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