Fractions
A fraction represents a part of a whole, written as a numerator over a denominator, such as 3/4 meaning 3 parts out of 4 equal parts. 11+ papers test simplifying, comparing, converting and calculating with fractions, including mixed numbers, all without a calculator.
Before you start
Make sure you're comfortable with these topics first:
Method
- To simplify a fraction, divide the numerator and denominator by their highest common factor until no common factor remains.
- To compare or add/subtract fractions with different denominators, first convert them to equivalent fractions with a common denominator.
- To multiply fractions, multiply the numerators together and the denominators together, cancelling common factors first where possible.
- To divide by a fraction, flip the second fraction to find its reciprocal and multiply instead.
- Convert mixed numbers to improper fractions before multiplying or dividing, then convert the answer back to a mixed number at the end if needed.
- To find a fraction of an amount, divide by the denominator then multiply by the numerator.
Worked example
Work out 2/5 + 1/4, giving your answer as a fraction in its simplest form.
- Find a common denominator for 5 and 4: the lowest common multiple is 20.
- Convert 2/5 to twentieths: 2/5 = 8/20, multiplying numerator and denominator by 4.
- Convert 1/4 to twentieths: 1/4 = 5/20, multiplying numerator and denominator by 5.
- Add the numerators, keeping the denominator the same: 8/20 + 5/20 = 13/20.
- Check whether 13/20 can be simplified: 13 is prime and is not a factor of 20, so it is already in its simplest form.
Practice questions
Try each question, then tap to reveal the answer.
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
Which of the following fractions is NOT equivalent to 2/5? A) 4/10 B) 6/15 C) 8/20 D) 10/20
A baker in Norwich makes 180 loaves one morning. By 9am, 2/5 of the loaves have been sold. Of the loaves that remain, 1/4 are sold by midday. How many loaves are left after midday?
On a school trip organised from a school in Leeds, 1/3 of the students travel by minibus. Of the students who do not travel by minibus, 2/5 walk and the rest cycle. Given that 24 students cycle, work out the total number of students who went on the trip.
Free printable worksheet
Want more practice on paper? Download the fractions worksheet pack - 11 pages of exam-style questions with a full mark scheme. No sign-up, no email wall - just the PDF, free for personal and classroom use.
Next topics
Build a full practice pack.
This topic is one of hundreds in the library - pick the ones a student needs and generate a printable PDF in minutes.