Fractions: Practice Set 3
Fractions: Practice Set 3 is a further practice set on working with fractions without a calculator, simplifying, comparing, converting between mixed numbers and improper fractions, and adding, subtracting, multiplying and dividing fractions, the same core skills tested in every 11+ paper's fractions questions but with a fresh set of numbers to build fluency.
Method
- Simplify a fraction by dividing the numerator and denominator by their highest common factor, repeating until no common factor remains.
- Before adding or subtracting fractions with different denominators, convert them to equivalent fractions sharing a common denominator, usually the lowest common multiple of the two denominators.
- To multiply two fractions, multiply the numerators together and the denominators together, cancelling any common factors first to keep the numbers small.
- To divide by a fraction, turn the second fraction upside down to find its reciprocal and multiply instead of dividing.
- Convert a mixed number to an improper fraction before multiplying or dividing it, then convert the final answer back to a mixed number if the question asks for one.
- Always check whether your final fraction can be simplified further before giving it as your answer.
Worked example
Work out 3/4 - 2/5, giving your answer as a fraction in its simplest form.
- Find a common denominator for 4 and 5: the lowest common multiple is 20.
- Convert 3/4 to twentieths: 3/4 = 15/20, multiplying numerator and denominator by 5.
- Convert 2/5 to twentieths: 2/5 = 8/20, multiplying numerator and denominator by 4.
- Subtract the numerators, keeping the denominator the same: 15/20 - 8/20 = 7/20.
- Check whether 7/20 can be simplified: 7 is prime and is not a factor of 20, so it is already in its simplest form.
Practice questions
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Q1Simplify 18/24 fully.Show answer
Answer: 3/4
Q2Write 29/8 as a mixed number.Show answer
Answer: 3 5/8
Q3Work out 2/9 + 4/9, giving your answer in its simplest form.Show answer
Answer: 2/3 (6/9 simplified)
Q4Work out 7/10 - 1/5, giving your answer in its simplest form.Show answer
Answer: 1/2 (7/10 - 2/10 = 5/10)
Q5Work out 3/5 x 5/6, giving your answer in its simplest form.Show answer
Answer: 1/2 (15/30 simplified)
Q6Find 5/8 of 96.Show answer
Answer: 60 (96 / 8 = 12, 12 x 5 = 60)
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
Work out 1 3/4 + 2 5/6, giving your answer as a mixed number in its simplest form.
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A tank is 3/8 full of water. After 45 litres are added, the tank is 3/4 full. Work out the capacity of the tank.
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A recipe uses 2/3 of a cup of sugar. A baker wants to make 1 1/2 times the recipe. How much sugar is needed, giving your answer as a fraction or whole number of cups in its simplest form?
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Free printable worksheet
Want more practice on paper? Download the fractions: practice set 3 worksheet pack - 9 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 32 of 11+ Maths Workbook 1, the whole course as one free printable PDF.
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