Fractions, Decimals and Percentages Depth
Fractions, Decimals and Percentages Depth is a harder follow-on topic that mixes fractions, decimals and percentages within a single question, rather than testing each in isolation. It covers fluent conversion between all three forms, ordering mixed sets of FDP values on one scale, and multi-step problems such as finding a percentage of a fraction of an amount, which are common in GL Assessment and CEM style papers.
Method
- Convert every value in the question to the same form (usually fraction or decimal) before comparing or calculating, since FDP items are often set as a mix on purpose.
- Learn the standard conversions by heart: halves, quarters, fifths, eighths and tenths as both fractions and percentages, so simple ones need no working.
- For 'percentage of a fraction of an amount' questions, work through in order: fraction first, then percentage of the result, following the words of the question exactly.
- When ordering a mixed set of fractions, decimals and percentages, convert everything to a percentage (or a decimal out of 1) so all values share one scale.
- Check the answer against a friendly benchmark, such as whether it is close to a half or a quarter of the whole amount.
- For two-step word problems, underline the two operations required and complete them one at a time, writing down the mid-answer before using it in the next step.
Worked example
A school has 360 pupils. Three-fifths of the pupils walk to school. Of the pupils who walk, 25% also cycle on some days. How many pupils cycle on some days?
- Find how many pupils walk: 3/5 of 360 = 360 / 5 x 3 = 72 x 3 = 216.
- Find 25% of 216, the pupils who walk and also cycle: 25% = 1/4, so 216 / 4 = 54.
- Check the answer is sensible: 54 is a reasonable fraction, about 15%, of the whole school of 360.
- Final answer: 54 pupils cycle on some days.
Practice questions
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Q1Convert 7/10 to a percentage.Show answer
Answer: 70%
Q2Convert 0.35 to a fraction in its simplest form.Show answer
Answer: 35/100, which simplifies to 7/20
Q3Which is greater: 3/8 or 0.4?Show answer
Answer: 0.4 is greater (3/8 = 0.375, which is less than 0.4)
Q4Find 15% of 200.Show answer
Answer: 30 (10% = 20, 5% = 10, so 15% = 30)
Q5A jug holds 2/5 of a litre of juice. Write this amount as a decimal.Show answer
Answer: 0.4 litres
Q6Order these from smallest to largest: 0.6, 3/4, 55%.Show answer
Answer: 55%, 0.6, 3/4 (since 55% = 0.55 and 3/4 = 0.75)
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
In a class of 32 pupils, 1/4 are left-handed. Of the left-handed pupils, 50% also play a musical instrument. How many pupils in the class are both left-handed and play a musical instrument?
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A shop reduces a jacket priced at 60 pounds by 30%. Express the new price as a fraction of the original price, giving your answer in its simplest form.
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Free printable worksheet
Want more practice on paper? Download the fractions, decimals and percentages depth 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 30 of 11+ Maths Workbook 1, the whole course as one free printable PDF.
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