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Ordering fractions

Put three fractions in order from least to greatest.

Practice + answer key · 2 pages

Worksheet settings10 questions · 2 columns · A4
Denominator range

All three denominators use these bounds; their shared denominator can be larger.

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Ordering fractionsOrdering fractions. Practice. Order these fractions from least to greatest: 5/8, 2/3, 2/3. Order these fractions from least to greatest: 1/5, 3/5, 1/3. Order these fractions from least to greatest: 1/3, 1/3, 1/7. Order these fractions from least to greatest: 4/7, 4/6, 4/5. Order these fractions from least to greatest: 2/5, 4/5, 4/6. Order these fractions from least to greatest: 3/8, 5/6, 2/3. Order these fractions from least to greatest: 2/6, 1/7, 6/7. Order these fractions from least to greatest: 6/7, 7/8, 1/2. Order these fractions from least to greatest: 1/3, 3/5, 4/8. Order these fractions from least to greatest: 4/7, 2/7, 5/8.Name __________________________Date _______________Ordering fractionsWrite the fractions in order from least to greatest.Worked exampleOrder 3/4, 1/2 and 2/3 from least to greatest. → 1/2, 2/3, 3/4A common denominator is 12.1.Order these fractions from leastto greatest: 5/8, 2/3, 2/3.2.Order these fractions from leastto greatest: 1/5, 3/5, 1/3.3.Order these fractions from leastto greatest: 1/3, 1/3, 1/7.4.Order these fractions from leastto greatest: 4/7, 4/6, 4/5.5.Order these fractions from leastto greatest: 2/5, 4/5, 4/6.6.Order these fractions from leastto greatest: 3/8, 5/6, 2/3.7.Order these fractions from leastto greatest: 2/6, 1/7, 6/7.8.Order these fractions from leastto greatest: 6/7, 7/8, 1/2.9.Order these fractions from leastto greatest: 1/3, 3/5, 4/8.10.Order these fractions from leastto greatest: 4/7, 2/7, 5/8.MathSprig · mathsprig.site · support@mathsprig.sitePage 1 of 1mathsprig-1 · mathsprig-v1 · beac4ab7
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Practice + answer key · 2 pages

Fractions

What you’ll practice

Order a set of three positive proper fractions from least to greatest.

Rewrite the fractions with a common denominator so their parts are the same size. Compare the new numerators, then list the original fractions in that order.

How this skill works

Find a denominator that is a common multiple of all three denominators. Rewrite each fraction with that denominator, keeping its value unchanged.

Compare the new numerators, then list the original fractions in the same order. Equal fractions may be placed in either order next to one another.

Worked example

Order 3/4, 1/2 and 2/3 from least to greatest.
  1. A common denominator is 12.
  2. 3/4 = 9/12, 1/2 = 6/12 and 2/3 = 8/12.
  3. Since 6 < 8 < 9, the order is 1/2, 2/3, 3/4.

Answer: 1/2, 2/3, 3/4

Teaching notes

  • Keep each rewritten fraction beside its original to avoid swapping labels.
  • Retain all three entries, including repeated or equal-valued fractions.
Practice questions
  1. Order these fractions from least to greatest: 5/8, 2/3, 2/3.
  2. Order these fractions from least to greatest: 1/5, 3/5, 1/3.
  3. Order these fractions from least to greatest: 1/3, 1/3, 1/7.
  4. Order these fractions from least to greatest: 4/7, 4/6, 4/5.
  5. Order these fractions from least to greatest: 2/5, 4/5, 4/6.
  6. Order these fractions from least to greatest: 3/8, 5/6, 2/3.
  7. Order these fractions from least to greatest: 2/6, 1/7, 6/7.
  8. Order these fractions from least to greatest: 6/7, 7/8, 1/2.
  9. Order these fractions from least to greatest: 1/3, 3/5, 4/8.
  10. Order these fractions from least to greatest: 4/7, 2/7, 5/8.
Answers and steps
  1. 5/8, 2/3, 2/3
    1. Use the common denominator 24: 15/24, 16/24, 16/24.
    2. Compare the numerators, giving 5/8, 2/3, 2/3 from least to greatest.
  2. 1/5, 1/3, 3/5
    1. Use the common denominator 15: 3/15, 9/15, 5/15.
    2. Compare the numerators, giving 1/5, 1/3, 3/5 from least to greatest.
  3. 1/7, 1/3, 1/3
    1. Use the common denominator 21: 7/21, 7/21, 3/21.
    2. Compare the numerators, giving 1/7, 1/3, 1/3 from least to greatest.
  4. 4/7, 4/6, 4/5
    1. Use the common denominator 210: 120/210, 140/210, 168/210.
    2. Compare the numerators, giving 4/7, 4/6, 4/5 from least to greatest.
  5. 2/5, 4/6, 4/5
    1. Use the common denominator 30: 12/30, 24/30, 20/30.
    2. Compare the numerators, giving 2/5, 4/6, 4/5 from least to greatest.
  6. 3/8, 2/3, 5/6
    1. Use the common denominator 24: 9/24, 20/24, 16/24.
    2. Compare the numerators, giving 3/8, 2/3, 5/6 from least to greatest.
  7. 1/7, 2/6, 6/7
    1. Use the common denominator 42: 14/42, 6/42, 36/42.
    2. Compare the numerators, giving 1/7, 2/6, 6/7 from least to greatest.
  8. 1/2, 6/7, 7/8
    1. Use the common denominator 56: 48/56, 49/56, 28/56.
    2. Compare the numerators, giving 1/2, 6/7, 7/8 from least to greatest.
  9. 1/3, 4/8, 3/5
    1. Use the common denominator 120: 40/120, 72/120, 60/120.
    2. Compare the numerators, giving 1/3, 4/8, 3/5 from least to greatest.
  10. 2/7, 4/7, 5/8
    1. Use the common denominator 56: 32/56, 16/56, 35/56.
    2. Compare the numerators, giving 2/7, 4/7, 5/8 from least to greatest.