### Numbers: Fractions

### Equivalent fractions

When we cut a pizza in #6# slices of equal size and take #2# of those slices, we have #\tfrac{2}{6}# of the pizza.

If we cut the pizza in #3# slices of equal size, and take #1# slice, we have the same amount of pizza.

We therefore see that #\tfrac{2}{6}= \tfrac{1}{3}#.

In the fraction #\require{color} \definecolor{blue}{RGB}{45, 112, 179}\tfrac{\orange{2}}{\blue{6}}#, we can divide both the numerator and denominator by #2#, and then we find #\tfrac{\orange{1}}{\blue{3}}#.

In general, we can say:

*A fraction does not change if we divide or multiply both the numerator and denominator by the same number.*

**Examples**

\[\begin{array}{rcl}

\dfrac{\orange{2}}{\blue{6}} = \dfrac{\orange{1}}{\blue{3}} \\

\dfrac{\orange{3}}{\blue{6}} = \dfrac{\orange{1}}{\blue{2}} \\

\dfrac{\orange{4}}{\blue{6}} = \dfrac{\orange{2}}{\blue{3}}

\end{array} \]

The value of a fraction does not change when we multiply the numerator and the denominator by the same number.

\[\begin{array}{rcl}

\dfrac{5}{9}&=&\dfrac{\box}{63} \\ &&\phantom{xxx}\blue{\text{denominator multiplied by } \dfrac{63}{9}=7 } \\

\dfrac{5}{9}&=&\dfrac{35}{63} \\ &&\phantom{xxx}\blue{\text{numerator also has to be multiplied by } 7 } \\

\end{array}\]

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