Speed Drills: Fractions and Percentages of Amounts
A speed drill on fractions and percentages of amounts trains fast mental methods for finding a fraction or a percentage of a whole number, for example finding 3/4 of 60 or 15% of 80, using building-block facts such as 10%, 1% and unit fractions rather than long written working. 11+ papers set many short 'find X of Y' questions, often as sub-parts of larger word problems, so answering these instantly rather than via a full written method matters for finishing the paper in time.
Method
- For a unit fraction, such as 1/5, of an amount, divide the amount by the denominator; for a non-unit fraction, such as 3/5, find the unit fraction first, then multiply by the numerator.
- For 10% of an amount, divide by 10 (move the decimal point one place); for 1%, divide by 100. Build any other percentage from these two building blocks.
- Use known percentage facts as shortcuts: 50% is a half, 25% is a quarter, 20% is one fifth, and 75% is three quarters.
- To find a percentage such as 35%, combine building blocks: 35% = 25% + 10% or 30% + 5%, whichever is faster to calculate mentally.
- Always check the size of the answer is sensible: a fraction or percentage under 100% of an amount must be smaller than the whole amount.
- Practise with round numbers first, such as multiples of 10 or 100, to build speed, then move on to less friendly numbers.
Worked example
Find 3/4 of 60, and separately find 35% of 40.
- For 3/4 of 60, find the unit fraction 1/4 of 60 first: 60 / 4 = 15.
- Multiply by the numerator: 3 x 15 = 45. So 3/4 of 60 is 45.
- For 35% of 40, split 35% into 25% + 10%.
- 25% of 40 is a quarter of 40, which is 10; 10% of 40 is 4.
- Add the two parts: 10 + 4 = 14. So 35% of 40 is 14.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1Find 1/3 of 27.Show answer
Answer: 9
Q2Find 2/5 of 45.Show answer
Answer: 18
Q3Find 10% of 250.Show answer
Answer: 25
Q4Find 20% of 90.Show answer
Answer: 18
Q5Find 3/8 of 64.Show answer
Answer: 24
Q6Find 15% of 60.Show answer
Answer: 9
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
A jug holds 800 ml of juice. Find 3/4 of the juice in ml, and find 15% of 800 ml. Which amount is greater?
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Tick each line you got. Your score builds from the marks on the scheme.
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A school has 320 pupils. 45% of the pupils are boys. How many boys are there, and how many girls?
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Free printable worksheet
Want more practice on paper? Download the speed drills: fractions and percentages of amounts worksheet pack - 17 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 4 of 11+ Maths Workbook 1, the whole course as one free printable PDF.
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