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Math 8

Math 8 · Worksheets

Multiplying and dividing fractions

Ten questions of mixed difficulty, covering Fractions. Print it, or work through it on screen — the answer key starts on its own page.

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Multiplying and dividing fractions

Math 8 · maddyhelps.com

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Circle the best answer for each question. Show your work in the space provided.

  1. 1½ × 2⅔ equals

    1. a) 2⅓
    2. b) 4
    3. c) ⅓
    4. d) 4 1/6

  2. Mia has 5 cups of juice. Each glass holds ⅔ cup. How many glasses can she fill, and how much juice is left over?

    1. a) 3 glasses, with ⅓ cup left over
    2. b) 8 glasses, with nothing left over
    3. c) 7 glasses, with ⅓ cup left over
    4. d) 7 glasses, with ½ cup left over

  3. 3¾ ÷ 1½ equals

    1. a) 2/5
    2. b) 5 5/8
    3. c) 2½
    4. d) 4½

  4. 3/4 ÷ 1/8 equals

    1. a) 6
    2. b) 32/3
    3. c) 1/6
    4. d) 3/32

  5. 2/3 × 3/5 equals

    1. a) 19/15
    2. b) 5/8
    3. c) 10/9
    4. d) 2/5

  6. 4 × 2/3 equals

    1. a) 4 2/3
    2. b) 8/12
    3. c) 1/6
    4. d) 2 2/3

  7. How many ⅓-cup scoops of rice are in 4 cups of rice?

    1. a) 1⅓
    2. b) 7
    3. c) 12
    4. d) 1/12

  8. In a class, ⅔ of the students play a sport, and ¾ of those play hockey. What fraction of the class plays hockey?

    1. a) 1/12
    2. b) 8/9
    3. c) ½
    4. d) 1 5/12

  9. A board 5¼ m long is cut into pieces that are each ¾ m long. How many pieces are there?

    1. a) 3 15/16
    2. b) 7
    3. c) 4½
    4. d) 1/7

  10. Without calculating, which of these is less than 6?

    1. a) 6 ÷ 4/5
    2. b) 6 × 4/5
    3. c) 6 ÷ 1/3
    4. d) 6 × 5/4

Answer key · Multiplying and dividing fractions

Math 8 · maddyhelps.com

  1. b) 4 — Change to improper fractions: 3/2 × 8/3 = 24/6 = 4. Multiplying the whole numbers and the fractions separately gives 1 × 2 + ½ × ⅔ = 2⅓, which misses the cross parts, 1 × ⅔ and ½ × 2 — another 1⅔. 4 1/6 adds instead of multiplying.
  2. c) 7 glasses, with ⅓ cup left over — 5 ÷ ⅔ = 5 × 3/2 = 7½, so 7 glasses fill and half a glass is left. Half a glass is half of ⅔ cup, which is ⅓ cup — check: 7 × ⅔ = 4⅔, and 5 − 4⅔ = ⅓. Reading the ½ in 7½ as half a cup is the usual slip: it is half of one glass.
  3. c) 2½ — Change to improper fractions and multiply by the reciprocal: 15/4 × 2/3 = 30/12 = 2½. Check: 1½ × 2½ = 3¾ ✓. Dividing the whole numbers and the fractions separately, 3 ÷ 1 and ¾ ÷ ½, gives 3 + 1½ = 4½ — that shortcut fails for dividing just as it does for multiplying.
  4. a) 6 — Dividing by 1/8 asks how many eighths fit into 3/4. 3/4 = 6/8, so the answer is 6 — the same as 3/4 × 8/1 = 24/4. 3/32 multiplies without flipping, and 1/6 flips the first fraction instead of the second.
  5. d) 2/5 — Multiply the numerators and the denominators: (2 × 3)/(3 × 5) = 6/15 = 2/5. 10/9 cross-multiplies, which is the answer to 2/3 ÷ 3/5, and 19/15 adds the fractions. Taking 2/3 of 3/5 must give less than 3/5, and 2/5 does.
  6. d) 2 2/3 — 4 × 2/3 is four lots of 2/3: 2/3 + 2/3 + 2/3 + 2/3 = 8/3 = 2 2/3. 8/12 multiplies the denominator by 4 as well, which only renames 2/3, and 4 2/3 puts the 4 beside the fraction instead of multiplying.
  7. c) 12 — Each cup holds 3 scoops of ⅓ cup, so 4 cups hold 4 × 3 = 12: that is 4 ÷ ⅓ = 12. 1⅓ multiplies 4 by ⅓, which finds a third of the rice, not the number of scoops, and 1/12 divides the wrong way round.
  8. c) ½ — ¾ of the ⅔ who play a sport is ¾ × ⅔ = 6/12 = ½ of the class. Adding the fractions gives 1 5/12 — more than the whole class — and 1/12 subtracts them; 'of' means multiply.
  9. b) 7 — How many ¾ m pieces fit into 5¼ m is a division: 5¼ ÷ ¾ = 21/4 ÷ 3/4 = 21 ÷ 3 = 7. Check: 7 × ¾ = 21/4 = 5¼ ✓. 3 15/16 multiplies instead, but pieces shorter than 1 m must number more than 5, and 4½ subtracts one piece.
  10. b) 6 × 4/5 — Multiplying by a fraction less than 1 takes only part of the number, so 6 × 4/5 = 4 4/5 is less than 6. Dividing by 4/5 asks how many 4/5s fit into 6, which is more than 6 (7½). Multiplying does not always make a number bigger, and dividing does not always make it smaller — it depends on whether the other number is more or less than 1.