Equivalent Fractions

In a Nutshell

Multiply or divide the top and bottom by the same number, and the fraction keeps its value.

Look at the bars below. The top bar shows 23\frac{2}{3}. The bottom bar shows 46\frac{4}{6}. They cover exactly the same amount.

That is because 46\frac{4}{6} is just 23\frac{2}{3} with the numerator and denominator both multiplied by 2.

The general rule: if you multiply (or divide) the numerator and denominator of a fraction by the same non-zero number, the value of the fraction does not change. We call the results equivalent fractions.

ab=a×nb×n(n≠0)\frac{a}{b} = \frac{a \times n}{b \times n} \quad (n \neq 0)
Equivalent fractions by splitting pieces A fraction bar for one half. Press Split to divide every piece into two, making two quarters, then four eighths. The shaded area stays the same.
Start:

Press "Split each piece" to divide every piece into smaller parts. The fraction label changes but the shaded area stays identical. That is equivalent fractions in action.

Watch it work

Question: Find three fractions equivalent to 35\frac{3}{5}.

Have a go

Q1. Write two fractions equivalent to 14\frac{1}{4}.

Q2. Are 35\frac{3}{5} and 915\frac{9}{15} equivalent? Explain how you know.

Q3. Fill in the blank: 27=?21\frac{2}{7} = \frac{?}{21}.

Q4. Marta says 410\frac{4}{10} and 615\frac{6}{15} are equivalent. Is she right? Show your working.