Fractions
Why Are Fractions So Hard for Children?
Why children struggle to compare fractions, how to recognise common mistakes, and ways to build understanding of fraction size.
Fraction Ordering Practice Test Worksheets
Fraction ordering questions test whether you can compare several fractions accurately, even when the denominators are different or some fractions are greater than one.
For students who know fractions, but lose marks comparing unlike denominators, mixed numbers, and close values.
Printable practice test worksheets
3 Test Sets — 30 questions per set
Full answer keys included
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What Do Fraction Ordering Questions Look Like?
Fraction ordering questions test whether you can compare several fractions accurately, even when the denominators are different or some fractions are greater than one. Students are given a list of fractions and must convert them to a common denominator to arrange them from smallest to largest. Here is a worked example.
Example
Convert to a Common Denominator
Question: Order 56, 724, and 58 from smallest to largest.
Worked Method
Step 1: Use common denominator 24.
Step 2: Convert: 56 = 2024, 724 stays 724, and 58 = 1524.
Step 3: Compare numerators: 7 < 15 < 20.
Answer: 724, 58, 56.
Rules to Help You Solve Fraction Ordering Questions
To solve fraction ordering questions like the example above, convert all fractions to a common denominator and compare their numerators directly.
🧮 Rule 1: Use a common denominator
Choose a common multiple of the denominators, usually the lowest common multiple. Multiply both the numerator and denominator by the same number to keep each fraction’s value unchanged.
Example: 24 is a common multiple of 6, 8, and 24. To convert sixths to twenty-fourths: 56 = 5 × 46 × 4 = 2024.
🔢 Rule 2: Compare numerators
When denominators are the same, the fraction with the smaller numerator is smaller.
Example: 724 < 1524 < 1924.
🚩 Rule 3: Watch improper fractions
When ordering smallest to largest, fractions greater than 1 come after fractions less than 1. Compare fractions within each group exactly.
Example: 1712 = 3424, so it is larger than 56.
🎯 Rule 4: Use benchmarks as a check
Benchmarks like 12 and 1 help you check whether your order makes sense before finalising it.
Example: 724 is below 12, while 1712 is above 1.
Two More Worked Examples
Here are two more examples showing how to order sets containing improper fractions and larger groups of fractions.
Example
Include an Improper Fraction
Question: Order 58, 1924, 1712 from smallest to largest.
Convert all three to twenty-fourths
58 = 152419241712 = 3424
1524 < 1924 < 3424
Multiplying both the numerator and denominator of 17/12 by 2 gives 34/24. These are two ways of writing the same amount, and both are greater than 1.
Worked Method
Step 1: Use common denominator 24.
Step 2: 58 = 1524, 1924 stays 1924, and 1712 = 3424.
Step 3: Compare the numerators: 15 < 19 < 34.
Answer: 58 < 1924 < 1712.
Tip: Here, 17/12 is greater than 1 and the other two fractions are less than 1, so 17/12 must be last.
Example
Order Five Fractions, Including Values Above 1
Question: Order 1112, 43, 1712, 16, 3524 from smallest to largest.
Compare all five in twenty-fourths
424<2224<3224<3424<3524
Worked Method
Step 1: The lowest common multiple of 12, 3, 6 and 24 is 24.
Step 2: Convert each fraction: 1112 = 2224, 43 = 3224, 1712 = 3424, 16 = 424, 3524 = 3524.
Step 3: Compare the numerators: 4 < 22 < 32 < 34 < 35.
Answer: 16 < 1112 < 43 < 1712 < 3524.
Tip: The last three fractions are all greater than 1. That benchmark separates them from the first two, but you still need an exact comparison to order them.