Mixed numbers and improper fractions · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Mixed numbers and improper fractions

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

  1. Write 2 1/4 as one fraction.

    • 7/4
    • 10/4
    • 9/4
    • 8/4

  2. Seven thirds make how many wholes and leftover thirds?

    • 3 wholes and 1 third
    • 2 wholes and 1 third
    • 2 wholes and 2 thirds
    • 1 whole and 1 third

  3. Which of these is an improper fraction?

    • 5/4
    • 3/4
    • 1/4

  4. A mixed number has a whole number and a fraction together, like 2 1/3.

    Circle one:   True   False

  5. To write 2 1/6 as one fraction with denominator 6, both the wholes and the extra part must be counted in sixths.

    Circle one:   True   False

  6. 6/5 + 4/5 = 10/5. What whole number does that equal?

    Answer: ______________

  7. When converting 11/4, which check proves that exactly two whole groups fit? Here, ≤ means 'less than or equal to'; < means 'less than'.

    • 4 ≤ 11 < 8
    • 12 ≤ 11 < 16
    • 8 ≤ 11 < 8
    • 8 ≤ 11 < 12

  8. A mixed number equals 17/5. Its fraction part is 2/5. What is its whole-number part?

    Answer: ______________

  9. Leo converts 2 3/5 to an improper fraction and writes 10/5. What did he forget to do?

    • Multiply the denominator by itself
    • Add the numerator (3) after multiplying
    • Divide instead of multiply

  10. Ari wants to write 16/7 as a finished mixed number with a proper fraction part. He writes 1 9/7 and says his conversion is finished.

    Circle one:   True   False

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Answer key

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

Mixed numbers and improper fractions W1-mt_o_p-3tCxiM-s1

  1. 9/4 · Two wholes contain eight quarters. The extra quarter makes nine quarters.
  2. 2 wholes and 1 third · Two groups of three thirds use six thirds. One third remains.
  3. 5/4 · In 5/4, the top number (5) is bigger than the bottom number (4), so it's improper.
  4. True · That's exactly what a mixed number is: a whole part plus a fraction part.
  5. True · A denominator of 6 counts sixths. The two wholes contain twelve sixths, and the extra sixth makes thirteen sixths: 13/6.
  6. 2 · 10 divided into groups of 5 makes exactly 2 whole groups, so 10/5 = 2.
  7. 8 ≤ 11 < 12 · Two groups use eight quarters. Three groups would need twelve, more than eleven.
  8. 3 · Remove the two extra fifths. The remaining fifteen fifths form three wholes.
  9. Add the numerator (3) after multiplying · He multiplied 2 x 5 = 10 but forgot to add the leftover 3, so it should be 13/5.
  10. False · The amounts match, but nine sevenths contain another whole. A finished mixed-number conversion needs a proper fraction part: 2 2/7.
Worksheet · LightMySky