What is the simplest form of fraction \(\frac{6}{10}\)?

$\frac{3}{5}$

Explanation

Strategy We will factor the numerator and denominator. Then we will look for any factors common to the numerator and denominator and remove them.

WHY We need to make sure that the numerator and denominator have no common factors other than 1. If that is the case, then the fraction is in simplest form.

Solution

\(\frac{6}{10}=\frac{\color{red}2 \cdot 3}{\color{red}2 \cdot 5}\)

To prepare to simplify, factor 6 and 10. Note the form of 1 highlighted in red.

\(\require{cancel}=\frac{\cancel{\color{red}2}^1 \cdot 3}{\cancel{\color{red}2}_1 \cdot 5}\)

Simplify by removing the common factor of 2 from the numerator and denominator. 

\(=\frac{3}{5}\)

Multiply the remaining factors in the numerator: \(1 \cdot 3 = 3\). Multiply the remaining factors in the denominator: \(1 \cdot 5 = 5\).

Since 3 and 5 have no common factors (other than 1), \(\frac{3}{5}\) is in simplest form.