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# How Do You Expand Fractions?

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A fraction is made up of a numerator, a fraction bar (vinculum) and a denominator. To expand a fraction means to multiply the numerator and denominator by the same factor.

Rule

### ExpandingaFraction

 $\frac{a}{b}=\frac{a\cdot c}{b\cdot c}$

When you expand a fraction, the value remains the same as before you expanded it. That’s why you can put an equal sign between the two expressions in the rule box, even though they look different. You can confirm this in the examples below with a calculator.

Example 1

Expand the fraction $\frac{2}{5}$ by the factor $2$.

 $\frac{2}{5}=\frac{2\cdot 2}{5\cdot 2}=\frac{4}{10}$

Expand the fraction $\frac{9}{7}$ by the factor $3$.

 $\frac{9}{7}=\frac{9\cdot 3}{7\cdot 3}=\frac{27}{21}$

Expand the fraction $\frac{2}{7}$ by the factor $10$.

 $\frac{2}{7}=\frac{2\cdot 10}{7\cdot 10}=\frac{20}{70}$

Expand the fraction $\frac{6}{5}$ by the factor $8$.

 $\frac{6}{5}=\frac{6\cdot 8}{5\cdot 8}=\frac{48}{40}$

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