Page 107 - Maths Class 06

4
EX AM PLE 5. Find an equiv a lent frac tion with nu mer a tor 12.
17

SO LU TION : The given ques tion im plies
4 12
=
17 ?
You know that 4 × 3 = 12. So, you need to multiply both the denominator and the
numerator with 3 to get the required equivalent fraction.
4 4 3´ 12
= =
17 17 3´ 51

Test for Equivalent Fractions
How would you find out whether the two given fractions are equivalent ? Let us learn to test the two
fractions for equivalence.
p r
In case of equivalent fractions and , you know that
q s
p r
=
q s

If you cross-multiply these equivalent fractions, you get ps = rq.

Product of numerator of the first fraction and the denominator of the second frac tion = Product of
nu mer a tor of the sec ond frac tion and the de nom i na tor of the first frac tion. So, now you can eas ily find
out whether the two given frac tions are equiv a lent.

EX AM PLE 6. Are the fol low ing frac tions equiv a lent?
2 3 3 5
(a) and (b) and
10 15 5 12
2 3
SOLUTION : (a) Cross prod ucts are 2 15 30´ = and 3 10 30´ = .
10 15
Since these are equal, then the fractions are equivalent.
3 5
(b) Cross products are 3 12´ = 36 and 5 5 25´ = .
5 12
Since these products are not equal, then the fractions are not equivalent.

Exercise 7.2

1. Draw number lines and locate following fractions on them:
1 7 3 5 2 0
, , , 2 , ,
5 2 8 7 3 5
2. Express the following as mixed fractions:
19 23 43 64
(a) (b) (c) (d)
3 4 8 5

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