Multiplying and dividing fractions worksheet

Part A: Working out and filling in

1. 1. 1913

   Make 19, the number divided, the numerator and 13, the divisor, the denominator; then see if it simplifies.

   The number divided is the numerator, the divisor the denominator: 1913, simplified 1913.

2. 2. 56

   Compare 50 minutes with the 60 minutes in an hour: write it as a fraction, then simplify.

   An hour is 60 minutes: 50 ÷ 60 = 56.

3. 3. 17 of 21 = 3

   17 of 21: divide by the denominator for one part, 21 ÷ 7 = 3, then multiply by the numerator, 3 × 1 = 3

4. 4. 38 of 48 = 18

   38 of 48: divide by the denominator for one part, 48 ÷ 8 = 6, then multiply by the numerator, 6 × 3 = 18

5. 5. 13 × 78 = 724

   13 × 78: numerators times numerators, 1 × 7 = 7; denominators times denominators, 3 × 8 = 24 → 724, already in simplest form

6. 6. 4 × 17 = 47

   4 × 17: the whole number times the numerator, 4 × 1 = 4, the denominator unchanged → 47, already in simplest form

7. 7. 92

   Turn both ÷ into × the reciprocal: ÷ 14 becomes × 41. What does ÷ 49 become?

   Both ÷ become × the reciprocal: 12 × 41 × 94 = 92.

8. 8. 35 ÷ 9 = 115

   35 ÷ 9: dividing by 9 is multiplying by 19: the numerator stays, the denominator 5 × 9 = 45 → 345; simplify, dividing the numerator and denominator by 3: 3 ÷ 3 = 1, 45 ÷ 3 = 15 → 115

9. 9. 356

   Division before subtraction: work out 13 ÷ 712 first, as × the reciprocal.

   Divide first: 13 ÷ 712 = 47; then 58 − 47 = 356.

10. 10. 48 dollars

    18 kg is 1 lots of 18 kg. Find the price of 18 kg first.

    6 ÷ 18 = 6 × 81 = 48; or 18 kg costs 6, so 1 kg costs 6 × 8.

Part B: Choose, or true or false

1. 11. False

   Compare the numerator 4 and the denominator 3 of 43: is the multiplier more or less than 1?

   43 is close to 1, but still compare its numerator and denominator: a smaller numerator means less than 1 and a smaller product; a bigger numerator means more than 1 and a bigger product.

2. 12. C

   Find B's bar first: “18 of B” means splitting B into how many equal cells?

   “A is 18 of B”: B is 8 equal cells, and A is 1 of those cells.

Part C: Word problems

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

1. 13. 37

   Find the size of the whole group first; the boys are the numerator and the whole group the denominator.

   The group has 15 + 20 = 35; 15 ÷ 35 = 37.

2. 14. A metre of wire weighs 34 kg. Ka-lok cuts off 14 m of it. How many kilograms does the piece weigh? (Answer: 316 kg)

   34 × 14 = 316

3. 15. C. Less

   Next week's is 30 × 67. Compare the numerator 6 with the denominator 7.

   Next week's = 30 × 67: times more than 1 gives more, times less than 1 gives less.

4. 16. 925 litres

   Find the litres in the whole crate first, 9 × 15, then take 15 of it.

   9 × 15 × 15, cancelling first: 925 litres.

5. 17. 67 L of juice is poured equally into 5 cups. How many litres are in each cup? (Answer: 635 L)

   67 ÷ 5 = 635

6. 18. 4 men

   4 parts are 16 women. Find 1 part first: how many parts are men?

   4 parts are 16, so 1 part is 4; men are 5 − 4 parts: 4.