Equivalent Fractions

≈ 20 min

A fraction describes part of a whole. In $\dfrac{3}{4}$ , the bottom number (denominator) says the whole is split into $4$ equal parts, and the top number (numerator) says we have $3$ of them.

Equivalent fractions look different but represent the same amount. You make them by multiplying — or dividing — the numerator and denominator by the same number:

\frac{1}{2} = \frac{2}{4} = \frac{3}{6} = \frac{4}{8}.

Simplest form means the numerator and denominator share no common factor except $1$ . To simplify, divide both by their highest common factor.

Worked example. Simplify $\dfrac{6}{8}$ . Both $6$ and $8$ divide by $2$ : $\dfrac{6\div2}{8\div2} = \dfrac{3}{4}$ . Since $3$ and $4$ share no further factor, $\dfrac{3}{4}$ is simplest.

Which fraction is equivalent to $\dfrac{1}{2}$ ?

$\dfrac{2}{3}$

$\dfrac{3}{6}$

$\dfrac{2}{5}$

$\dfrac{4}{6}$

Complete the equivalent fraction: $\dfrac{3}{4} = \dfrac{?}{12}$ . What is the missing numerator?

Write $\dfrac{8}{12}$ in its simplest form, as a fraction like a/b.

Which fraction is already in its simplest form?

$\dfrac{4}{8}$

$\dfrac{6}{9}$

$\dfrac{3}{5}$

$\dfrac{10}{12}$