Fractions with different denominators worksheet

Part A: Working out and filling in

1. 1. 18 − 112 = 124

   18 − 112: a common denominator, the L.C.M. of 8 and 12, 24: 18 = 324, 112 = 224; subtract the numerators, 3 − 2 = 1 → 124, already in simplest form

2. 2. 58 − 12 = 18

   58 − 12: a common denominator, the L.C.M. of 8 and 2, 8: 12 = 48; subtract the numerators, 5 − 4 = 1 → 18, already in simplest form

3. 3. 13 + 14 = 712

   13 + 14: a common denominator, the L.C.M. of 3 and 4, 12: 13 = 412, 14 = 312; add the numerators, 4 + 3 = 7 → 712, already in simplest form

4. 4. 5, 5, 6

   Add the wholes and the fractions separately: put 12 and 13 over a common denominator and see whether they pass 1.

   Add the wholes, 1 + 4; add the fractions over a common denominator and carry any whole: 5 56.

5. 5. 1, 3, 8

   Put 14 and 78 over a common denominator first. Is 14 big enough? If not, borrow 1 from 5.

   14 is less than 78, so borrow 1 from 5 as a fraction, then subtract: 1 38.

6. 6. 78

   Find the L.C.M. of 2, 8 and 4 as the common denominator, and rewrite all three fractions over it.

   The L.C.M. of the three denominators is 8; add the numerators over 8 and simplify: 78.

7. 7. 14

   Find the L.C.M. of 3, 6 and 4 as the common denominator, then subtract one at a time, left to right.

   Over a common denominator of 12, subtract left to right: 14.

8. 8. 1124

   No brackets, so go left to right: 12 − 38 first, then add 13.

   Left to right: subtract first, then add; don't work out 38 + 13 first. Over 24: 1124.

Part B: Choose, or true or false

1. 9. False

   The strips are the same length. Into how many pieces must each part of the top strip be cut so that it has 8 parts like the bottom one?

   Cut each part of the top strip into 2, and it has 8 parts like the bottom one: 14 = 28. Compare the numerators, 2 and 6.

2. 10. C. 1112

   12 is a multiple of 3. Rewrite 13 over 12, then compare the numerators.

   12 is 4 times 3: multiply the numerator and denominator of 13 by 4 to get 412, then compare its numerator with 1112's.

3. 11. C. 23

   Sort the four fractions against 12 first, then put the ones above 12 over a common denominator and compare.

   Over a common denominator of 24: 23 = 1624, 18 = 324, 12 = 1224, 712 = 1424. The one with the biggest numerator is 23.

4. 12. D. 9 and 10

   Add the wholes, 5 + 3, first, then see whether 34 + 1112 goes past 1.

   The wholes make 5 + 3 = 8; 34 + 1112 is more than 1, so carry 1: the answer is between 9 and 10.

Part C: Word problems

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

1. 13. A. Chi-keung

   The bottles are the same size, so just compare 12, 79 and 112: against 12 first, or over a common denominator.

   The bottles are the same size, so compare the fractions: over a common denominator the largest is 79.

2. 14. 3

   Rewrite 12 and 710 over a multiple of 5, then see which fraction with denominator 5 fits between them.

   Put 12 and 710 over a multiple of 5: only 35 fits between.

3. 15. From a tin of paint, Tsz-hin used 13 and Chi-keung used 18. What fraction of the tin did they use altogether? (Answer: 1124)

   13 + 18 = 1124

4. 16. Ka-yee drank 37 L of water and Ming drank 14 L. How many litres more did Ka-yee drink than Ming? (Answer: 528 L)

   37 − 14 = 528

5. 17. 1120 litres

   Compare the wholes, 5 and 6, then 710 and 14 over a common denominator, to see which bottle holds more.

   See which is more, then take the smaller from the bigger (borrowing if needed): 1120 litres.

6. 18. 16

   The whole pizza is 1, and all three shares come off it. Find a common denominator for 12, 4 and 2 first.

   The whole pizza is 1: 1 − 112 − 14 − 12 = 16.