# Solutions to Questions on How to Reduce Fractions in Maths

Detailed solutions and explanations to the questions on how to reduce fractions are presented.

 A Reduce Fractions Calculator may be used to check your answers. Detailed Solutions to questions below Reduce the fractions a) 24 / 36 b) 52 / 120 c) 156 / 208 d) 122 / 6100 Solution a) We start by the prime factorization of the numerator 24 and denominator 36 as follows: 24 = 2 × 2 × 2 × 3 36 = 2 × 2 × 3 × 3 Rewrite the given fraction using the prime factorization of the numerator and denominator found above: $\dfrac{24}{36} = \dfrac{2 × 2 × 2 × 3}{2 × 2 × 3 × 3}$ Simplify $\dfrac{24}{36} = \dfrac{\cancel{2 × 2} × 2 × \cancel{3}}{\cancel{2 × 2} × \cancel{3} × 3} = \dfrac{2}{3}$ b) The prime factorization of the numerator 52 and denominator 120 is as follows: 52 = 2 × 2 × 13 120 = 2 × 2 × 2 × 3 × 5 Rewrite the given fraction using the prime factorization of 52 and 120: $\dfrac{52}{120} = \dfrac{2 × 2 × 13}{2 × 2 × 2 × 3 × 5}$ Simplify $\dfrac{52}{120} = \dfrac{\cancel{2 × 2} × 13}{\cancel{2 × 2} × 2 × 3 × 5} = \dfrac{13}{30}$ c) We start with the prime factorization of the numerator 156 and denominator 208: 156 = 2 × 2 × 3 × 13 208 = 2 × 2 × 2 × 2 × 13 Use the prime factorization of 156 and 208: $\dfrac{156}{208} = \dfrac{2 × 2 × 3 × 13 }{2 × 2 × 2 × 2 × 13}$ Simplify $\dfrac{156}{208} = \dfrac{\cancel{2 × 2} × 3 × \cancel{13}}{\cancel{2 × 2} × 2 × 2 × \cancel{13}} = \dfrac{3}{4}$ d) We start with the prime factorization of the numerator 122 and denominator 6100 as follows: 122 = 2 × 61 6100 = 2 × 2 × 5 × 5 × 61 Rewrite the given fraction using the prime factorization of 122 and 6100: $\dfrac{122}{6100} = \dfrac{2 × 61}{2 × 2 × 5 × 5 × 61 }$ Simplify $\dfrac{122}{6100} = \dfrac{\cancel{2} ×\cancel{61}}{\cancel{2} × 2 × 5 × 5 × \cancel{61}} = \dfrac{1}{50}$ Reduce and compare each pair of fractions. a) 26 / 39 and 14 / 42 b) 45 / 75 and 52 / 65 Solution a) We start by the prime factorization and simplification of the pair of fractions: $\dfrac{26}{39} = \dfrac{2 × 13}{3 × 13} = \dfrac{2}{3}$ $\dfrac{14}{42} = \dfrac{2 × 7}{2 × 3 × 7} = \dfrac{1}{3}$ Comparing the reduced fractions 2/3 is greater than 1/3 and therefore the fraction 26 / 39 is greater than 14 / 42. b) The prime factorization and simplification of the pair of fractions gives: $\dfrac{45}{75} = \dfrac{3 × 3 × 5}{3 × 5 × 5} = \dfrac{3}{5}$ $\dfrac{52}{65} = \dfrac{2 × 2 × 13}{5 × 13} = \dfrac{4}{5}$ Comparing the reduced fractions 4/5 is greater than 3/5 and therefore the fraction 52 / 65 is greater than 45 / 75.