Dividing fractions worksheet

Part A: Working out and filling in

1. 1. 16 ÷ 2 = 112

   16 ÷ 2: dividing by 2 is multiplying by 12: the numerator stays, the denominator 6 × 2 = 12 → 112, already in simplest form

2. 2. 49 ÷ 8 = 118

   49 ÷ 8: dividing by 8 is multiplying by 18: the numerator stays, the denominator 9 × 8 = 72 → 472; simplify, dividing the numerator and denominator by 4: 4 ÷ 4 = 1, 72 ÷ 4 = 18 → 118

3. 3. 56 ÷ 4 = 524

   56 ÷ 4: dividing by 4 is multiplying by 14: the numerator stays, the denominator 6 × 4 = 24 → 524, already in simplest form

4. 4. 811 ÷ 211 = 4

   811 ÷ 211: dividing by 211 is multiplying by its reciprocal 112: 811 × 112, numerators 8 × 11 = 88, denominators 11 × 2 = 22 → 8822; simplify, dividing the numerator and denominator by 22: 88 ÷ 22 = 4, 22 ÷ 22 = 1 → 4

5. 5. 8 ÷ 89 = 9

   8 ÷ 89: multiply by the reciprocal 98: 8 × 9 = 72, 72 ÷ 8 = 9

6. 6. 14 ÷ 8 = 132

   14 ÷ 8: dividing by 8 is multiplying by 18: the numerator stays, the denominator 4 × 8 = 32 → 132, already in simplest form

7. 7. 12 ÷ 23 = 34

   12 ÷ 23: dividing by 23 is multiplying by its reciprocal 32: 12 × 32, numerators 1 × 3 = 3, denominators 2 × 2 = 4 → 34, already in simplest form

8. 8. 67 ÷ 27 = 3

   67 ÷ 27: dividing by 27 is multiplying by its reciprocal 72: 67 × 72, numerators 6 × 7 = 42, denominators 7 × 2 = 14 → 4214; simplify, dividing the numerator and denominator by 14: 42 ÷ 14 = 3, 14 ÷ 14 = 1 → 3

9. 9. 56 ÷ 16 = 5

   56 ÷ 16: dividing by 16 is multiplying by its reciprocal 61: 56 × 61, numerators 5 × 6 = 30, denominators 6 × 1 = 6 → 306; simplify, dividing the numerator and denominator by 6: 30 ÷ 6 = 5, 6 ÷ 6 = 1 → 5

10. 10. 37 ÷ 6 = 114

    37 ÷ 6: dividing by 6 is multiplying by 16: the numerator stays, the denominator 7 × 6 = 42 → 342; simplify, dividing the numerator and denominator by 3: 3 ÷ 3 = 1, 42 ÷ 3 = 14 → 114

11. 11. 14 ÷ 7 = 128

    14 ÷ 7: dividing by 7 is multiplying by 17: the numerator stays, the denominator 4 × 7 = 28 → 128, already in simplest form

12. 12. 3 ÷ 35 = 5

    3 ÷ 35: multiply by the reciprocal 53: 3 × 5 = 15, 15 ÷ 3 = 5

Part B: Word problems

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

1. 13. 25 kg of sugar is put into small bags of 15 kg each. How many bags can be filled? (Answer: 2 bags)

   25 ÷ 15 = 2

2. 14. A roll of ribbon is 15 m long, and each bow takes 29 m of it. At most how many bows can the roll make? (Answer: 67 bows)

   15 ÷ 29 = 15 × 92 = 1352; only finished bows count: 67 at most

3. 15. Ka-lok has a roll of ribbon 8 m long, and each bow takes 38 m. After Ka-lok makes as many bows as the roll allows, how many metres of ribbon are left? (Answer: 18 m)

   8 ÷ 38: 21 bows at most, using 21 × 38 = 638 m; 8 − 638 = 18 m is left

4. 16. 34 kg of sugar is put into small bags of 18 kg each. How many bags can be filled? (Answer: 6 bags)

   34 ÷ 18 = 6

5. 17. 47 L of juice is poured equally into 5 cups. How many litres are in each cup? (Answer: 435 L)

   47 ÷ 5 = 435

6. 18. A ribbon is 5 m long and is cut into pieces 14 m long. How many pieces can be cut? (Answer: 20 pieces)

   5 ÷ 14 = 20