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The Simplest Form of a Fraction

Example:

Find the simplest form of 30/45.

Solution:

A fraction is in simplest form when its numerator and denominator have no common factors other than 1.

30 = 1 × 30, 2 × 15, 3 × 10, 5 × 6

Therefore, factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30.

45= 1 × 45, 3 × 15, 5 × 9

Therefore, factor of 45 are 1, 3, 5, 9, 15, 45.

The common factors of 30 and 45 are 1, 3, 5, 15.

The greatest common factor (GCF) of 30 and 45 is 15.

Note:

When the numerator and denominator of a fraction divide by the greatest common factor (GCF), the fraction is the simplest form.