Fractions Solutions

Equivalent Fractions

 1. All answers are given by multiplying the numerator and denominator by 2 and 3 respectively. You may have different answers which are also correct.

a) 4/6 , 6/9 b) 6/14 , 9/21 c) 6/8 , 9/12
d) 4/18, 6/27
e)26/14 = 112/14, 39/21 = 118/21

2.
a) 2/13 (÷ n and d by 3) b) 4/5 (÷ n and d by 3) c) 7/9 (÷ n and d by 4)
d) 4/7 (÷ n and d by 4) e) 7/11 (÷ n and d by 3)

3.
a) 3/4 b) 10/14
=5/7 		c) 19/18
= 1 1/18 		d) 27/34 e) 27/20
= 1 7/20

4.
a)9 b) 4 c) 15 d) 5/14
e)15/42= 5/14 f) 3/48 = 1/16 g) 10/36= 3/4 h) 42
i) 25/8 = 3 1/8 j)63/35= 9/5
= 14/5

5.
a) 4, 41/2, 51/3, 61/4, 71/5, 81/6, 91/7, 101/8, 111/9, 121/10

b) 4, 41/2, 51/3, 61/4, 71/5, 81/6, 91/7, 101/8, 111/9, 121/10

c) You could show that n× n/(n-1) is the same as n + n/(n-1).

  • On the left hand side n× n/(n-1) = n2/(n-1)
  • = n(n-1)/(n-1) + n/(n-1)
  • = n + n/(n-1)
  • = n + (n-1)/(n-1) + 1/(n-1)
  • = (n + 1) + 1/(n-1)

  • On the right hand side we start with n + n/(n-1) which is what we have on the 2nd line on the left hand side so the result (n + 1) + 1/(n-1) follows.
6.
a) 1/2, 11/3, 21/4, 31/5, 41/6, 51/7, 61/8, 71/9, 81/10, 91/11,

b) The results are the same as for question a).
c) You can use a similar method as question 5c) to show that n× n/(n+1) is the same as n - n/(n+1).
  • lhs we have n× n/(n+1)
  • n2 n/(n+1)
  • n × (n+1)/(n+1) - n/(n+1)
  • n - n/(n+1)
  • n - (n+1)/(n+1) + 1/(n+1)
  • (n - 1) + 1/(n+1)

  • The right hand side follows the same steps starting with the 2nd line of the left hand side.

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