P3 Fraction Addition and Subtraction

You cannot join one big slice and one tiny slice by counting the slice names. First redraw them so every piece is the same size. Then addition or subtraction is just counting matching pieces.

Parents: ask your child to predict which denominator will make the parts match before revealing the operation.

By the end you will be able to add and subtract exactly two related fractions within one whole, with given denominators no greater than 12.

Add related fractions

Two fractions are related when one denominator fits exactly into the other. For $\frac{1}{2}$ plus $\frac{1}{4}$, change the $\frac{1}{2}$ into $\frac{2}{4}$. Now all pieces are quarters, so count two plus one.

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Fraction strips: related parts

🤔 Predict first: What is $\frac{1}{2}$ plus $\frac{1}{4}$?

$\frac{1}{4}$$\frac{3}{4}$$\frac{4}{6}$

Add related fractions

$$\frac{1}{2} = \frac{2}{4}$$

$$\frac{2}{4} + \frac{1}{4} = \frac{3}{4}$$

Subtract related fractions

Subtraction uses the same redraw. $\frac{5}{6}$ minus $\frac{1}{3}$ becomes $\frac{5}{6}$ minus $\frac{2}{6}$. The answer is $\frac{3}{6}$, which can be written as $\frac{1}{2}$ in simplest form.

Subtract related fractions

$$\frac{1}{3} = \frac{2}{6}$$

$$\frac{5}{6} - \frac{2}{6} = \frac{3}{6}$$

$$\frac{3}{6} = \frac{1}{2}$$

Keep the result within one whole

The P3 skill uses exactly two related fractions and keeps the result within one whole. For a bottle, $\frac{3}{8}$ plus $\frac{1}{4}$ becomes $\frac{3}{8}$ plus $\frac{2}{8}$, or $\frac{5}{8}$. The result is still less than a whole bottle.

Add two drink amounts

$$\frac{1}{4} = \frac{2}{8}$$

$$\frac{3}{8} + \frac{2}{8} = \frac{5}{8}$$

Practise with worked steps

Practice 1: Find $\frac{1}{2}$ plus $\frac{1}{4}$

Use quarters

$$\frac{1}{2} = \frac{2}{4}$$

$$\frac{2}{4} + \frac{1}{4} = \frac{3}{4}$$

The sum is $\frac{3}{4}$.

Practice 2: Find $\frac{5}{6}$ minus $\frac{1}{3}$

Use sixths

$$\frac{1}{3} = \frac{2}{6}$$

$$\frac{5}{6} - \frac{2}{6} = \frac{3}{6}$$

$$\frac{3}{6} = \frac{1}{2}$$

The difference is $\frac{1}{2}$.

Practice 3: Mei drinks $\frac{3}{8}$ and $\frac{1}{4}$ of a bottle

Change the quarter to eighths

$$\frac{1}{4} = \frac{2}{8}$$

$$\frac{3}{8} + \frac{2}{8} = \frac{5}{8}$$

Mei drinks $\frac{5}{8}$ altogether.

Watch out — easily mixed up

Follow the fraction path

Use P3 equivalent fractions when the task is to rename or compare an amount. When you are ready for representations beyond one whole, continue to P4 mixed numbers and improper fractions.

Quick recap

🎯 Mastery check

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

1. What is $\frac{1}{3}$ plus $\frac{1}{6}$?

   $\frac{1}{2}$$\frac{2}{9}$$\frac{2}{6}$

2. What is $\frac{7}{8}$ minus $\frac{1}{4}$?

   $\frac{3}{8}$$\frac{5}{8}$$\frac{6}{8}$

3. What is $\frac{2}{5}$ plus $\frac{1}{10}$?

   $\frac{3}{10}$$\frac{3}{15}$$\frac{1}{2}$

4. Why is $\frac{3}{4}$ changed to $\frac{6}{8}$ before subtracting $\frac{1}{8}$?

   Quarters and eighths are different-sized parts.Subtracting denominators gives the part size.The numerator and denominator must be equal.

5. A ribbon is $\frac{3}{4}$ of a metre long. Sam cuts off $\frac{1}{8}$ of a metre. How much remains?

   $\frac{5}{8}$ m$\frac{6}{8}$ m$\frac{1}{2}$ m

6. Noor eats $\frac{1}{3}$ of a pizza at lunch and $\frac{1}{6}$ at tea. What fraction has she eaten?

   $\frac{2}{9}$$\frac{4}{6}$$\frac{1}{2}$

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