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How Do You Simplify Fractions?

Simplifying a fraction is the opposite of expanding a fraction. There are two methods to simplify a fraction:

1.: Dividing the numerator and denominator by the same number
2.: Cancellation

You will simplify fractions all throughout your years in school, so practice this until it’s second nature!

Although cancellation is the smartest method, we will start by looking at the method of dividing the numerator and denominator by the same number.

Rule

Simplifying a Fraction

\frac{a}{b} = \frac{a : c}{b : c}

Example 1

Let’s simplify the fraction $\frac{3}{6}$ , dividing it by $3$ , and check that the two fractions are equal:

\frac{3}{6} = \frac{3 : 3}{6 : 3} = \frac{1}{2}

If you take your calculator and enter $3$ divided by $6$ , you’ll get the answer $0.5$ . If you enter $1$ divided by $2$ , you’ll also get $0.5$ . Therefore, even if you simplify the fraction, the value of it remains the same!

$Two equivalent fractions that both have a numerical decimal value of 0.5$

Example 2

Simplify the fraction $\frac{2}{4}$ by the factor 2.

\frac{2}{4} = \frac{2 : 2}{4 : 2} = \frac{1}{2}

Example 3

Simplify the fraction $\frac{20}{70}$ by a factor 10.

\frac{20}{70} = \frac{20 : 10}{70 : 10} = \frac{2}{7}

Example 4

Simplify the fraction $\frac{27}{21}$ by a factor 3.

\frac{27}{21} = \frac{27 : 3}{21 : 3} = \frac{9}{7}

Example 5

Simplify the fraction $\frac{48}{40}$ by a factor 8.

\frac{48}{40} = \frac{48 : 8}{40 : 8} = \frac{6}{5}

Example 6

Simplify the fraction $\frac{48}{18}$ by a factor 6.

$\frac{48}{18} = \frac{48 : 6}{18 : 6} = \frac{8}{3}$

Example 7

Simplify the fraction $\frac{32}{36}$ by a factor 4.

\frac{32}{36} = \frac{32 : 4}{36 : 4} = \frac{8}{9}

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How Do You Expand Fractions?

How to Simplify a Fraction by Canceling

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