Calculations with fractions, decimals and negatives · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Mixed and Improper Fractions

Mathematics · Fractions · ages 11-13
Name ______________________   Date ____________

  1. The improper fraction 11/4 is the same as the mixed number 2 3/4.

    Circle one:   True   False

  2. What is 2 3/4 + 5?

    • 7 3/4
    • 6 3/4
    • 7 1/4
    • 8 3/4

  3. Which mixed number equals 9/4?

    • 2 1/4
    • 4 1/4
    • 2 1/2

  4. In a mixed number, a negative sign applies to the whole number and the fraction together, not just the whole number.

    Circle one:   True   False

  5. What is 3 2/5 written as an improper fraction?

    • 17/5
    • 15/5
    • 6/5
    • 32/5

  6. Work out 1 1/2 x 2/3.

    • 1
    • 1/3
    • 9/4

  7. Work out -1 1/2 + 3/4.

    • -1/4
    • 3/4
    • -3/4

  8. What is 2 1/4 written as an improper fraction? Type just the numerator (the denominator stays 4).

    Answer: ______________

  9. Work out -3/4 + 1/2 - 1 1/4 using written methods.

    • 1 1/2
    • -2 1/2
    • -1 1/2

  10. Nina works out -1 1/2 as -1 + 1/2, getting -1/2. What went wrong?

    • She used the wrong denominator
    • She made only the whole number negative, not the whole mixed number
    • She added the numerators without a common denominator
LightMySky · lightmysky.comW1-mt_gNUE4B3vuk-s1

Answer key

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

Mixed and Improper Fractions W1-mt_gNUE4B3vuk-s1

  1. True · Divide 11 by 4 and you get 2 with a remainder of 3, which becomes 2 3/4.
  2. 7 3/4 · When you add a mixed number and a whole number, the fraction part stays the same.
  3. 2 1/4 · 9 divided by 4 is 2 with remainder 1, so 9/4 = 2 1/4.
  4. True · -1 1/2 means -(1 1/2), which is -3/2. The whole mixed number is negative.
  5. 17/5 · Multiply the whole number by the denominator, add the numerator, and keep the same denominator.
  6. 1 · Convert 1 1/2 to 3/2, then multiply: 3/2 x 2/3 = 6/6 = 1.
  7. -3/4 · Convert -1 1/2 to -6/4, then add 3/4: -6/4 + 3/4 = -3/4.
  8. 9 · 2 x 4 = 8, then 8 + 1 = 9, so 2 1/4 = 9/4.
  9. -1 1/2 · Convert every term to quarters: -3/4 + 2/4 - 5/4 = -6/4, which simplifies to -1 1/2.
  10. She made only the whole number negative, not the whole mixed number · -1 1/2 means the whole amount is negative: -1 1/2 = -3/2. Splitting the sign from the fraction part changes the value.
Worksheet · LightMySky