Page 78 - Revised Maths Wisdom Class - 6

76 MATHS

3 4
By cross multiplication
7 9 Remember!er!
Rememb
3 × 9 = 27 and 4 × 7 = 28
› Cross-multiplication is used to compare only two fractions at a time.
Since, 27 < 28 › If two fractions have the same denominator, then larger the numerator,
larger the fraction.
3 4
Thus, < › If two fractions have the same numerator, then larger the denominator,
7 9 smaller the fraction.

(b) Method of converting the given fractions into like fractions
Here, we can convert each fraction into like fractions and then compare.
We follow these steps to convert the unlike fractions into like fractions:

Step 1: Find the LCM of the denominators of the fractions to be compared.
Step 2: Convert unlike fractions into like fractions with denominator as LCM obtained in step 1.

Step 3: Compare the numerators. The fraction with the greater numerator has greater value.
This method can be used for comparing or ordering more than two fractions. For example, compare

2 4 3 .
, and
3 5 5

LCM of 3, 5 and 5 is 15

25× 10 43× 12 33× 9 12 10 9 4 2 3
⇒ = ; = and = Hence, > > or > >
35× 15 53× 15 53× 15 15 15 15 5 3 5

ILLUSTRATIONS

Example 1: Compare the fractions:

4 1 8 13
(a) and (b) and
9 2 13 21
4 1 8 13
Solution: (a) Given fractions are and (b) Given fractions are and
9 2 13 21
By cross multiplication, we get By cross multiplication, we get

4 × 2 = 8 and 9 × 1 = 9 8 × 21 = 168 and 13 × 13 = 169
Since, 8 < 9 Since, 168 < 169
4 1 8 13
⇒ < ⇒ <
9 2 13 21

Example 2: Arrange the following fractions in ascending order:
7 7 3 1 , 2
,
,
5 16 7 3
7 7 3 5
Solution: Given fractions are , , and
5 16 7 3

LCM of 5, 16, 7 and 3 is 1680