Dividing by Fractions · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Dividing a Whole Number by a Fraction

Mathematics · Fractions · ages 10-11
Name ______________________   Date ____________

  1. Mia says 9 ÷ 1/3 = 27. To check, she computes 27 × 1/3. True or false: her check gives 9, so her answer is correct.

    Circle one:   True   False

  2. What is 3 ÷ 1/4?

    Answer: ______________

  3. Which multiplication checks the answer to 10 ÷ 1/2 = 20?

    • 20 × 1/2 = 10
    • 20 × 2 = 40
    • 10 × 1/2 = 5
    • 20 ÷ 2 = 10

  4. True or false: 4 ÷ 1/5 is less than 4.

    Circle one:   True   False

  5. Compute 4 ÷ 1/5. Type the answer.

    Answer: ______________

  6. Leo has 2 meters of string. Each gift tag needs 1/8 meter of string. How many gift tags can he make?

    • 16
    • 4
    • 10
    • 6

  7. Mia has 6 metres of rope for a craft class. Each bracelet uses 1/4 metre. How many bracelets can she make?

    • 1.5
    • 24
    • 10

  8. Which story matches 6 ÷ 1/4?

    • A jug holds 6 liters of juice. Each glass holds 1/4 liter. How many glasses can you fill?
    • A jug holds 6 liters of juice. You pour it into 1/4 of a glass. How much is in the glass?
    • You fill 6 glasses with 1/4 liter each. How much juice did you use in all?
    • A jug holds 6 liters and you drink 1/4 liter. How much is left?

  9. Leo says, '4 ÷ 1/5 must be a small number because dividing always shrinks things.' What is his mistake?

    • He added 4 and 5
    • He mixed up fifths with fourths
    • He forgot that 4 ÷ 1/5 counts fifths, so its answer is bigger than 4

  10. Dan has 5 metres of rope. He cuts pieces that are 1/3 metre each. Type how many pieces he can cut.

    Answer: ______________

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Answer key

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

Dividing a Whole Number by a Fraction W1-mt_1PAWhRhpdg-s1

  1. True · 27 × 1/3 means 27 thirds, and 27 thirds make 9 wholes. The check works, so 27 is correct.
  2. 12 · Each whole fits 4 fourths, so 3 wholes fit 12 fourths. That is why the answer is bigger than 3.
  3. 20 × 1/2 = 10 · Division and multiplication undo each other, so 20 × 1/2 should give back the starting number 10. It does.
  4. False · 4 ÷ 1/5 = 20, and 20 is bigger than 4. Dividing by a small fraction makes the answer bigger, not smaller.
  5. 20 · Each of the 4 wholes breaks into 5 fifths, so 4 × 5 = 20 fifths in all.
  6. 16 · This is 2 ÷ 1/8. Each meter fits 8 eighths, so 2 meters fit 16 eighths. He can make 16 tags.
  7. 24 · 6 ÷ 1/4 asks how many fourths fit in 6 wholes: 6 × 4 = 24.
  8. A jug holds 6 liters of juice. Each glass holds 1/4 liter. How many glasses can you fill? · 6 ÷ 1/4 asks how many quarter liters fit in 6 liters. The answer is 6 × 4 = 24 glasses.
  9. He forgot that 4 ÷ 1/5 counts fifths, so its answer is bigger than 4 · Here, dividing 4 by 1/5 counts fifths, so the answer is greater than 4.
  10. 15 · 5 wholes cut into thirds give 5 × 3 = 15 equal pieces.
Worksheet · LightMySky