Open Math›Year 7›Fractions, decimals and percentages›Fractions

Fractions

Add, subtract, multiply and divide fractions, including unlike fractions.

Worked examples

Adding like fractions

Straightforward

Problem

Calculate

\dfrac{3}{7} + \dfrac{2}{7}

Check that the denominators are the same.

Both fractions have denominator

7

, so they are like fractions.

Add the numerators and keep the denominator.

\frac{3}{7} + \frac{2}{7} = \frac{3 + 2}{7} = \frac{5}{7}

Check whether the fraction can be simplified.

5

and

7

share no common factors other than

1

, so

\dfrac{5}{7}

is already in simplest form.

Answer

\dfrac{5}{7}

Adding unlike fractions

Moderate

Problem

Calculate

\dfrac{1}{3} + \dfrac{1}{4}

Find the lowest common denominator (LCD) of

3

and

4

Multiples of

3

3, 6, 9, 12, \ldots

Multiples of

4

4, 8, 12, \ldots

The LCD is

12

Convert each fraction to an equivalent fraction with denominator

12

\frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12}

\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}

Add the like fractions.

\frac{4}{12} + \frac{3}{12} = \frac{4 + 3}{12} = \frac{7}{12}

Check whether the fraction can be simplified.

7

and

12

share no common factors other than

1

, so

\dfrac{7}{12}

is already in simplest form.

Answer

\dfrac{7}{12}

Dividing fractions

Challenging

Problem

Calculate

\dfrac{3}{4} \div \dfrac{1}{2}

Apply the rule: to divide by a fraction, keep the first fraction, change

\div

\times

, and flip (find the reciprocal of) the second fraction.

\frac{3}{4} \div \frac{1}{2} = \frac{3}{4} \times \frac{2}{1}

Multiply the numerators together and the denominators together.

\frac{3}{4} \times \frac{2}{1} = \frac{3 \times 2}{4 \times 1} = \frac{6}{4}

Simplify the result.

Divide numerator and denominator by

2

\frac{6}{4} = \frac{3}{2}

Answer

\dfrac{3}{2}

Practise

Q1·Straightforward

Calculate

\dfrac{2}{7} + \dfrac{3}{7}

Explanation

The denominators are the same, so add the numerators and keep the denominator:

\frac{2}{7} + \frac{3}{7} = \frac{2 + 3}{7} = \frac{5}{7}

Q2·Straightforward

Calculate

\dfrac{7}{9} - \dfrac{4}{9}

Explanation

Subtract the numerators and keep the denominator:

\frac{7}{9} - \frac{4}{9} = \frac{7 - 4}{9} = \frac{3}{9}

Simplify by dividing numerator and denominator by

3

\frac{3}{9} = \frac{1}{3}

Q3·Straightforward

Calculate

\dfrac{3}{5} + \dfrac{1}{5}

Explanation

The denominators are the same, so add the numerators and keep the denominator:

\frac{3}{5} + \frac{1}{5} = \frac{3 + 1}{5} = \frac{4}{5}

Q4·Straightforward

Calculate

\dfrac{11}{12} - \dfrac{5}{12}

Explanation

Subtract the numerators and keep the denominator:

\frac{11}{12} - \frac{5}{12} = \frac{11 - 5}{12} = \frac{6}{12}

Simplify by dividing numerator and denominator by

6

\frac{6}{12} = \frac{1}{2}

Q5·Moderate

Calculate

\dfrac{1}{3} + \dfrac{1}{4}

Explanation

The lowest common denominator (LCD) of

3

and

4

12

.

Convert each fraction:

\frac{1}{3} = \frac{4}{12}, \quad \frac{1}{4} = \frac{3}{12}

Add:

\frac{4}{12} + \frac{3}{12} = \frac{7}{12}

Q6·Moderate

Calculate

\dfrac{3}{4} - \dfrac{1}{3}

Explanation

The LCD of

4

and

3

12

.

Convert each fraction:

\frac{3}{4} = \frac{9}{12}, \quad \frac{1}{3} = \frac{4}{12}

Subtract:

\frac{9}{12} - \frac{4}{12} = \frac{5}{12}

Q7·Moderate

Calculate

\dfrac{2}{3} + \dfrac{1}{6}

Explanation

The LCD of

3

and

6

6

.

Convert

\dfrac{2}{3}

\frac{2}{3} = \frac{4}{6}

Add:

\frac{4}{6} + \frac{1}{6} = \frac{5}{6}

Q8·Moderate

Calculate

\dfrac{5}{6} - \dfrac{1}{4}

Explanation

The LCD of

6

and

4

12

.

Convert each fraction:

\frac{5}{6} = \frac{10}{12}, \quad \frac{1}{4} = \frac{3}{12}

Subtract:

\frac{10}{12} - \frac{3}{12} = \frac{7}{12}

Q9·Challenging

Calculate

\dfrac{2}{3} \times \dfrac{3}{4}

Explanation

Multiply numerators and denominators:

\frac{2}{3} \times \frac{3}{4} = \frac{2 \times 3}{3 \times 4} = \frac{6}{12}

Simplify by dividing by

6

\frac{6}{12} = \frac{1}{2}

Q10·Challenging

Calculate

\dfrac{3}{5} \times \dfrac{2}{9}

Explanation

Multiply numerators and denominators:

\frac{3}{5} \times \frac{2}{9} = \frac{3 \times 2}{5 \times 9} = \frac{6}{45}

Simplify by dividing by

3

\frac{6}{45} = \frac{2}{15}

Q11·Challenging

Calculate

\dfrac{3}{4} \div \dfrac{1}{2}

Explanation

Keep the first fraction, change

\div

\times

, and flip the second fraction:

\frac{3}{4} \div \frac{1}{2} = \frac{3}{4} \times \frac{2}{1}

Multiply:

\frac{3 \times 2}{4 \times 1} = \frac{6}{4} = \frac{3}{2}

Q12·Challenging

Calculate

\dfrac{5}{6} \div \dfrac{2}{3}

Explanation

Keep the first fraction, change

\div

\times

, and flip the second fraction:

\frac{5}{6} \div \frac{2}{3} = \frac{5}{6} \times \frac{3}{2}

Multiply:

\frac{5 \times 3}{6 \times 2} = \frac{15}{12}

Simplify by dividing by

3

\frac{15}{12} = \frac{5}{4}