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
  1. Reduce the fractions

    a) 24 / 36

    b) 52 / 120

    c) 156 / 208

    d) 122 / 6100


  2. Reduce and compare each pair of fractions.

    a) 26 / 39 and 14 / 42

    b) 45 / 75 and 52 / 65

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Updated: 20 January 2017 (A Dendane)
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