Page 78 - ICSE Math 5

Reducing a Fraction to Its Lowest Terms

A fraction is said to be in its lowest terms (simplest form), when the only common factor of the
1 1 2 2
numerator and the denominator is 1. For example, fractions such as , ,
and are all in their
2 3 3 5
lowest terms since the only common factor of the numerators and denominators of the given

fractions is 1.

We can reduce a fraction to its lowest terms by following two methods. These methods are H.C.F.
method and prime factorization method.
H.C.F. Method

• Find the factors of the numerator and the denominator, and then identify the common
factors.

• Find the H.C.F. of the numerator and denominator of the given fraction.

• Divide the numerator and the denominator of the fraction by their H.C.F. to get the lowest terms.
Prime Factorization Method

• Find the prime factors of the numerator and the denominator, and then identify the
common prime factors.

• Multiply the common prime factors.
• Divide the numerator and the denominator of the fraction by the product of the common
prime factors to get the lowest terms.

15
Example 5: Reduce to its lowest terms, using H.C.F. method and prime factorization method.
25
Solution: H.C.F. Method

Step 1: Find the factors of 15 and 25 by listing method and identify the common
factors.

Factors of 15 are 1, 3, 5 and 15.
Factors of 25 are 1, 5 and 25.

Common factors of 15 and 25 are 1 and 5.

Step 2: Find the H.C.F. of 15 and 25.
H.C.F. of 15 and 25 is 5.

Step 3: Divide the numerator and the denominator of the given fraction by their
H.C.F., i.e., 5.

15 ÷ 5 = 3
25 ÷ 5 5
15 3
So, the lowest terms of is .
25 5

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