Compare and order fractions
Objective. Compare fractions using common denominators and benchmarks.
- 1. Learn
- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: the key idea
Comparing fractions means deciding which of two or more fractions is bigger, which usually requires rewriting them with a common denominator first. To compare 3/4 and 5/6, convert both to twelfths: 3/4=9/12 and 5/6=10/12, showing 5/6 is larger. Benchmark fractions like 1/2 also help with quick comparisons, since any fraction with a numerator more than half its denominator is bigger than 1/2. Ordering several fractions follows the same idea: find a common denominator for all of them, then compare the numerators directly. The fraction with the larger numerator, once denominators match, is the larger fraction.
Worked example
Order the fractions 2/3, 5/8 and 7/12 from smallest to largest.
- 1Find a common denominator: the LCM of 3, 8 and 12 is 24.
- 2Convert each fraction: 2/3=16/24, 5/8=15/24, 7/12=14/24.
- 3Compare numerators: 14 < 15 < 16.
- 4Translate back to the original fractions in order.
Answer: 7/12, 5/8, 2/3
Concept mastery
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Practice
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Start practisingCommon mistake. Pupils often compare numerators alone, thinking 3/8 is bigger than 1/2 because 3 is more than 1. Always convert to a common denominator before comparing numerators.
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