# How to Reduce Fractions in Math - Grade 7 Math Questions With Detailed Solutions

How to reduce fractions in math? Grade 7 math questions are presented along with detailed solutions. Detailed Solutions and explanations are included.

 What is a reduced fraction in math? If the only common factor to a numerator and denominator of a fraction is 1, that fraction is in reduced form. $\dfrac{2}{3}$ is a reduced fraction because its denominator and denominator have no common factor except 1. $\dfrac{5}{7}$, $\dfrac{12}{13}$ and $\dfrac{101}{103}$ are all reduced fractions. $\dfrac{5}{15}$ is not a reduced fraction because 5 is a common factor to the numerator 5 and the denominator 15 or in other words both 5 and 15 are divisible by 5. $\dfrac{12}{18}$ is not a reduced fraction because 12 and 18 have several common factor:1, 2, 3 and 6. How to reduce a fraction? One way to reduce a fraction is to write the prime factorization of the numerator and denominator then simplify. Example 1: Reduce the fraction $\dfrac{9}{15}$ step 1 - The prime factorization of 9 is: 9 = 3 × 3 step 2 - The prime factorization of 15 is: 15 = 3 × 5 step 3 - Rewrite the given fraction with numerator and denominator in factored form $\dfrac{9}{15} = \dfrac{3\times 3}{3 \times 5}$ step 4 - Simplify $\dfrac{9}{15} = \dfrac{\cancel{3}\times 3}{\cancel{3}\times 5}$ = $\dfrac{3}{5}$ Example 2: Reduce the fraction $\dfrac{12}{72}$ step 1 - The prime factorization of 12 is: 12 = 2 × 2 × 3 step 2 - The prime factorization of 72 is: 72 = 2 × 2 × 2× 3 × 3 step 3 - Rewrite the given fraction with numerator and denominator in factored form $\dfrac{12}{72} = \dfrac{2\times 2 \times 3}{2 \times 2 \times 2 \times 3 \times 3}$ step 4 - Simplify $\dfrac{12}{72} = \dfrac{\cancel{2\times 2} \times \cancel{3}}{\cancel{2 \times 2} \times 2 \times \cancel{3} \times 3}$ = $\dfrac{1}{6}$ Example 3: Reduce the fraction $\dfrac{504}{600}$ step 1 - The prime factorization of 504 is: 504 = 2 × 2 × 2 × 3 × 3 × 7 step 2 - The prime factorization of 600 is: 600 = 2 × 2 × 2× 3 × 5 × 5 step 3 - Rewrite the given fraction with numerator and denominator in factored form $\dfrac{504}{600} = \dfrac{2\times 2 \times 2 \times 3 \times 3 \times 7}{2 \times 2 \times 2 \times 3 \times 5 \times 5}$ step 4 - Simplify $\dfrac{504}{600} = \dfrac{\cancel{2\times 2 \times 2} \times \cancel{3} \times 3 \times 7}{\cancel{2 \times 2 \times 2} \times \cancel{3} \times 5 \times 5}$ = $\dfrac{21}{25}$ A Reduce Fractions Calculator may be used to check your answers. Answer the following questions Reduce the fractions a) 24 / 36 b) 52 / 120 c) 156 / 208 d) 122 / 6100 Reduce and compare each pair of fractions. a) 26 / 39 and 14 / 42 b) 45 / 75 and 52 / 65

Updated: 20 January 2017 (A Dendane)