P4 Fraction Addition and Subtraction

At P4, your two pieces may not fit neatly into the same strip yet. Find a common denominator, redraw both amounts in that part size, and then the arithmetic is ordinary counting. A result may pass one whole, so learn to read it in both fraction forms.

Parents: ask your child to name the common denominator before they add or subtract.

By the end you will be able to add and subtract proper fractions with at most two given denominators, then write an improper result as a mixed number when useful.

Add unlike fractions

The common denominator makes the pieces match. For $\frac{5}{6}$ plus $\frac{3}{4}$, twelve is a useful common denominator. $\frac{5}{6}$ becomes $\frac{10}{12}$ and $\frac{3}{4}$ becomes $\frac{9}{12}$.

🔬

Fraction strips: unlike operations

🤔 Predict first: What is $\frac{5}{6}$ plus $\frac{3}{4}$ after both fractions use twelfths?

$\frac{14}{12}$$\frac{19}{12}$$\frac{20}{12}$

Add the fractions

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

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

$$\frac{10}{12} + \frac{9}{12} = \frac{19}{12}$$

$$\frac{19}{12} = 1\frac{7}{12}$$

Subtract unlike fractions

Subtraction follows the same route. With $\frac{7}{8}$ minus $\frac{1}{3}$, use twenty-fourths. $\frac{7}{8}$ is $\frac{21}{24}$ and $\frac{1}{3}$ is $\frac{8}{24}$, leaving $\frac{13}{24}$.

Subtract the fractions

$$\frac{7}{8} = \frac{21}{24}$$

$$\frac{1}{3} = \frac{8}{24}$$

$$\frac{21}{24} - \frac{8}{24} = \frac{13}{24}$$

Read an improper answer

An answer such as $\frac{19}{12}$ is correct, but a mixed number can make its size easier to see. $\frac{19}{12}$ contains one complete $\frac{12}{12}$ whole and $\frac{7}{12}$ left over.

Read the result two ways

$$19 \div 12 = 1 \text{ remainder } 7$$

$$\frac{19}{12} = 1\frac{7}{12}$$

Practise with worked steps

Practice 1: Add $\frac{2}{5}$ and $\frac{3}{10}$

Start with related parts

$$\frac{2}{5} = \frac{4}{10}$$

$$\frac{4}{10} + \frac{3}{10} = \frac{7}{10}$$

The sum is $\frac{7}{10}$, still less than one whole.

Practice 2: Subtract $\frac{7}{8}$ minus $\frac{1}{3}$

Use denominator twenty-four

$$\frac{7}{8} = \frac{21}{24}$$

$$\frac{1}{3} = \frac{8}{24}$$

$$\frac{21}{24} - \frac{8}{24} = \frac{13}{24}$$

The difference is $\frac{13}{24}$.

Practice 3: Add $\frac{5}{6}$ and $\frac{3}{4}$

Finish with an improper result

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

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

$$\frac{10}{12} + \frac{9}{12} = \frac{19}{12} = 1\frac{7}{12}$$

The sum is $\frac{19}{12}$, or 1 $\frac{7}{12}$.

Watch out — easily mixed up

Follow the fraction path

Review P4 mixed numbers and improper fractions when an answer passes one whole. For a related P4 representation, see fraction of a set and keep the denominator's equal groups visible.

Quick recap

🎯 Mastery check

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

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

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

2. What is $\frac{5}{6}$ minus $\frac{1}{4}$?

   $\frac{1}{2}$$\frac{7}{12}$$\frac{4}{10}$

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

   $\frac{7}{10}$$\frac{5}{15}$$\frac{1}{2}$

4. What is $\frac{3}{4}$ minus $\frac{2}{5}$?

   $\frac{7}{20}$$\frac{1}{5}$$\frac{1}{20}$

5. A joined ribbon is $\frac{5}{6}$ of a metre plus $\frac{3}{4}$ of a metre. What length is it?

   $\frac{19}{12}$ m$\frac{8}{10}$ m1 $\frac{5}{12}$ m

6. A 2 litre jug contains $\frac{7}{8}$ of a litre. $\frac{1}{3}$ of a litre is poured out. How much remains?

   $\frac{13}{24}$ L$\frac{5}{24}$ L$\frac{2}{11}$ L

See my score