How to Reduce Fractions in Maths
Grade 7 Questions With Detailed Solutions

This page is designed to help students master the process of reducing fractions. Below, you will find a clear explanation of the prime factorization method, followed by carefully selected practice questions and step-by-step solutions.

What is a reduced fraction?

If the only common factor to a numerator and denominator of a fraction is $1$, that fraction is in its reduced form.

How to Reduce a Fraction

One of the most reliable ways to reduce a fraction is to write the prime factorization of the numerator and denominator, and then simplify by canceling common factors.

Example 1: Reduce the fraction $\dfrac{9}{15}$

Step 1: The prime factorization of $9$ is: $9 = 3 \times 3$

Step 2: The prime factorization of $15$ is: $15 = 3 \times 5$

Step 3: Rewrite the given fraction with the numerator and denominator in factored form: $$\dfrac{9}{15} = \dfrac{3 \times 3}{3 \times 5}$$

Step 4: Simplify by canceling the common factors: $$\dfrac{9}{15} = \dfrac{\cancel{3} \times 3}{\cancel{3} \times 5} = \dfrac{3}{5}$$

Example 2: Reduce the fraction $\dfrac{12}{72}$

Step 1: The prime factorization of $12$ is: $12 = 2 \times 2 \times 3$

Step 2: The prime factorization of $72$ is: $72 = 2 \times 2 \times 2 \times 3 \times 3$

Step 3: Rewrite in factored form: $$\dfrac{12}{72} = \dfrac{2 \times 2 \times 3}{2 \times 2 \times 2 \times 3 \times 3}$$

Step 4: Simplify: $$\dfrac{12}{72} = \dfrac{\cancel{2 \times 2} \times \cancel{3}}{\cancel{2 \times 2} \times 2 \times \cancel{3} \times 3} = \dfrac{1}{2 \times 3} = \dfrac{1}{6}$$

Example 3: Reduce the fraction $\dfrac{504}{600}$

Step 1: Prime factorization of $504$: $504 = 2 \times 2 \times 2 \times 3 \times 3 \times 7$

Step 2: Prime factorization of $600$: $600 = 2 \times 2 \times 2 \times 3 \times 5 \times 5$

Step 3: Rewrite 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: $$\dfrac{504}{600} = \dfrac{\cancel{2 \times 2 \times 2} \times \cancel{3} \times 3 \times 7}{\cancel{2 \times 2 \times 2} \times \cancel{3} \times 5 \times 5} = \dfrac{3 \times 7}{5 \times 5} = \dfrac{21}{25}$$

Tip: A Reduce Fractions Calculator may be used to verify your work!

Practice Questions

  1. Reduce the following fractions:
    1. $\dfrac{24}{36}$
    2. $\dfrac{52}{120}$
    3. $\dfrac{156}{208}$
    4. $\dfrac{122}{6100}$
    View Solutions

    1. We start with the prime factorization of numerator $24$ and denominator $36$:

      $24 = 2 \times 2 \times 2 \times 3$
      $36 = 2 \times 2 \times 3 \times 3$

      Rewrite the fraction using the factorization and simplify by canceling common factors:

      $$\dfrac{24}{36} = \dfrac{\cancel{2} \times \cancel{2} \times 2 \times \cancel{3}}{\cancel{2} \times \cancel{2} \times \cancel{3} \times 3} = \mathbf{\dfrac{2}{3}}$$

    2. Prime factorization of numerator $52$ and denominator $120$:

      $52 = 2 \times 2 \times 13$
      $120 = 2 \times 2 \times 2 \times 3 \times 5$

      Rewrite the fraction and simplify:

      $$\dfrac{52}{120} = \dfrac{\cancel{2} \times \cancel{2} \times 13}{\cancel{2} \times \cancel{2} \times 2 \times 3 \times 5} = \mathbf{\dfrac{13}{30}}$$

    3. Prime factorization of numerator $156$ and denominator $208$:

      $156 = 2 \times 2 \times 3 \times 13$
      $208 = 2 \times 2 \times 2 \times 2 \times 13$

      Rewrite the fraction and simplify:

      $$\dfrac{156}{208} = \dfrac{\cancel{2} \times \cancel{2} \times 3 \times \cancel{13}}{\cancel{2} \times \cancel{2} \times 2 \times 2 \times \cancel{13}} = \mathbf{\dfrac{3}{4}}$$

    4. Prime factorization of numerator $122$ and denominator $6100$:

      $122 = 2 \times 61$
      $6100 = 2 \times 2 \times 5 \times 5 \times 61$

      Rewrite the fraction and simplify:

      $$\dfrac{122}{6100} = \dfrac{\cancel{2} \times \cancel{61}}{\cancel{2} \times 2 \times 5 \times 5 \times \cancel{61}} = \dfrac{1}{2 \times 5 \times 5} = \mathbf{\dfrac{1}{50}}$$

  2. Reduce and compare each pair of fractions:
    1. $\dfrac{26}{39}$ and $\dfrac{14}{42}$
    2. $\dfrac{45}{75}$ and $\dfrac{52}{65}$
    View Solutions

    1. Prime factorization and simplification of the pair:

      $$\dfrac{26}{39} = \dfrac{2 \times 13}{3 \times 13} = \dfrac{2}{3}$$

      $$\dfrac{14}{42} = \dfrac{2 \times 7}{2 \times 3 \times 7} = \dfrac{1}{3}$$

      Comparing the simplified fractions, $\dfrac{2}{3} > \dfrac{1}{3}$. Therefore, $\mathbf{\dfrac{26}{39} > \dfrac{14}{42}}$.

    2. Prime factorization and simplification of the pair:

      $$\dfrac{45}{75} = \dfrac{3 \times 3 \times 5}{3 \times 5 \times 5} = \dfrac{3}{5}$$

      $$\dfrac{52}{65} = \dfrac{2 \times 2 \times 13}{5 \times 13} = \dfrac{4}{5}$$

      Comparing the simplified fractions, $\dfrac{4}{5} > \dfrac{3}{5}$. Therefore, $\mathbf{\dfrac{52}{65} > \dfrac{45}{75}}$.

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