Year 9: Simplify fractions

Simplifying fractions means reducing them to their lowest form. This means the numerator (top number) and denominator (bottom number) share no common factors other than 1.

What is a Common Factor?

A common factor is a number that divides evenly into both the numerator and the denominator. For example, 2 and 4 are common factors of 6/8 because both numbers are divisible by 2.

Steps to Simplify a Fraction

1. Find the Greatest Common Factor (GCF): This is the largest number that divides evenly into both the numerator and the denominator. You can use prime factorization or listing factors to find the GCF.
2. Divide Both Numerator and Denominator by the GCF: Divide both the top and bottom of the fraction by the GCF.
3. Simplify: The resulting fraction is the simplified form.

Example

Simplify 12/18

1. Find the GCF of 12 and 18: The factors of 12 are 1, 2, 3, 4, 6, and 12. The factors of 18 are 1, 2, 3, 6, 9, and 18. The GCF is 6.
2. Divide by 6: 12 / 6 = 2 and 18 / 6 = 3
3. Simplified Fraction: 2/3

Tip: Always check if you can divide the numerator and denominator by the same number before simplifying.