Three fractions with the same denominator worksheet

Part A: Working out and filling in

1. 1. 1112

   All three are counted in 12ths. Count how many 12ths there are altogether, then see if it simplifies.

   Keep the denominator and add the numerators: 1 + 5 + 5 = 11, giving 1112, in simplest form 1112.

2. 2. 25

   Keep the denominator and look at the numerators: start from 9 and subtract one at a time. Simplify at the end.

   Keep the denominator and subtract the numerators left to right: 9 − 4 − 1 = 4, giving 410, in simplest form 25.

3. 3. 38

   All three are counted in 8ths. Count how many 8ths there are altogether, then see if it simplifies.

   Keep the denominator and add the numerators: 1 + 1 + 1 = 3, giving 38, in simplest form 38.

4. 4. 611

   With subtraction then addition, go left to right: deal with 10 − 6 first, keeping the denominator 11.

   Keep the denominator and work the numerators left to right: 10 − 6 = 4, 4 + 2 = 6, giving 611, in simplest form 611.

5. 5. 910

   Keep the denominator 10. Work the numerators left to right, the adding first, then the subtracting; simplify if you can.

   Keep the denominator and work the numerators left to right: 9 + 5 − 5 = 9, giving 910, in simplest form 910.

6. 6. 59

   Keep the denominator 9. Work the numerators left to right, the adding first, then the subtracting; simplify if you can.

   Keep the denominator and work the numerators left to right: 6 + 6 − 7 = 5, giving 59, in simplest form 59.

7. 7. 7

   All in 10ths, so look only at the numerators. Just before 710 is subtracted, what must the numerator be?

   Look at the numerators: 9 + □ − 7 = 9, so □ = 9 + 7 − 9 = 7.

8. 8. 5

   All in 10ths, so look only at the numerators. Just before 310 is subtracted, what must the numerator be?

   Look at the numerators: 6 + □ − 3 = 8, so □ = 8 + 3 − 6 = 5.

Part B: Choose, or true or false

1. 9. C. 68

   All three are added and the denominator stays 8. Add the numerators, then compare the total with the denominator.

   Keep the denominator and add the numerators: 4 + 1 + 1 = 6, giving 68.

2. 10. True

   The denominator stays the same. Work the numerators yourself, left to right, then compare with 10.

   Numerators left to right: 7 + 4 − 1 = 10, so the answer is 109.

3. 11. True

   The denominator stays the same. Work the numerators yourself, left to right, then compare with 2.

   Numerators left to right: 3 + 8 − 9 = 2, so the answer is 211.

4. 12. C. 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: 3 + 1 + 3 = 7, giving 79.

Part C: Word problems

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

1. 13. 15 litres

   What's left is 510 minus both days. Keep the denominator and take the numerators from 5 one at a time.

   510 − 110 − 210: keep the denominator, and the numerators give 5 − 1 − 2 = 2, so 210 litre is left, in simplest form 15.

2. 14. 1 m

   All three are in 9ths of a metre. Keep the denominator, add the numerators, then see if it simplifies.

   Keep the denominator and add the numerators: 1 + 5 + 3 = 9, so 99 m altogether, in simplest form 1.

3. 15. 29 of a tank

   Subtract what is used, then add what is poured in: work the numerators left to right, keeping 9 as the denominator.

   Used means subtract, poured in means add: 69 − 59 + 19; keep the denominator and work the numerators left to right, 6 − 5 + 1 = 2, giving 29 of a tank, in simplest form 29.

4. 16. 79 of a tank

   Subtract what is used, then add what is poured in: work the numerators left to right, keeping 9 as the denominator.

   Used means subtract, poured in means add: 69 − 19 + 29; keep the denominator and work the numerators left to right, 6 − 1 + 2 = 7, giving 79 of a tank, in simplest form 79.

5. 17. 89 m

   All three are in 9ths of a metre. Keep the denominator, add the numerators, then see if it simplifies.

   Keep the denominator and add the numerators: 1 + 4 + 3 = 8, so 89 m altogether, in simplest form 89.

6. 18. 311 litres

   What's left is 1011 minus both days. Keep the denominator and take the numerators from 10 one at a time.

   1011 − 311 − 411: keep the denominator, and the numerators give 10 − 3 − 4 = 3, so 311 litre is left, in simplest form 311.