Fractions, Decimals and Percentages Depth Set 2
Fractions, Decimals and Percentages Depth Set 2 continues the harder, blended style of question found in the first FDP Depth set, mixing 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, common in GL Assessment and CEM style papers.
Before you start
Make sure you're comfortable with these topics first:
Method
- Convert every value in a question into the same form, usually a decimal or a percentage, before comparing or calculating with them together.
- Keep the standard conversions, halves, quarters, fifths, eighths and tenths as fractions, decimals and percentages, ready to use without working them out each time.
- For 'percentage of a fraction of an amount', or the reverse, complete the operations strictly in the order given in the question.
- When ordering a mixed set of fractions, decimals and percentages, convert everything onto one common scale, usually a percentage, before placing them in order.
- Sense-check every answer against a simple benchmark, such as whether it is close to a half, a quarter or a tenth of the starting amount.
- For two-step or three-step word problems, write down the result of each step before using it in the next, so an error in one step is easy to trace.
Worked example
A concert hall has 450 seats. Two-fifths of the seats are in the stalls. Of the seats in the stalls, 40% are already booked. How many seats in the stalls are still available?
- Find the number of seats in the stalls: 2/5 of 450 = 450 / 5 x 2 = 90 x 2 = 180.
- Find how many of the stalls seats are booked: 40% of 180 = 0.4 x 180 = 72.
- Subtract the booked seats from the stalls total to find those still available: 180 - 72.
- Check the size is sensible: 108 is a little more than half of 180, which fits with 40% being booked.
- The final answer is 108 seats.
Practice questions
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Q1Convert 9/20 to a percentage.Show answer
Answer: 45%
Q2Convert 0.28 to a fraction in its simplest form.Show answer
Answer: 28/100, which simplifies to 7/25
Q3Which is greater: 5/8 or 0.6?Show answer
Answer: 5/8 is greater (5/8 = 0.625, which is more than 0.6)
Q4Find 35% of 160.Show answer
Answer: 56 (10% = 16, 30% = 48, 5% = 8, 48 + 8 = 56)
Q5A bottle holds 3/8 of a litre of oil. Write this amount as a decimal.Show answer
Answer: 0.375 litres
Q6Order these from smallest to largest: 0.45, 2/5, 48%.Show answer
Answer: 2/5, 0.45, 48% (since 2/5 = 0.4 and 48% = 0.48)
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
In a class of 36 pupils, 1/3 are in the school choir. Of the choir members, 25% also play a musical instrument. How many pupils in the class are both in the choir and play a musical instrument?
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A shop reduces a coat priced at 80 pounds by 35%. Express the new price as a fraction of the original price, giving your answer in its simplest form.
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A school raises 540 pounds at a fair. Three-fifths of the money is spent on new sports equipment, and 20% of what remains is donated to a local charity. Work out how much money is left after the equipment purchase and the donation.
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Free printable worksheet
Want more practice on paper? Download the fractions, decimals and percentages depth set 2 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 31 of 11+ Maths Workbook 1, the whole course as one free printable PDF.
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