Improper fractions and mixed numbers worksheet

Part A: Working out and filling in

1. 1. 255 = 5

   255: the numerator is a multiple of the denominator, so it's a whole number: 25 ÷ 5 = 5

2. 2. 1911 = 1 811

   1911: divide the numerator by the denominator. How many 11s in 19? 11 × 1 = 11, 19 − 11 = 8; 1911 = 1 811, the remainder is the numerator: 8

3. 3. 425 = 8 25

   425: divide the numerator by the denominator. How many 5s in 42? 5 × 8 = 40, 42 − 40 = 2; 425 = 8 25, the quotient is the whole part: 8

4. 4. 189 = 2

   189: the numerator is a multiple of the denominator, so it's a whole number: 18 ÷ 9 = 2

5. 5. 3 910 = 3910

   3 910: the whole number times the denominator, plus the numerator, over the same denominator: 3 × 10 = 30, 30 + 9 = 39 → 3910

6. 6. 5 13 = 163

   5 13: the whole number times the denominator, plus the numerator, over the same denominator: 5 × 3 = 15, 15 + 1 = 16 → 163

7. 7. 418 = 5 18

   418: divide the numerator by the denominator. How many 8s in 41? 8 × 5 = 40, 41 − 40 = 1; 418 = 5 18, the remainder is the numerator: 1

8. 8. 376 = 6 16

   376: divide the numerator by the denominator. How many 6s in 37? 6 × 6 = 36, 37 − 36 = 1; 376 = 6 16, the quotient is the whole part: 6

9. 9. 3910 = 3 910

   3910: divide the numerator by the denominator. How many 10s in 39? 10 × 3 = 30, 39 − 30 = 9; 3910 = 3 910, the remainder is the numerator: 9

10. 10. 7 38 = 598

    7 38: the whole number times the denominator, plus the numerator, over the same denominator: 7 × 8 = 56, 56 + 3 = 59 → 598

11. 11. 5010 = 5

    5010: the numerator is a multiple of the denominator, so it's a whole number: 50 ÷ 10 = 5

12. 12. 8711 = 7 1011

    8711: divide the numerator by the denominator. How many 11s in 87? 11 × 7 = 77, 87 − 77 = 10; 8711 = 7 1011, the remainder is the numerator: 10

Part B: Word problems

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

1. 13. There are 1 13 pizzas on the table, each cut into 3 equal slices. How many slices are there altogether? (Answer: 4 slices)

   1 × 3 + 1 = 4

2. 14. There are 1 38 pizzas on the table, each cut into 8 equal slices. How many slices are there altogether? (Answer: 11 slices)

   1 × 8 + 3 = 11

3. 15. Tsz-hin drank 2 47 glasses of juice. Written as an improper fraction, how many glasses is that? (Answer: 187 glasses)

   2 × 7 + 4 = 18, so it is 187

4. 16. Tsz-ching drank 2 34 glasses of juice. Written as an improper fraction, how many glasses is that? (Answer: 114 glasses)

   2 × 4 + 3 = 11, so it is 114

5. 17. A ribbon is 136 m long. Written as a mixed number, what is the whole-number part? (Answer: 2)

   13 ÷ 6 = 2 R 1, so 2 16

6. 18. Each cake is cut into 3 equal slices. There are 43 slices. What is the greatest number of whole cakes these slices can make? (Answer: 14 cakes)

   43 ÷ 3 = 14 R 1