Fractions, Decimals and Percentages Depth
Fractions, Decimals and Percentages Depth covers harder Year 6 skills building on the basics: multiplying a fraction by a whole number or another fraction, dividing a fraction by a whole number, calculating a percentage increase or decrease, and working backwards to find a whole amount from a known fraction or percentage of it.
Before you start
Make sure you're comfortable with these topics first:
Method
- To multiply a fraction by a whole number, multiply the numerator by that whole number and keep the denominator the same, then simplify if possible.
- To multiply a fraction by a fraction, multiply the numerators together and the denominators together, then simplify if possible.
- To divide a fraction by a whole number, multiply the denominator by that whole number, keeping the numerator the same.
- To find a percentage increase, work out the percentage of the amount and add it on; for a decrease, subtract it from the amount instead.
- To find the whole when given a fraction of it, divide the known part by its numerator to find one part (the value of one unit fraction), then multiply by the denominator.
- Convert between fractions, decimals and percentages where useful, to check your final answer is a sensible size.
Worked example
In a school, 3/8 of the pupils are boys, and there are 240 boys. How many pupils are in the school altogether?
- 3/8 of the pupils is 240, so first find what 1/8 of the pupils is worth: 240 divided by 3 = 80.
- So 1/8 of the pupils is 80 pupils.
- The whole school is 8/8, so multiply the value of 1/8 by 8: 80 x 8 = 640.
- So there are 640 pupils in the school altogether. Check: 3/8 of 640 is 640 divided by 8 = 80, then 80 x 3 = 240, which matches.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1Work out 2/5 x 20.Show answer
Answer: 8
Q2Work out 3/4 x 1/2.Show answer
Answer: 3/8
Q3Work out 3/5 divided by 3.Show answer
Answer: 1/5
Q4A shop increases a 60 pounds price by 15%. What is the new price?Show answer
Answer: 69 pounds (15% of 60 is 9, and 60 + 9 = 69)
Q5A price of 80 pounds is reduced by 25%. What is the new price?Show answer
Answer: 60 pounds (25% of 80 is 20, and 80 - 20 = 60)
Q61/6 of a number is 14. What is the number?Show answer
Answer: 84
Exam-style questions
Written in the style of a KS2 Maths exam paper, with a full mark scheme.
A car costs 12000 pounds. Its value decreases by 15% in the first year. Work out the car's value after one year.
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2/9 of the sweets in a bag are red. There are 18 red sweets. a) How many sweets are in the bag altogether? b) 1/3 of the remaining (non-red) sweets are green. How many green sweets are there?
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Free printable worksheet
Want more practice on paper? Download the fractions, decimals and percentages depth worksheet pack - 8 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.
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