P3 Equivalent Fractions

A $\frac{1}{2}$ portion of a sandwich can look different after you cut each piece again. The number of pieces changes, but the amount of sandwich does not. That is the big idea behind equivalent fractions.

Parents: let your child predict the shaded amount before the strip reveals its new parts.

By the end you will be able to recognise equivalent fractions, simplify a fraction, compare unlike fractions, and complete a missing numerator or denominator.

Same amount, different names

Equivalent fractions show the same amount. If you split each $\frac{1}{2}$ into three equal pieces, one $\frac{1}{2}$ becomes $\frac{3}{6}$. Both the numerator and denominator are scaled by the same whole number.

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Fraction strips: same amount, new parts

🤔 Predict first: How many sixths are equal to $\frac{1}{2}$?

2 sixths3 sixths4 sixths

Simplest form

Simplest form is the shortest fraction name for an amount. For $\frac{6}{8}$, divide the numerator and denominator by their common factor two. The amount stays fixed while the labels become smaller.

Simplify the fraction

$$6 \div 2 = 3$$

$$8 \div 2 = 4$$

$$\frac{6}{8} = \frac{3}{4}$$

Compare unlike fractions

Unlike fractions have different denominators, so their pieces are not the same size yet. Make equal-sized parts before comparing. To compare $\frac{2}{3}$ and $\frac{3}{5}$, use fifteenths: $\frac{2}{3}$ is $\frac{10}{15}$ and $\frac{3}{5}$ is $\frac{9}{15}$.

Compare the fractions

$$\frac{2}{3} = \frac{10}{15}$$

$$\frac{3}{5} = \frac{9}{15}$$

$$\frac{10}{15} > \frac{9}{15}$$

$$\frac{2}{3} > \frac{3}{5}$$

Fill a missing part

When one numerator or denominator is missing, find the scale factor first. In $\frac{2}{3}$ equals a missing numerator over twelve, the denominator changed from three to twelve, so every part was split into four. The numerator must also be multiplied by four.

Find the missing numerator

$$3 \times 4 = 12$$

$$2 \times 4 = 8$$

$$\frac{2}{3} = \frac{8}{12}$$

Practise with worked steps

Practice 1: Complete $\frac{2}{3}$ equals a missing numerator over twelve

Find the missing numerator

$$3 \times 4 = 12$$

$$2 \times 4 = 8$$

$$\frac{2}{3} = \frac{8}{12}$$

The missing numerator is 8 because both parts were scaled by four.

Practice 2: Express $\frac{6}{8}$ in simplest form

Divide by the common factor

$$6 \div 2 = 3$$

$$8 \div 2 = 4$$

$$\frac{6}{8} = \frac{3}{4}$$

The simplest form is $\frac{3}{4}$.

Practice 3: Order $\frac{2}{3}$, $\frac{3}{4}$ and $\frac{5}{6}$

Use denominator twelve

$$\frac{2}{3} = \frac{8}{12}$$

$$\frac{3}{4} = \frac{9}{12}$$

$$\frac{5}{6} = \frac{10}{12}$$

$$\frac{2}{3} < \frac{3}{4} < \frac{5}{6}$$

From smallest to largest, the order is $\frac{2}{3}$, $\frac{3}{4}$, $\frac{5}{6}$.

Watch out — easily mixed up

Follow the fraction path

Next, use these equal-sized parts in P3 fraction addition and subtraction.

Quick recap

🎯 Mastery check

Answer all 6 — your progress is saved on this device.

1. Which fraction is equal to $\frac{3}{4}$?

   $\frac{6}{8}$$\frac{5}{8}$$\frac{7}{10}$

2. What is $\frac{8}{12}$ in simplest form?

   $\frac{3}{5}$$\frac{2}{3}$$\frac{4}{7}$

3. Which comparison is true?

   $\frac{5}{8} = \frac{2}{3}$$\frac{5}{8} > \frac{2}{3}$$\frac{5}{8} < \frac{2}{3}$

4. $\frac{3}{5}$ equals six over what denominator?

   81210

5. A strip has $\frac{2}{3}$ shaded. It is cut into six equal parts. How many parts are shaded?

   3 parts4 parts5 parts

6. Three identical containers hold $\frac{1}{2}$, $\frac{5}{9}$ and $\frac{3}{4}$ of their capacity. Which is fullest?

   $\frac{3}{4}$$\frac{1}{2}$$\frac{5}{9}$

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