Page 29 - ICSE Math 7

Prime factorization method
In this method, write both the numerator and denominator as the product of prime factors and then
cancel the common factors to get the fraction in its simplest form.

HCF method

In this method, find the HCF of the numerator and denominator and then divide each term of the
fraction by this HCF to get the fraction in its simplest form.
280
Example 5: Reduce the fraction to its simplest form by,
952
(a) Prime factorization method (b) HCF method

Solution: (a) 280 = 2 × 2 × 2 ×5× 7 = 5
952 2 × 2 × 2 × 7 ×17 17 3

(b) The HCF of 280 and 952 is 56. 280 952
280 –840 2
Divide the numerator and denominator of 952 112 280
by 56, to get: –224 2

280 = 280 ÷ 56 = 5 56 112
952 952 ÷ 56 17 –112
×
Like and unlike fractions

Fractions having the same denominator are known as like fractions and fractions with different
1 3
11 11
5
,
denominators are known as unlike fractions. For example, , and are like fractions and 13 15
7 7
7
and 14 are unlike fractions.
17
Conversion of unlike fractions into like fractions
Follow the steps given below to convert unlike fractions into like fractions.

Step 1: Find the LCM of the denominators of the given fractions.
Step 2: Divide the LCM by the denominator of the first fraction. Multiply both the numerator and
the denominator of the first fraction by the quotient obtained.
Step 3: Repeat step 2 for all the given fractions.

3 4
Example 6: Reduce , and 7 to like fractions.
4 5 10
Solution: LCM of 4, 5 and 10 is 20.

3 3 × 5 15
Now, = = ( 20 ÷ 4 = 5)
4 4 × 5 20
4
= 4 × 4 = 16 ( 20 ÷ 5 = 4)
5 5 × 4 20
7 = 7 × 2 = 14 ( 20 ÷ 10 = 2)
10 10 × 2 20

Hence, the required like fractions are 15 16 and 14 .
,
20 20 20

15