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Comparing fractions

Use <, > or = to compare the values of two fractions.

Practice + answer key · 2 pages

Worksheet settings12 questions · 2 columns · A4
Denominator range

Each original denominator is within the bounds. Numerators are positive and smaller than their own denominator.

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Comparing fractionsComparing fractions. Practice. Fill the box with <, > or =: 3/8 □ 8/9. Fill the box with <, > or =: 6/8 □ 5/6. Fill the box with <, > or =: 1/2 □ 4/9. Fill the box with <, > or =: 1/4 □ 4/5. Fill the box with <, > or =: 1/10 □ 2/3. Fill the box with <, > or =: 1/6 □ 2/6. Fill the box with <, > or =: 1/2 □ 2/7. Fill the box with <, > or =: 8/9 □ 2/3. Fill the box with <, > or =: 1/2 □ 1/2. Fill the box with <, > or =: 3/6 □ 8/10. Fill the box with <, > or =: 1/8 □ 3/9. Fill the box with <, > or =: 8/9 □ 5/6.Name __________________________Date _______________Comparing fractionsWrite <, > or = between each pair of fractions.Worked exampleCompare 2/3 and 3/5. → >Cross-multiply: 2 × 5 = 10 and 3 × 3 = 9.1.Fill the box with <, > or =: 3/8□ 8/9.2.Fill the box with <, > or =: 6/8□ 5/6.3.Fill the box with <, > or =: 1/2□ 4/9.4.Fill the box with <, > or =: 1/4□ 4/5.5.Fill the box with <, > or =: 1/10□ 2/3.6.Fill the box with <, > or =: 1/6□ 2/6.7.Fill the box with <, > or =: 1/2□ 2/7.8.Fill the box with <, > or =: 8/9□ 2/3.9.Fill the box with <, > or =: 1/2□ 1/2.10.Fill the box with <, > or =: 3/6□ 8/10.11.Fill the box with <, > or =: 1/8□ 3/9.12.Fill the box with <, > or =: 8/9□ 5/6.MathSprig · mathsprig.site · support@mathsprig.sitePage 1 of 1mathsprig-1 · mathsprig-v1 · e00353e8
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Practice + answer key · 2 pages

Fractions

What you’ll practice

Choose <, > or = by comparing two positive proper fractions.

A larger numerator does not always mean a larger fraction. Give the fractions a common denominator, or compare their cross-products, to decide which value is greater.

How this skill works

Fractions with different denominators name different-sized parts. Compare equivalent forms with a common denominator, or compare the cross-products of the original pair.

For positive denominators, a/b and c/d have the same comparison as a × d and c × b. Equal cross-products mean equal fraction values.

Worked example

Compare 2/3 and 3/5.
  1. Cross-multiply: 2 × 5 = 10 and 3 × 3 = 9.
  2. 10 > 9, so 2/3 > 3/5.

Answer: >

Teaching notes

  • Do not compare only the top numbers when denominators differ.
  • Equal-valued pairs are possible even if the written fractions differ.
Practice questions
  1. Fill the box with <, > or =: 3/8 □ 8/9.
  2. Fill the box with <, > or =: 6/8 □ 5/6.
  3. Fill the box with <, > or =: 1/2 □ 4/9.
  4. Fill the box with <, > or =: 1/4 □ 4/5.
  5. Fill the box with <, > or =: 1/10 □ 2/3.
  6. Fill the box with <, > or =: 1/6 □ 2/6.
  7. Fill the box with <, > or =: 1/2 □ 2/7.
  8. Fill the box with <, > or =: 8/9 □ 2/3.
  9. Fill the box with <, > or =: 1/2 □ 1/2.
  10. Fill the box with <, > or =: 3/6 □ 8/10.
  11. Fill the box with <, > or =: 1/8 □ 3/9.
  12. Fill the box with <, > or =: 8/9 □ 5/6.
Answers and steps
  1. <
    1. Compare cross-products: 3 × 9 = 27, and 8 × 8 = 64. Since 27 < 64, the same comparison holds for the fractions.
  2. <
    1. Compare cross-products: 6 × 6 = 36, and 5 × 8 = 40. Since 36 < 40, the same comparison holds for the fractions.
  3. >
    1. Compare cross-products: 1 × 9 = 9, and 4 × 2 = 8. Since 9 > 8, the same comparison holds for the fractions.
  4. <
    1. Compare cross-products: 1 × 5 = 5, and 4 × 4 = 16. Since 5 < 16, the same comparison holds for the fractions.
  5. <
    1. Compare cross-products: 1 × 3 = 3, and 2 × 10 = 20. Since 3 < 20, the same comparison holds for the fractions.
  6. <
    1. Compare cross-products: 1 × 6 = 6, and 2 × 6 = 12. Since 6 < 12, the same comparison holds for the fractions.
  7. >
    1. Compare cross-products: 1 × 7 = 7, and 2 × 2 = 4. Since 7 > 4, the same comparison holds for the fractions.
  8. >
    1. Compare cross-products: 8 × 3 = 24, and 2 × 9 = 18. Since 24 > 18, the same comparison holds for the fractions.
  9. =
    1. Compare cross-products: 1 × 2 = 2, and 1 × 2 = 2. Since 2 = 2, the same comparison holds for the fractions.
  10. <
    1. Compare cross-products: 3 × 10 = 30, and 8 × 6 = 48. Since 30 < 48, the same comparison holds for the fractions.
  11. <
    1. Compare cross-products: 1 × 9 = 9, and 3 × 8 = 24. Since 9 < 24, the same comparison holds for the fractions.
  12. >
    1. Compare cross-products: 8 × 6 = 48, and 5 × 9 = 45. Since 48 > 45, the same comparison holds for the fractions.