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.

More Middle School Math (Grades 6, 7, 8, 9)  Free Questions and Problems With Answers
More High School Math (Grades 10, 11 and 12)  Free Questions and Problems With Answers
More Primary Math (Grades 4 and 5) with Free Questions and Problems With Answers
Author 
email
Home Page