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

Fractions as pieces added together

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

  1. 5/8 is the same as which sum?

    • 1/8 + 1/8 + 1/8 + 1/8
    • 1/8 + 1/8 + 1/8 + 1/8 + 1/8
    • 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8

  2. Amara says 7/4 means seven copies of 1/4 added together. Is Amara right?

    Circle one:   True   False

  3. A frog jumps 1/8 metre five times in a row. How far does it travel in metres? Give your answer as a decimal.

    Answer: ______________

  4. Which sum equals 3/5?

    • 1/5 + 1/5 + 1/5
    • 1/5 + 1/5
    • 1/5 + 1/5 + 1/5 + 1/5

  5. Noah ate 3/8 of a pie. His brother ate 2/8 of the same pie. How much did they eat altogether?

    • 5/8 of the pie
    • 5/16 of the pie
    • 6/8 of the pie
    • 1/8 of the pie

  6. What is 7/4 as a decimal?

    Answer: ______________

  7. Which fraction do you get by putting four 1/3 pieces end to end on a number line?

    • 3/4
    • 1/12
    • 2/3
    • 4/3

  8. A pizza is cut into 6 equal slices. Zoe eats 4 slices. Which sum shows how much she ate?

    • 1/6 + 1/6 + 1/6 + 1/6
    • 1/6 + 1/6 + 1/6
    • 1/6 + 1/6 + 1/6 + 1/6 + 1/6

  9. Tom says 7/4 is impossible because you can't have more pieces than a whole. Is Tom right?

    • Yes, a fraction can never be bigger than 1
    • No, 7/4 just means seven 1/4 pieces, even though that's more than one whole
    • No, 7/4 actually means 4/7

  10. Lena says 7/4 is greater than 2. Is Lena right?

    Circle one:   True   False

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Answer key

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

Fractions as pieces added together W1-mt_09sySPqM9Z-s1

  1. 1/8 + 1/8 + 1/8 + 1/8 + 1/8 · The top number, 5, tells you how many 1/8 pieces to add.
  2. True · Amara is right: 7/4 is seven quarters joined together.
  3. 0.625 · Five jumps of 1/8 m cover 5/8 m, which is 0.625 m.
  4. 1/5 + 1/5 + 1/5 · 3/5 means three copies of 1/5, so you add 1/5 three times.
  5. 5/8 of the pie · 3/8 + 2/8 = 5/8 of the pie.
  6. 1.75 · 7/4 equals 1.75.
  7. 4/3 · Four copies of 1/3 make 4/3.
  8. 1/6 + 1/6 + 1/6 + 1/6 · Zoe ate 4 of the 6 slices, so you add four copies of 1/6.
  9. No, 7/4 just means seven 1/4 pieces, even though that's more than one whole · A fraction counts unit pieces. Having seven 1/4 pieces just means more than one whole, which is fine.
  10. False · Lena is wrong: 7/4 equals 1.75, which is less than 2.
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