Equivalent Fractions & Comparing

≈ 25 min

Two fractions are equivalent when they describe the same amount. Multiply (or divide) the top and bottom by the same number and the value is unchanged:

\frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6} = \frac{8}{12}

Simplifying means dividing top and bottom by their HCF to reach the smallest names: $\dfrac{6}{8} = \dfrac{6 \div 2}{8 \div 2} = \dfrac{3}{4}$ .

Comparing fractions with different denominators is unfair until they are rewritten over a common denominator. To compare $\frac{2}{3}$ and $\frac{3}{5}$ , use twelfths — no, use fifteenths (the LCM of $3$ and $5$ ): $\frac{2}{3} = \frac{10}{15}$ and $\frac{3}{5} = \frac{9}{15}$ . Since $10 > 9$ , we get $\frac{2}{3} > \frac{3}{5}$ .

Which fraction is equivalent to $\dfrac{2}{3}$ ?

$\dfrac{3}{4}$

$\dfrac{4}{6}$

$\dfrac{2}{6}$

$\dfrac{5}{6}$

Simplify $\dfrac{6}{8}$ to its lowest terms. Give your answer as a fraction, e.g. 3/4.

Which is larger, $\dfrac{2}{3}$ or $\dfrac{3}{5}$ ?

$\dfrac{2}{3}$

$\dfrac{3}{5}$

They are equal

It cannot be decided

Fill in the missing number: $\dfrac{3}{4} = \dfrac{?}{12}$