 page 115 A. 1. 0·2 7. 2·1 B 1. 2·41 7. 5·81 13. 0·28

2. 8.

0 ·6 1 ·9

3. 9.

3·1 2·6

4. 10.

2. 8. 14.

2·89 0·25 2·76

3. 9.

7·98 5·02

4. 10.

4·3 0 ·7 1·09 1·51

6.

5. 0·88 11. 0·48

0·9

6. 7·18 12. 2·88

Fractions and decimals 22 page 116 1. 2·13 2·15 2·28 2·75 2·78 2·96 2. 6·09 6·2 6·23 6·24 6·5 6·61 3. 38·01 38·02 38·12 38·13 38·30 38·34 4. 1·004 1·04 1·041 1·14 1·4 1·44 5. 0·001 0·017 0·111 0·17 0·701 0·710 Fractions and decimals 23 page 117 A. 1. 7. B 1. 7. 13.

1·8 24·8 14·12 36·7 78·21

2. 8.

3 ·5 34·8

2. 8·75 8. 14·88 14. 48·48

3. 9.

7·4 30·6

3. 18·96 9. 36·42

4. 10.

14·4 62·4

5.

4. 20·64 5. 10. 61·92 11.

39

6.

10·36 16·2

21·6

6. 19·02 12. 68·46

Fractions and Decimals 24 page 118 A. 1. 4·15 7. 2·6 B 1. 18·02 7. 2·97 13. 2·38

2. 8.

4 ·3 4 ·3

2. 2·34 8. 1·36 14. 0·46

3. 9.

6·4 1·5

3. 6·12 9. 1·69

4. 10.

3 ·4 3 ·6

4. 3·12 10. 0·38

5.

5·9

5. 4·62 11. 5·68

6.

2 ·3

6. 7·21 12. 4·49

234


24 100

7.

12%

9.

1 3

30 100

2 2 10

1 4

0·35 40% 50%

3..

1 10

35%

0.4

4 6

11. 50% 12. 25% 13. 36%

9 10

4.

3 4

5.

8. 0·54 59% 60% 17 20

10.

0 0·89

9 10

6.

1 4

6.

3 4

7 8

0·98 99%

14. 88%

Fractions and decimals 26 page 120 1. £150 £75 5. £70 £280 9. £7 £3·5

2. £34 £17 3. £45 £22·5 6. £2·60 £10.4 7. £2·75 £13·75 10. £6·60 £39·60 11. £5·40 £32·40

4. £7 £28 8. £20 £10 12. £7·80 £70·20

Fractions and Decimals 27 page 121 2.17

2

17 100

217%

0.2

1 5

20%

0.05

1 20

5%

0.78

39 50

78%

1

17 100 24 25 7 20

1.17

117%

0.96

96%

0.35

35%

Fractions and Decimals 28 page 122 1. a. 25 children b. 5 children c. 30% 2. a. 12 people b. 25% c. 6 people Fractions and Decimals 29 page 123 1. 8 children 2. 80% 3. 20% 2 4. 20% of £55 = £11. of £30 = £12 . So 5

2 5

of £30 is more by £1.

235

Ratio and Probability 1 page 124 A B

1. The ratio is 2 red squares to every 3 yellow squares. 2. The ratio is 2 red squares to every 2 yellow squares. 1. 2 in 5 are red 2. 2 in 4 are red

Ratio and Probability 2 page 125 1. 2. 3. 4.

a. a. a. a.

1:3 1:6 12 24

b. b. b. b.

3 in 4 4 1 in 6 1 in 3

c.

4

Ratio and Probability 3 page 126 1. 1·75 × 6 = 10·5 litres of white paint. 2. a 1: 2 b. 1 in every 3 c. 3. a 1: 4 b. 1 in every 5 c.

2 3 1 5

1

d. d.

.2 1 4

Ratio and Probability 4 page 127 1 2=

1 out of 2 =

= 0·5

3. 1 out of 10 =

1 10

= 0.1

5. 10 out of 10 =

=10 10

= 1

=-

2. 5 out of 10 =

1 2

4. 4 out of 10 =

=-4 10

= 0·5 = 0· 4

=-

=-

Ratio and Probability 5 page 128 1. equal chance 2. certain 3. good chance 6. random 7. fifty-fifty chance

4. impossible 8. unlikely

5. biased

Ratio and Probability 6 page 129 1.

3 9 =-

=

1 3 =-

2.

4 20 =-

=

1 5 =-

236

Ratio and Probability 7 page 130 A die will roll a six

A die will roll an even number.

0

A die roll a number.

A die roll a zero.

0·5

impossible

1 certain

evens

A die roll a one or two.

A 6 will be picked.

0 0·1 impossible

A ten will be picked.

A die will roll a seven

A die will not roll a 4.

0·3

0·4 evens

A 2 or 3 will be picked.

An odd number will be picked

A number from 5 to 9 will be picked

0·2

A die will roll a number greater than three.

0·5

A 6,7, or 8 will be picked.

0·6

0·7

A 2 will not be picked.

0·8

0·9

1 certain

A number above 3 will be picked.

Handling Data 1 page 131 A. B.

1. 1 2. 22 1. 9-3=6 5. 455- 75= 380

3. 100 4. 4 2. 24-7=17 6. 77-22=55

5. 8 6. 5 3. 10-3=7 4. 55-24= 31 7. 207-202=5

Handling Data 2 page 132 A

1. 3,4,4,5,6,7,8 = 5 2. 1,2,5,6,7,8,9 =6 4. 2,6,8,11,12,14,15=11 5. 24, 35,67=35

3. 1,2,5,7,7,8,9 =7 6. 0,0,0,2,4,5,9 =2

B

1. 14 + 18 = 32 ÷ 2 = 16 2. 4+6=10 ÷ 2 = 5 3. 14 + 16 = 30 ÷2=15 4. 3+5=8÷2=4 5. 7+7=14÷2=7 6. 56+68= 124÷2=62

237

Handling Data 3 page 133 A.

B.

1. 36÷6=6 4. 60÷6=10 7. 14÷7=2 1. £4·50÷3=£1.50 4. £600÷3=£200

2. 30÷6=5 5. 35÷7=5

3. 28÷7=4 6. 198÷3=66

2. £1·00÷4=25p 5. £9·60÷3

3. £5·70÷3=£1·90 6. 60p÷4=15p

Handling Data 4 page 134 1. 32

2.

5

3. Only 1 Child scored 2

Data Handling 5 page 135 Type of Vehicle Lorry Bike Car Motor bike Bus 2.

Number of Vehicles 7 0 15 4 2

Car

3. 28

Handling Data 6 page 136 1. 13 cm

2. 28 minutes

3. 15 minutes

4. 3:05 pm

Handling Data 7 page 137 1. a. At Valley Junior school 50 pupils walk. b. At Star Primary school 90 pupils walk. 2. At Valley Junior school about one third of the pupils catch the bus this is around 66 pupils. At Star Primary school about a quarter of the pupils catch the bus this is around 90 pupils. So more children catch the bus to Star Primary School. Handling Data 8 page 138 1. 8 children

2. 12 children

3. 12 children

4. 4 children

Handling Data 9 page 139 a. 14

b. 32

c. 10

d. 30

e. 48

f. 22

g. 46

h. 26

d. 27

e. 7.5

f. 63

g. 9

h. 39


b. 6.5

c. 51

238


b. 5.5

c. 60

d. 76

e. 11.5

f. 100

g. 44

h. 12

Handling Data 12 page 142 1. 20 km

2. 25 km

3. 5 minutes

4.

20 km

5. 75 minutes

Handling Data 13 page 143 70 60 50 Distance from Jute in kilometres

40

× ×

30 20

×

×

×

10 0

1. 20 km

× 2. 30 km

10

20

3. 10km

30


60

×

70

4. 1km

Handling Data 14 check page 144 1. 5.

40 litres 2. 80 litres 3. 45 litres 4. 130 litres 9 gallons 6. 20 gallons 7. 31.5 gallons 8. 16 gallons Gallons 0 2 4 6 8 10

Litres(l) 0 9 18 27 36 45

Shape 1 page 145 1. AB and DC 2. Includes BC and DC or CF and EF or AB and BC or DC and AD or GE and EF 3. CF 4. AD or BC 5. 5 6. 24 7. 9

239

80

Shape 2 page 146 1. × 2. × 3 ×

4. √ 5. √ 6. × 7. √ 8. √

Shape 3 page 147 Four parallelograms such as the ones below.

Four rhombi such as the ones below.

240

Shape 4 page 148 Draw 4 different trapezia such as the ones below.

. 4 different kites such as the ones below.

241

Shape 5 page 149

square √

rectangle

parallelogram

traprzium √

kite √

rhombus √

242

Shape 6 page 150 1. b 2. c 6.

3. a

4. d

5.

Mirror line Shape 7 page 151 1.

Mirror line

243

2.

Mirror line Shape 8 page 152 A (-4,2)

B(1,2)

C(1,-1)

D(-4,-1)

5 4 B 3 A 2 1 -8

-7

-6

-5

-4

-3

-2

-1 0 1

1

2

3

4

5

6

7

-2 D

C -3 -4

244

8

Shape 9 page 153 Shape A has been translated 5 to the right, then 2 up. Shape C has been translated 7 places to the left, then 1 down. Shape 10 page 154 A square, rotated and translated C pentagon, rotated and translated E right-angle triangle, translated

B right-angle triangle, translated D right-angle triangle, rotated and translated F Hexagon, rotated

Shape 11 page 155 ( 0 , -3 )

( -3 ,0 )

( 0 , 3)

( 3, -2 )

( -2 , -3)

( -3 , 2)

Shape 12 page 156 1. 30º 2. 65º 3. 50º 6. 21º 54º 105º = 180º

4. 125º

5. 37 º 63 º

80 º = 180º

Shape 13 page 157

acute 27º 11º 89º

13.

right 90º

right angle

14.

obtuse 105º 145º 125º

straight 180º

obtuse

15.

3. 102º

4. 49º

acute

reflex 270º 310º 190º 256º 16.

obtuse

Shape 14 page 158 1. 270º

2. 136º

5. 138

6. 18º

Shape 15 page 159 1. A 36º 3. G 58 º

B 108 º H 45 º

C 36 º I 77 º

2. D 100º E 34 º F 46 º

Shape 16 page 160 1. 3. 6. 7.

2 × (7+5)cm 2×12cm=24cm 2. 2 × (16+4)cm 2×20cm=40cm 2 × (23+28)cm 2×51cm=102cm 4. 2 × (19+12)cm 2×31cm=62cm 6m-4m=2m, 3m-2m=1m 2×(2+1)m = 6m 5m-2·5m = 2·5m = 2×(2·5+2·5)m = 10m

245

Shape 17 page 161 A. 14cm²

B 17cm²

C 17cm²

D 147cm² E 252 cm² F 117 cm²

Shape 18 page 162 1. 190cm² 2. 600 cm²- 72cm²=528cm² 3. 135cm²-55cm²= 80cm² 4. 100cm- 12cm²-12cm²=76cm² Shape 19 page 163 1. 375cm²-60cm²= 315 cm² 2. 187cm²² – 35cm²=152 cm² 3. 300cm² -20cm² =280 cm² 4. 416cm²-120cm²=296 cm² Shape 20 page 164 A 6cm² B 18cm² ÷2= 9cm² E 40cm² ÷2=20 cm²

C 24cm² ÷2= 12 cm² D 28cm² ÷2=14 cm² F 120cm² ÷2= 60 cm²

Shape 21 page 165 A

27cm²

B 33cm²

Shape 22 page 166 1. 11 blocks

2200cm² 2. 15 blocks 3000 cm²

Time 1 page 167 1. a. 35 minutes

b. 1 hr 30 minutes

c. 17:45 2. a. The monsters b. 2hrs 15 min

Time 2 page 168 1. 1:45

2. 20:41

3. 8:08 (20:08)

Time 3 page 169 1. 2 hours

2. 1 hr 30 min

3. 20 hours

4. Saturday 5. 39 hrs 30 min

Time 4 page 170 1. No she will be home at 7.20 pm 2. 3 × 25min = 75 min + 30 min = 1 hour 45 minutes 3. a. 35 minutes b. 2.35 Time 5 page 171 1. Bangkok 2. Rio de Janeiro

3. Los Angeles

4. 15 hours

5. 7 hours

246

Measuring 1 page 172 1. 167m 2. 570m 3. 1289m 4. 7·823km 5. 5·834km 6. 5·6cm 7. 2·3cm 8. 160cm 9. 270cm 10. 0·0085km 11. 1950mm 12. 3380mm 13. 456mm 14. 0·00064km 15. 0·00894km Measuring 2 page 173 a. 5miles g. 24km

b. 10miles h. 5km

c. 12miles

d. 19miles

3. 273·6cm

4. 30

e. 27km

f. 38km

Measuring 3 page 174 1. 0·32m 7. 2·3m

2. 42·1km

5. 50cm

6 2·7m

Measuring 4 page 175 A. 7 kg 345g = 6345g B. 4kg 869g = 4869g C. 6kg 88g= 6088g D. 5 kg 613g = 5613g A. 6g B. 60g C. 6000g D. 600g A 7·3 kg B. 4·9 kg C. 6·1 kg E. 5·5kg The difference between A and C = 1·258kg The difference between B and D = 0·744kg Measuring 5 page 176 a. 200g g. 19oz

b. 450g h. 11oz

c. 280g

d. 110g

e. 4oz

f. 5oz

Measuring 6 page 177 1. 2. 3. 4.

700g × 30 = 21000g = 21kg. 21÷5 = 4·2 Answer 5 journeys. 5000 ÷ 120 = 41.66 Answer she can carry 41 paperbacks. 11 × 230g = 2·53kg 10 × 190g = 1.90kg 17 × 350g = 5·95kg Total = 10·38kg Hardbacks 10.38kg + paperbacks 5·04kg + encyclopaedias 21kg = 36·42 kg 36·42 – 30 kg = 6·42 Answer 2 journeys left.

Measuring 7 page 178 1. 2m × 2m × 2m = 8m³=8 tonnes 2. 6m × 2m × 2m = 24m³=24tonnes 3. 10m × 5m × 1m = 50m³=50tonnes 4. 4m × 2m × 1m = 8m³ × 1000 = 8000 kg³ 5. 6m × 8m ×2m = 96m³ × 1000 = 96000 kg³ Money 1 page 179 1.

24050 rupees

2. 15020 yen

3. 357euro

4. 382·5 franc 5. $621

247

Money 2 page 180 1. 5.

580 euro 1400krone

2. $ 875 6. $474

3. 5414 ringitt

4. 10129 peso

Money 3 page 181 Country

Australia Denmark India Japan South Africa Thailand

Exchange rate May 1·69 12·67 50·34 157·78 10·36 54·01

Exchange rate July 1·79 12·9 51·26 157·77 11·02 53·78

or

0·10 0·23 0·92 0·01 0·66 0·23

Difference between changing £100 in May or July $10 23 krone 92 ruppees 1 yen 66 rand 23 baht

Best time to travel May May May July May July

Money 4 page 182 1. 4. 7.

45 ÷ 14 = £3.00 93 ÷ 3 = £31 100 ÷ 14 = £7

2. 5. 8.

144 ÷ 7 = £21 152 ÷ 12 = £13 122 ÷ 3 = £41

3. 6.

132 ÷ 13 = £10 14 ÷ 3 = £5

Money 5 page 183 1. £391

2. £378

3. £40

5. £133

3. a. £261

b. 125 hours

6. £18·50

Money 6 page 184 1. £5·25

2. 44coins

248

Number Problems 1 page 185 1.

factors of 18 1

multiples of 3

2

2.

6 3 9 18

square numbers 4

16

3.

25 9 49

36

1

12 11

5

7

multiples of 2 3 5 7 11 13 15 17 19 21 23 27 29

2 6 8 10 12 14 18 20

16

25

12 15 odd numbers

square numbers 9

4 5 7 8 11 13 14 16 17 19 20

4 22 24 26 28 30

Number Problems 2 page 186

1.

23

28

21

17

89

71

22

24

26

113

59

5

27

20

25

47

2.

29

101

Total =

72

Total =

Total =

3.

177

4.

36

16

3

32

4

4

1

12

144

1

8

64

4

16

16

2

Total =

48

Total =

9

1728

Total =

512

249

5.

6.

28

49

2

2

9

12

1

14

196

36

6

1

98

4

7

3

4

18

Total =

216

2744

Total =

Number Problems 3 page 187 1.

2. 92610

735 35 5

24000 126

21 7

300 6

3

30 2

6

3.

10 5

300 10

2

4

236196

720 30

5

486 24

6

486

18 4

6

5.

27 3

18 9

2

6. 1728000

960 24 3

8

4. 216000

2

80

1800 40

8

204120 756

45 5

42 9

7

270 18

6

15 3

5

Number Problems 4 page 188 1. 8 2. 15 3. 2 9. ÷ + × 10. × - +

4. 5 11. ÷ + ×

5. 11 12. ( + ) ×

6. 2 13. × - ×

7. 17 8. 99 14. ÷ × -

250

Number Problems 5 page 189 1. a. 4 boxes

b.

768

2. a. £22·01

b. £4·90

c. £67·95

Number Problems 6 page 190 1. a. 940 marbles 2. a. 160 cakes

b. 20 boxes b. 100 packs

c. 94000 c. £17·40

Number Problems 7 page 191 1. a. 28 2. a. 17p

b. £15·40 b. £20·40

c. 84 bottles c. 68p

Number Problems 8 page 192 1. a. b. c. 2. a.

£300·75 - £48·45 = £252 ÷ 36 = 7 hours. £1260 ÷ 36 = 35 hours. 21 × £36 = £756 + £246 = £1002 300 balls b. 1% = 12 12 × 42 = 504 balls

Number Problems 9 page 193 1. a. 28p b. 18p c. £11·20 2. a. £5- £3·20 = £1·80 ÷ 4 = 45p b. £4·50

c. £2·70 ÷,45 = 6 pears

Number Problems 10 page 194 1. 870 ÷145 = 6 visits

2. a. Sofia

b. 4 seconds

Number Problems 11 page 195 1. 45

2. 36

3. 56

4. 49

Number Problems 12 page 196 1. a. 5 7 11 23 13

b. 7 + 13 = 20

2. a. 4 9 16 25

b. 16-9=7

Number Problems 13 page 197 1. a. 64 2 4 1 16 8 32 b. 16 × 4 = 64 2. a. 1 2 4 5 6 8 9 10 12 15 18 30 36 40 45 60 72 90 120 180 360 b. 180-72=108 Number Problems 14 page 198 1. a. -7ºc

b. 3ºc

2. a. -3ºc b. 8ºc

251

Number Problems 15 page 199 1. a=4 2. b=1 3. c=5 4. d=7 5. e=15 6. g=2 7. h=6 8. i = 2 j=3 or i = 4 j = 6 or i = 6 j = 9 9. k= 32 10. l=9 11. m=8 12. n =14 13. o= 6 14. p=17 Number Problems 16 page 200 1. a = 3 2. b = 2 3. c = 4 4. d = 7 5. e = 5 6. f = 3 7. g = 6 9. j = 1 k = 3 or j = 2 k = 1 10. m = 2 n = 1 or m = 4 n = 7 11. p = 1 r = 5 12. s = 4 t = 6

8. h =9

Number Problems 17 page 201 1. False

2. True

3. True

4. False

5. True

6. True

7. False

Number Problems 18 page 202 1. ÷ 2. ˂ 3. × 4. - 5. ÷ 11. × 12. ÷ 13. - 14. ×

6. =

7. ÷

8. +

9. ˃

10. +

252

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