Fraction operations

Add and subtract fractions with unlike denominators; multiply and divide fractions; perform multi-step calculations with mixed numerals.

Worked examples

Adding fractions with unlike denominators

Straightforward

Problem

Calculate

\dfrac{2}{3} + \dfrac{3}{8}

Dividing fractions and simplifying

Moderate

Problem

Calculate

\dfrac{3}{4} \div \dfrac{9}{10}

. Give your answer in simplest form.

Adding mixed numerals in a word problem

Challenging

Problem

A painter uses

1\dfrac{3}{4}

litres of paint on Monday and

2\dfrac{1}{3}

litres on Tuesday. How many litres did the painter use in total?

Practise

Q1·Straightforward

Calculate

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

. Give your answer as a fraction in simplest form.

Q2·Straightforward

Calculate

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

. Give your answer as a fraction in simplest form.

Q3·Straightforward

Calculate

\dfrac{2}{5} + \dfrac{1}{4}

. Give your answer as a fraction in simplest form.

Q4·Straightforward

Calculate

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

. Give your answer as a fraction in simplest form.

Q5·Moderate

Calculate

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

. Give your answer in simplest form.

Q6·Moderate

Calculate

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

. Give your answer as a fraction in simplest form.

Q7·Moderate

Calculate

\dfrac{5}{6} \times \dfrac{4}{5}

. Give your answer in simplest form.

Q8·Moderate

Calculate

\dfrac{4}{5} \div \dfrac{2}{3}

. Give your answer as a fraction in simplest form.

Q9·Challenging

Calculate

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

. Give your answer as an improper fraction in simplest form.

Q10·Challenging

Calculate

3\dfrac{1}{4} \times 1\dfrac{1}{5}

. Give your answer as an improper fraction in simplest form.

Q11·Challenging

A bag of rice weighs

2\dfrac{1}{4}

kg. A shop orders

1\dfrac{1}{2}

bags. What is the total weight in kilograms? Give your answer as a fraction.

Q12·Challenging

Calculate

2\dfrac{1}{2} - 1\dfrac{3}{4} + \dfrac{1}{2}

. Give your answer as a fraction in simplest form.