Equivalent fractions

$\frac{1}{2}$ and $\frac{2}{4}$ look different, but they're the same amount. If you cut each piece into 2, you get twice as many pieces, and you have twice as many of them.

\frac{1}{2}

\frac{2}{4}

, the same amount in smaller pieces.

\frac{a}{b} = \frac{a \times k}{b \times k}

. Multiplying by

\frac{k}{k}

is multiplying by 1, so the value doesn't change.

Work through it

Simplify $\frac{18}{24}$ .

Find the largest number that divides both.6

Divide the top and the bottom by it. $\frac{18 \div 6}{24 \div 6} = \frac{3}{4}$

Compare $\frac{3}{4}$ and $\frac{5}{8}$ .

Make the denominators match. $\frac{3}{4}$ needs 8 on the bottom. $\frac{3}{4} = \frac{6}{8}$

Now the pieces are the same size, so compare tops. $\frac{6}{8} > \frac{5}{8}$

Compare $\frac{2}{3}$ and $\frac{3}{5}$ .

Use 15 as a common denominator. $\frac{10}{15}$ and $\frac{9}{15}$

Compare tops. $\frac{2}{3} > \frac{3}{5}$

Watch out for this

$\frac{2}{3} = \frac{4}{5}$ , by adding 2 to the top and the bottom.

Adding changes the amount. Only multiplying or dividing by the same number keeps it.

The short version
Multiply or divide the top and the bottom by the same number. To compare, get the same denominator first.

Your turn

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