Fractions, Decimals and Percentages
Fractions, Decimals and Percentages covers converting fluently between the three forms using known equivalents and by treating a fraction as a division, for example 3/8 means 3 divided by 8, then applying this to find a percentage of an amount or compare percentage changes.
Before you start
Make sure you're comfortable with these topics first:
Method
- Learn the standard fraction-decimal-percentage equivalents by heart (halves, quarters, fifths, eighths and tenths) so common conversions do not need to be calculated from scratch.
- To convert a fraction to a decimal when it is not a known equivalent, treat the fraction as a division and divide the numerator by the denominator.
- To convert a decimal to a percentage, multiply by 100; to convert a percentage to a decimal, divide by 100.
- To find a percentage of an amount, find 1% by dividing by 100, then multiply by the percentage required, or build up from 10% and 1% using addition and subtraction.
- To find what percentage one quantity is of another, divide the first quantity by the second and convert the resulting decimal to a percentage.
- When comparing amounts given in mixed forms (some as fractions, some as decimals, some as percentages), convert everything to the same form, usually decimals, before comparing.
- Show each conversion as a clear step, since many marks in this topic are awarded for a correct method even when the final answer has a small error.
Worked example
In a school of 350 pupils, 84 pupils walk to school. What percentage of the pupils walk to school?
- Write the amount that walks to school as a fraction of the whole school: 84/350.
- Simplify the fraction if possible: dividing both parts by 14 gives 6/25 (since 84 divided by 14 = 6 and 350 divided by 14 = 25).
- Convert the simplified fraction to a decimal by treating it as a division: 6 divided by 25 = 0.24.
- Convert the decimal to a percentage by multiplying by 100: 0.24 x 100 = 24.
- So 24% of the pupils walk to school.
Practice questions
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Q1Write 7/8 as a decimal.Show answer
Answer: 0.875
Q2Write 0.35 as a percentage.Show answer
Answer: 35%
Q3Find 45% of 260.Show answer
Answer: 117
Q4Out of 24 counters in a bag, 9 are red. What percentage of the counters are red?Show answer
Answer: 37.5%
Q5Write these in order from smallest to largest: 3/8, 0.4, 30%.Show answer
Answer: 30%, 3/8, 0.4
Q6A price of 72 pounds is increased by 15%. Work out the new price.Show answer
Answer: 82.80 pounds
Q7A jug holds 2 litres. 650ml is poured out. What percentage of the jug's contents is poured out?Show answer
Answer: 32.5%
Exam-style questions
Written in the style of a KS2 Maths exam paper, with a full mark scheme.
Write 5/8 as a percentage.
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In a survey of 150 people, 42% said their favourite fruit was strawberries. Work out how many people said strawberries.
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Two market stalls sell the same type of bicycle. Stall A sells the bicycle for 180 pounds and reduces the price by 15% in a sale. Stall B sells the same bicycle for 190 pounds and reduces the price by 20% in a sale. Work out which stall has the cheaper sale price, and by how much.
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Tick each line you got. Your score builds from the marks on the scheme.
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Free printable worksheet
Want more practice on paper? Download the fractions, decimals and percentages worksheet pack - 6 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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