Improper fractions, mixed numbers and same denominators worksheet

Part A: Working out and filling in

1. 1. 1, 4

   How many lots of 8 fit into 12? The parts left over give the numerator.

   12 parts make 1 lots of 8, with 4 left: 1 48.

2. 2. 5 59 = 509

   5 59: the whole number times the denominator, plus the numerator, over the same denominator: 5 × 9 = 45, 45 + 5 = 50 → 509

3. 3. 94 = 2 14

   94: divide the numerator by the denominator. How many 4s in 9? 4 × 2 = 8, 9 − 8 = 1; 94 = 2 14, the quotient is the whole part: 2

4. 4. 3

   The denominator goes from 30 to 5: divided by what? Divide the numerator by the same number.

   The denominator 30 ÷ 6 is 5, so the numerator is ÷ 6 too: 18 ÷ 6 = 3.

5. 5. 89 − 79 = 19

   89 − 79: keep the denominator, subtract the numerators, 8 − 7 = 1 → 19, already in simplest form

6. 6. 14 + 14 = 12

   14 + 14: keep the denominator, add the numerators, 1 + 1 = 2 → 24; simplify, dividing the numerator and denominator by their highest common factor 2: 2 ÷ 2 = 1, 4 ÷ 2 = 2 → 12

Part B: Choose, or true or false

1. 7. True

   1 = 33. Compare the numerator, 4, with the denominator, 3: which is bigger?

   1 = 33. A numerator greater than the denominator means more than 1; a smaller numerator means less than 1.

2. 8. D. 530

   Equal fractions have the numerator and denominator multiplied by the same number. Check each option: are both multiplied by the same number?

   Numerator and denominator both times 5: 16 = 530.

3. 9. C. 811

   All four are in 11ths, so the parts are the same size: just compare the numerators.

   All are in 11ths: the biggest numerator, 811, is biggest.

4. 10. B

   Every picture has 8 same-sized parts. Count the shaded parts in each.

   The parts are all the same size: the most shaded, 78, is biggest.

5. 11. A. 79

   All three are added and the denominator stays 9. Add the numerators, then compare the total with the denominator.

   Keep the denominator and add the numerators: 2 + 4 + 1 = 7, giving 79.

6. 12. D. 7 78

   Borrow 1 from 8 as 88. What is the whole part after borrowing?

   8 = 7 88; subtract 18 to get 7 78.

Part C: Word problems

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

1. 13. 37 compartments

   Each pizza has 8 slices. First work out how many slices 4 whole pizzas make.

   4 pizzas are 4 × 8 slices, and 5 more: 37 slices.

2. 14. A ribbon is 485 m long. Written as a mixed number, what is the whole-number part? (Answer: 9)

   48 ÷ 5 = 9 R 3, so 9 35

3. 15. 4 chocolates

   Write 15 with denominator 20: 5 times what makes 20?

   The whole box is 2020, and 15 = 420: 4 chocolates.

4. 16. 5 cocktail buns

   A whole box is 77. How many more parts is 127? Each part is one of the cocktail buns.

   A whole box is 77; 127 is 57 more, which is 5.

5. 17. Chi-keung ate 27 of a pizza and Tsz-hin ate 47 of the same pizza. What fraction of the pizza is left? (Answer: 17)

   27 + 47 = 67; 1 − (27 + 47) = 17

6. 18. 4, 3

   5 litres has no fraction part: borrow 1 as 55 first, then subtract.

   5 = 4 55; subtract 25 to leave 4 35 litres.