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Comparison of Fractions

In like fractions, the fraction with the larger numerator is greater.
23 12
For example, > as the numerator 23 of the first fraction is greater than the numerator of
25 25
the other fraction, which is 12. That is 23 > 12.
In unlike fractions, first, we change the fractions into We convert a group of unlike
like fractions or their respective equivalent fractions fractions to like fractions, or to
with the same denominator by finding the LCM of the Note: equivalent fractions having a
denominators of the given fractions and compare them denominator equal by taking he
LCM of the denominators of the
as like fractions. given fractions.
2 4
For example: Let us compare and .
7 5
First, we find the LCM of the denominators 7 and 5, which is 35.
2 2 × 5 10 4 4 × 7 28
Now, = = and = =
7 7 × 5 35 5 5 × 7 35
10 28
Q 10 < 28. Therefore, 35 < 35
2 4
Thus, <
7 5

Enrichment

We have another way to compare the unlike fractions.
a
Let and c be two unlike fractions, by cross-multiplication of both fractions.
b d a c

b d
a c a c
(i) If ad > bc, then > (ii) If ad < bc, then <
b d b d
(iii) If ad = cd, then a = c (we can say these are equivalent fractions)
b d

Ordering of Fractions

In a class, Varun, Dinesh, Maya and Sonam are friends, they are walking on a track. They decided
to check their strength by covering their walking distance in 10 minutes.
3 5 2 1
Varun covers , Dinesh covers , Maya covers and Sonam covers of the walking track in
10 8 5 3
10 minutes. Who covers the maximum part of the track?

Arrange the following fractions in ascending order. Let us find the LCM of the denominators
10, 8, 5 and 3 is 120. Write the fractions into like fractions with denominator 120.
×
×
3 = 312 = 36 ; 5 = 515 = 75
As, 10 10 12 120 8 815 120
×
×
×
×
2 = 224 = 48 ; 1 = 1 140 = 40
×
×
5 524 120 3 340 120
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