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When you expand a fraction, the value of the fraction stays the same as it was before you expanded it. Therefore, you can equate the two expressions in the rule box, even though they look quite different. They actually have equal value.

Rule

You expand a fraction with numerator $a$ and denominator $b$ as follows:

$$\frac{a}{b}=\frac{a\times c}{b\times c}$$ |

Example 1

**Expand the fraction $\frac{4}{5}$ by 3 **

$$\frac{4}{5}=\frac{4\times 3}{5\times 3}=\frac{12}{15}$$ |

You have now expanded the fraction $\frac{4}{5}$ by $3$ and gotten $\frac{12}{15}$. If you input these two very different looking expressions into a calculator, it will tell you that both of them are equal to $0.8$. The fractions have the same value!

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