Page 205 - Ganit Kaushal

7.5 COMPARISON OF FRACTIONS

Comparing Like Fractions

To compare two like fractions, it is enough to compare their numerators. If there are two like fractions, then
the fraction with the greater numerator is greater.
5 3
For example: > as 5 > 3
7 7
It can be interpreted from the following figure that, out of 7 equal parts, 5
the portion corresponding to 5 shaded parts is greater than the portion 7
corresponding to 3 shaded parts. 3
7 11 8 9 6 13 7
Similarly, < , < , < .
12 12 13 13 17 17

Comparing Unlike Fractions

Comparison of unlike fractions is further divided into two cases:
(a) Unlike fractions with the same numerator 5

If two unlike fractions with the same numerator are given, the 7
fraction with the smaller denominator is greater than the fraction (i)
with the greater denominator. 5
5 5 8
For example: > as 7 < 8 (ii)
7 8
The shaded part of figure (i) is greater than the shaded part of figure (ii).
5 5
So, > .
7 8
(b) Algorithm to compare unlike fractions with distinct numerators
Step 1: Find the Least Common Multiple (LCM) of the denominators. (Though any common
multiple will work.)
Step 2: Convert each fraction to an equivalent fraction with a denominator equal to the LCM
obtained. This can be done by multiplying both the numerator and denominator by some suitable
number. They are all like fractions now.
Step 3: Compare the resulting ‘like fractions’. The fraction with the greater numerator is greater.
3 7
Ex. Compare and .
5 15
Sol. We know that LCM (5, 15) = 15.

Now, we convert the given fractions to equivalent fractions with a denominator of 15 as given below.
×
3 = 33 = 9 and 7 = 71 = 7
×
×
5 53 15 15 15 1 15
×
3 7
We conclude that, > as 9 > 7 (numerators after making the fractions ‘like’).
5 15
Ordering of Fractions
After comparing fractions, we can arrange them in ascending or descending order based on their size.

Fractions 203