Comparing fractions (age 9+) · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Comparing fractions with different denominators

Mathematics · Fractions · ages 9-10
Name ______________________   Date ____________

  1. Is 3/7 more than one-half, less than one-half, or exactly one-half?

    • More than one-half
    • Less than one-half
    • Exactly one-half

  2. True or false: 5/8 is greater than 3/7.

    Circle one:   True   False

  3. Which fraction is bigger: 3/5 or 3/7?

    • 3/5
    • 3/7
    • They are equal
    • There is no way to tell

  4. What is the smallest common denominator for 3/8 and 5/12?

    • 20
    • 24
    • 48

  5. Put these fractions in order from smallest to largest: 2/5, 1/2, 3/4.

    • 2/5, 1/2, 3/4
    • 1/2, 2/5, 3/4
    • 3/4, 1/2, 2/5
    • 2/5, 3/4, 1/2

  6. Which fraction is bigger: 4/6 or 5/8?

    • 4/6
    • 5/8
    • They are equal
    • There is no way to tell

  7. Which fraction is bigger: 3/4 or 2/3?

    • 3/4
    • 2/3
    • They are equal
    • There is no way to tell

  8. Which fraction is bigger: 5/8 or 3/7?

    • 5/8
    • 3/7
    • They are equal

  9. Without finding a common denominator, how can you tell that 7/10 is bigger than 2/5?

    • 7 is a bigger number than 2
    • 10 is a bigger number than 5
    • 7/10 is more than half, and 2/5 is less than half

  10. Jamal compared 3/8 and 5/12 by just looking at the top numbers and said 5/12 is bigger because 5 is more than 3. What's wrong with his reasoning, even though his answer happens to be correct?

    • Top numbers only compare fairly once the denominators match
    • He should have compared the bottom numbers instead
    • He needed to add the two fractions together
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Comparing fractions with different denominators W1-mt_SXbZ3bC9z7-s1

  1. Less than one-half · Half of 7 is 3.5, and 3 is less than 3.5, so 3/7 falls just under one-half.
  2. True · 5/8 is more than 1/2, and 3/7 is less than 1/2, so the statement is true.
  3. 3/5 · When the numerators are the same, the fraction with the smaller denominator is bigger, so 3/5 is bigger than 3/7.
  4. 24 · 8 and 12 both divide evenly into 24, and it's the smallest number that works for both.
  5. 2/5, 1/2, 3/4 · Compare each fraction to 1/2. 2/5 is less than 1/2 and 3/4 is more than 1/2, so the order is 2/5, 1/2, 3/4.
  6. 4/6 · First reduce 4/6 to 2/3, then use the common denominator 24: 2/3 is 16/24 and 5/8 is 15/24, so 4/6 is bigger.
  7. 3/4 · Using the common denominator 12, 3/4 becomes 9/12 and 2/3 becomes 8/12, so 3/4 is bigger.
  8. 5/8 · 5/8 is more than half (half of 8 is 4), while 3/7 is less than half (half of 7 is 3.5), so 5/8 is bigger.
  9. 7/10 is more than half, and 2/5 is less than half · Half of 10 is 5, and 7 is more than 5, so 7/10 is over one-half. Half of 5 is 2.5, and 2 is less than that, so 2/5 is under one-half.
  10. Top numbers only compare fairly once the denominators match · 5/12 is bigger, but not just because 5 is more than 3. Once the denominators match (9/24 vs 10/24), the top numbers compare fairly.
Worksheet · LightMySky