Comparing and Ordering Fractions, Decimals and Percentages
Comparing and ordering fractions, decimals and percentages means converting values written in different forms into a single common form so they can be placed accurately in order. This is a distinct 11+ reasoning skill from calculating with fractions, decimals or percentages separately, because the challenge is recognising which of several mixed-format values is bigger or smaller, often under strict time pressure with no calculator allowed.
Method
- Convert every value in the list to the same form, usually decimals, so they can be compared directly.
- To convert a fraction to a decimal, divide the numerator by the denominator, or recall a known equivalent such as 1/4 = 0.25.
- To convert a percentage to a decimal, divide by 100 by moving the decimal point two places to the left.
- Learn common fraction, decimal and percentage equivalents by heart (halves, quarters, fifths, tenths, eighths) to save time in the exam.
- Once every value is in the same form, order them by comparing digit by digit starting from the largest place value.
- Convert the ordered list back to its original form only if the question specifically asks for that.
Worked example
Put these in order, smallest first: 3/5, 0.52, 55%, 0.5.
- Convert 3/5 to a decimal: 3 divided by 5 = 0.6.
- Convert 55% to a decimal: 55 divided by 100 = 0.55.
- Compare all four values as decimals: 0.6, 0.52, 0.55, 0.5.
- Order the decimals from smallest to largest: 0.5, 0.52, 0.55, 0.6.
- Match each decimal back to its original value: 0.5, 0.52, 55%, 3/5.
Practice questions
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Q1Convert 7/20 to a decimal.Show answer
Answer: 0.35
Q2Convert 0.08 to a percentage.Show answer
Answer: 8%
Q3Which is larger, 2/3 or 68%?Show answer
Answer: 68% (2/3 = 0.666..., which is less than 0.68)
Q4Order these from smallest to largest: 1/4, 0.3, 20%.Show answer
Answer: 20%, 1/4, 0.3 (0.2, 0.25, 0.3)
Q5True or False: 0.75 is the same value as 3/4.Show answer
Answer: True
Q6Write 9/25 as a percentage.Show answer
Answer: 36% (9/25 = 36/100)
Q7Explain why it can be easier to compare fractions with different denominators by first converting them to decimals, rather than finding a common denominator.Show answer
Answer: Converting to decimals puts every value into the same base-10 place-value system, so they can be compared digit by digit directly, which is especially useful when comparing more than two fractions at once instead of finding one common multiple for several different denominators.
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
Four students record the fraction of their homework they have completed: Amit 5/8, Bea 0.6, Cho 58%, Dev 13/20. Put the four students in order from the least homework completed to the most, showing your working.
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A charity shop prices three identical books differently: Shop A prices a book at 3/4 of 8 pounds, Shop B prices it at 70% of 8 pounds, and Shop C prices it at 0.8 x 8 pounds. Work out each price, and state which shop is cheapest.
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Free printable worksheet
Want more practice on paper? Download the comparing and ordering 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.
This topic is chapter 42 of 11+ Maths Workbook 1, the whole course as one free printable PDF.
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