Comparing fractions with the same numerator or denominator worksheet

Part A: Working out and filling in

1. 1. D → C → B → A

   All have denominator 9, so the parts match: just put the numerators in order, smallest first.

   All in 9ths, so order by the numerators: 1, 2, 4, 6.

2. 2. 7

   All in 13ths, so look at the numerators: which whole number lies between 6 and 8?

   Same denominators, so the numerator is between 6 and 8: 7.

3. 3. 5

   All in 14ths, so look at the numerators: which whole number lies between 4 and 6?

   Same denominators, so the numerator is between 4 and 6: 5.

4. 4. 5

   All in 12ths, so look at the numerators: which whole number lies between 4 and 6?

   Same denominators, so the numerator is between 4 and 6: 5.

Part B: Choose, or true or false

1. 5. B

   Every picture has 10 same-sized parts. Count the shaded parts in each.

   The parts are all the same size: the most shaded, 910, is biggest.

2. 6. True

   Both are cut into 12 parts: which one has more of them?

   Same denominators mean same-sized parts: just compare the numerators, 7 and 2.

3. 7. C. 810

   All four are in 10ths, so the parts are the same size: just compare the numerators.

   All are in 10ths: the biggest numerator, 810, is biggest.

4. 8. D

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

   The parts are all the same size: the most shaded, 88, is biggest.

5. 9. True

   Both are cut into 12 parts: which one has more of them?

   Same denominators mean same-sized parts: just compare the numerators, 10 and 8.

6. 10. False

   Both are cut into 11 parts: which one has more of them?

   Same denominators mean same-sized parts: just compare the numerators, 1 and 4.

7. 11. B. 1210

   A fraction is more than 1 when its numerator is greater than its denominator. Compare each numerator with 10.

   The numerator, 12, is greater than the denominator, 10, so 1210 is more than 1.

8. 12. A. 166

   First write 2 and 3 as fractions with denominator 6, then see which numerator lies between them.

   2 = 126 and 3 = 186: the numerator between 12 and 18 is in 166.

Part C: Word problems

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

1. 13. 6 pineapple buns

   A whole box is 88. How many more parts is 148? Each part is one of the pineapple buns.

   A whole box is 88; 148 is 68 more, which is 6.

2. 14. 15 litre

   The denominators are the same: compare the numerators to see who drinks more, then take the smaller from the bigger.

   Same denominator, so the bigger numerator is more: Ka-yee drinks more. 45 − 35 = 15 litre, in simplest form 15.

3. 15. A. Ka-yan

   The bottles are the same size and all in 8ths: compare the three numerators.

   Same denominators, so compare the numerators 2, 4, 5: the biggest drank most.

4. 16. A. Ka-lok

   The bottles are the same size and all in 12ths: compare the three numerators.

   Same denominators, so compare the numerators 7, 8, 5: the biggest drank most.

5. 17. 17 litre

   The denominators are the same: compare the numerators to see who drinks more, then take the smaller from the bigger.

   Same denominator, so the bigger numerator is more: May drinks more. 47 − 37 = 17 litre, in simplest form 17.

6. 18. 9 cocktail buns

   A whole box is 1212. How many more parts is 2112? Each part is one of the cocktail buns.

   A whole box is 1212; 2112 is 912 more, which is 9.