uem sol to exerc chap 002

© 2014, John Bird

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CHAPTER 2 FRACTIONS EXERCISE 5 3

1. Change the improper fraction 157

into a mixed number.

The improper fraction 157

= 2 17

as a mixed number

2. Change the improper fraction 375

into a mixed number.

The improper fraction 375

= 7 25

as a mixed number

3. Change the mixed number 2 49

into an improper fraction.

The mixed number 2 49

= 2 9 49

× + = 229

as an improper fraction

4. Change the mixed number 8 78

into an improper fraction.

The mixed number 8 78

= 8 8 78

× + = 718

as an improper fraction

5. A box contains 165 paper clips. 60 clips are removed from the box. Express this as a fraction in its simplest form.

Fraction of paper clips removed = 60 12165 33

= = 411

in its simplest form

6. Order the following fractions from the smallest to the largest:

49

, 58

, 37

, 12

, 35

© 2014, John Bird

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49

= 0.4444... 58

= 0.625 37

= 0.42857.... 12

= 0.500 35

= 0.6000

Hence, the order from smallest to largest is: 37

, 49

, 12

, 35

, 58

7. A training college has 375 students of which 120 are girls. Express this as a fraction in its simplest form.

Fraction of girls in the college = 120 24375 75

= = 825

in its simplest form

8. Evaluate in fraction form 1 23 5+

1 2 5 63 5 15

++ = = 11

15

9. Evaluate in fraction form 5 46 15−

5 4 25 86 15 30

−− =

= 17

30


1 2 5 42 5 10

++ = = 9

10

11. Evaluate in fraction form 7 116 4

−

7 1 7 4

16 4 16−

− = = 3

16

© 2014, John Bird

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2 3 (11 2) (7 3) 22 217 11 77 77

× + × ++ = = =

4377

13. Evaluate in fraction form 2 1 29 7 3− +

( ) ( ) ( )7 2 9 1 21 22 1 2 14 9 42

9 7 3 63 63× − × + × − +

− + = = = 4763

14. Evaluate in fraction form 2 13 25 3−

3 25

– 2 13

= 2 13 25 3

+ − +

= 3 + 25

– 2 – 13

= 1 + 25

– 13

= 1 + 3 2 5 115

× − × = 1 + 6 515− = 1 + 1

15

= 1 115

15. Evaluate in fraction form 7 2 527 3 9

− +

( ) ( ) ( )7 1 2 9 5 37 2 5 7 18 15

27 3 9 27 27× − × + × − +

− + = = = 4

27

16. Evaluate in fraction form 5 3 3313 4

+

5 3 3313 4

+ = 3 35 3

13 4 + + +

= 5 + 313

+ 3 + 34

= 8 + 313

+ 34

= 8 + 4 3 13 352

× + × = 8 + 12 3952+ = 8 + 51

52

= 8 5152

© 2014, John Bird

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4 5 238 5− = 5 24 3

8 5 + − +

= 4 + 58

– 3 – 25

= 1 + 58

– 25

= 1 + 5 5 8 240

× − × = 1 + 25 1640− = 1 + 9

40

= 1 940


( ) ( ) ( ) ( )7 10 3 3 8 2 3 73 7 263 2 73 26 219 182 3710 8

7 3 7 3 7 3 21 21 21× + × + × − × −

− = − = − = = = =

16121

19. Evaluate in fraction form 3 1 4 54 14 5 6− +

( )1 4 5 1 4 5 1 4 5 15 48 503 4 1 3 4 1 3 4 14 5 6 4 5 6 4 5 6 60

− + − + = + − + + + = − + + − + =

= 1760

20. Evaluate in fraction form 3 2 15 1 34 5 2− −

( )3 2 1 3 2 1 3 2 1 15 8 10 35 1 3 5 1 3 5 1 3 1 14 5 2 4 5 2 4 5 2 20 20

− − − − = + − + − + = − − + − − = + = −

= 1720

© 2014, John Bird

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EXERCISE 6 Page 15

1. Evaluate 2 45 7×

2 4 2 45 7 5 7

×× =

× = 8

35

2. Evaluate 5 49

×

5 49

× = 5 41 9× = 5 4

1 9××

= 209

= 229


3 84 11× = 3 2

1 11× by cancelling

= 611


3 54 9× = 1 5

4 3× by cancelling

= 512

5. Evaluate 17 1535 68

×

17 1535 68

× = 1 37 4× by cancelling

= 328

© 2014, John Bird

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6. Evaluate 3 7 215 9 7× ×

3 7 2 3 7 915 9 7 5 9 7× × = × × = 3

5 by cancelling

7. Evaluate 13 7 44 317 11 39

× ×

13 7 4 13 51 121 1 3 114 317 11 39 17 11 39 1 1 3

× × = × × = × × = 11 by cancelling

8. Evaluate 1 3 514 11 39× ×

1 3 5 1 3 44 1 1 11 1 1 114 11 39 4 11 39 1 11 13 1 1 13× × = × × = × × = × ×

= 1

13 by cancelling

9. Evaluate 2 49 27÷

2 49 27÷ = 2 27

9 4× = 1 3

1 2× by cancelling

= 1 31 2××

= 32

= 112

10. Evaluate 3 458 64÷

3 45 3 64 1 88 64 8 45 1 15÷ = × = × = 8

15 by cancelling

11. Evaluate 3 58 32÷

3 5 3 32 3 4 128 32 8 5 1 5 5÷ = × = × = = 22

5 by cancelling

© 2014, John Bird

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12. Evaluate 3 414 5÷

3 4 3 9 3 5 1 514 5 4 5 4 9 4 3÷ = ÷ = × = × = 5

12 by cancelling

13. Evaluate 1 22 14 3×

1 2 9 5 3 5 152 14 3 4 3 4 1 4× = × = × = = 33

4 by cancelling

14. Evaluate 1 1 523 9÷

1 1 5 4 23 4 9 4 323 9 3 9 3 23 1 23÷ = ÷ = × = × = 12

23 by cancelling

15. Evaluate 4 725 10÷

4 7 14 7 14 10 2 2 425 10 5 10 5 7 1 1 1÷ = ÷ = × = × =

= 4 by cancelling

16. Evaluate 3 22 34 3÷

3 2 11 11 11 3 11 32 34 3 4 3 4 11 4 11

×÷ = ÷ = × =

× = 3

4 by cancelling

17. Evaluate 1 3 119 4 3× ×

1 3 1 1 3 4 1 1 119 4 3 9 4 3 9 1 1× × = × × = × × = 1

9 by cancelling

© 2014, John Bird

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18. Evaluate 1 3 23 14 5 5× ÷

1 3 2 13 8 5 13 2 1 13 1 13 14 5 5 4 5 2 1 1 2 1 1 1× ÷ = × × = × × = × ×

= 13 by cancelling

19. A ship’s crew numbers 105, of which 17

are women. Of the men, 16

are officers. How many

male officers are on board?

Number of women in crew = 17

× 105 = 15

Hence, number of men in crew = 105 – 15 = 90

Number of male officers = 16

× 90 = 15

20. If a storage tank is holding 450 litres when it is three-quarters full, how much will it contain

when it is two-thirds full?

If 450 litres is 34

full, then 14

full would be 450 ÷ 3 = 150 litres

Thus, a full tank would have 4 × 150 = 600 litres 23

of the tank will contain 2 6003× = 400 litres

21. Three people, P, Q and R, contribute to a fund. P provides 35

of the total, Q provides 23

of the

remainder and R provides £8. Determine (a) the total of the fund, (b) the contributions of P and

Q.

(a) If P provides 35

of the total, and Q provides 23

of the remainder, then R provides 13

of the

remainder, i.e. 1 3 1 2 2of 13 5 3 5 15

− = × =

of the total.

© 2014, John Bird

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Thus, if 215

is £8 then 115

is £4 and the total fund is 15 × £4 = £60

(b) The contribution of P = 3 605× = £36

The contribution of Q = 2 2(60 36) 243 3× − = × = £16

22. A tank contains 24 000 litres of oil. Initially, 710

of the contents are removed, then 35

of the

remainder is removed. How much oil is left in the tank?

If 710

of the contents are removed then 310

of 24 000 litres remains

3 3 24 000 3 240024 00010 10 1 1 1

× = × = × = 7200 litres

If 35

of the remainder is removed then 25

of 7200 litres is left in the tank

2 2 7200 2 144072005 5 1 1 1× = × = × = 2880 litres

i.e. oil left in the tank = 2880 litres

© 2014, John Bird

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EXERCISE 7 Page 17

1. Evaluate 1 3 2022 5 27− ×

1 3 20 5 1 4 5 4 45 8 3722 5 27 2 1 9 2 9 18 18

−− × = − × = − = =

= 12

18

2. Evaluate 1 3 163 4 27− ×

1 3 16 1 1 4 1 4 3 43 4 27 3 1 9 3 9 9

−− × = − × = − =

= 1

9−

3. Evaluate 1 3 9 12 5 15 3+ ÷ −

1 3 9 1 1 3 15 1 1 1 1 3 6 2 72 5 15 3 2 5 9 3 2 1 3 6 6

+ − + ÷ − = + × − = + − = =

= 116

4. Evaluate 1 2 5 125 3 9 4+ ÷ −

1 2 5 1 1 8 9 1 1 8 3 1 1 24 1 4 96 5 95 1925 3 9 4 5 3 5 4 5 1 5 4 5 5 4 20 20 4

+ −+ ÷ − = + × − = + × − = + − = = =

= 34

4

5. Evaluate 4 1 1 2 25 2 6 5 3× − ÷ +

4 1 1 2 2 2 1 1 5 2 2 5 2 24 25 40 395 2 6 5 3 5 1 6 2 3 5 12 3 60 60

− +× − ÷ + = × − × + = − + = =

= 13

20 by cancelling

6. Evaluate 3 2 1 5 35 3 2 6 2

− − ÷ ×

3 2 1 5 3 3 4 3 5 1 3 1 4 3 1 2 3 2 9 25 3 2 6 2 5 6 2 2 5 6 5 5 3 5 5 15 15

− − − − ÷ × = − ÷ × = − × = − × = − =

= 715

© 2014, John Bird

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7. Evaluate 1 2 7 1 2 2of 4 3 32 5 10 3 3 5

− + ÷ −

1 2 7 1 2 2 1 22 37 10 2 2of 4 3 32 5 10 3 3 5 2 5 10 3 3 5

− + ÷ − = × − + ÷ −

1 44 37 10 3 2 1 7 5 1 22 10 3 2 5 2 10 1 1 5

− = × + × − = × + × −

7 5 2 7 100 8 9920 1 5 20 20

+ −= + − = =

= 194

20

8. Evaluate

2 2 16 13 5 3

3 16 14 2

× −

÷

2 2 1 20 7 1 4 7 1 28 1 276 1 27 2 3 2 1 23 5 3 3 5 3 3 1 3 3 3 33 1 27 3 27 2 9 1 9 3 9 3 1 1 16 14 2 4 2 4 3 2 1 2

× − × − × − −= = = = = × = × = × =

÷ ÷ × ×2

9. Evaluate 1 1 21 23 5 5× ÷

1 1 2 4 11 5 2 11 1 221 23 5 5 3 5 2 3 1 1 3× ÷ = × × = × × =

= 17

3

10. Evaluate 1 2 1 2 44 5 5 3 15× − ÷ +

1 2 1 2 4 1 1 1 3 4 1 3 4 3 9 8 24 5 5 3 15 2 5 5 2 15 10 10 15 30 30

− +× − ÷ + = × − × + = − + = =

= 1

15

11. Evaluate

2 1 1 13 2 13 5 2 3

1 18 33 3

+ × +

÷

© 2014, John Bird

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2 1 1 1 2 16 5 4 2 8 1 4 2 8 4 2 24 4 303 2 1 30 2 6 23 5 2 3 3 5 2 3 3 1 1 3 3 1 3 3 31 1 25 10 25 3 5 1 5 5 3 5 3 18 33 3 3 3 3 10 1 2 2 2

+ ++ × + + × + + × + + +

= = = = = = × = ×÷ ÷ × ×

2 21 1

= ×

= 4

12. Evaluate 1 9 3 1 2 3of 2 1 213 10 5 3 3 4

− + ÷ −

1 9 3 1 2 3of 2 1 2

13 10 5 3 3 4 − + ÷ −

= 1 29 8 7 3 3 1 29 16 7 313 10 5 3 2 4 13 10 2 4

− × − + × − = × + −

= 1 13 7 3 1 7 3 2 70 15

13 10 2 4 10 2 4 20+ −

× + − = + − =

= 5720

= 17220

uem sol to exerc chap 002

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