Common denominators: comparing fractions with different denominators worksheet

Part A: Working out and filling in

1. 1. 18

   List the multiples of 9 and find the first one that is also a multiple of 2.

   The common denominator is the L.C.M. of 9 and 2: 18.

2. 2. B → A → C

   First find any fraction whose numerator is greater than its denominator: it is more than 1. Then compare the rest over a common denominator.

   Improper fractions are over 1, proper ones under; within each kind, compare with a common denominator.

3. 3. 7

   Rewrite 56 over 8: roughly what is the numerator? □ must be greater than that.

   56 is 5 × 8 ÷ 6 lots of 18; the smallest whole number above that is 7.

4. 4. 3

   Rewrite 25 over 7: roughly what is the numerator? □ must be greater than that.

   25 is 2 × 7 ÷ 5 lots of 17; the smallest whole number above that is 3.

Part B: Choose, or true or false

1. 5. B. 920

   20 is a multiple of 5. Rewrite 15 over 20, then compare the numerators.

   20 is 4 times 5: multiply the numerator and denominator of 15 by 4 to get 420, then compare its numerator with 920's.

2. 6. False

   The strips are the same length. Into how many pieces must each part of the top strip be cut so that it has 12 parts like the bottom one?

   Cut each part of the top strip into 3, and it has 12 parts like the bottom one: 14 = 312. Compare the numerators, 3 and 5.

3. 7. False

   The strips are the same length. Into how many pieces must each part of the top strip be cut so that it has 10 parts like the bottom one?

   Cut each part of the top strip into 2, and it has 10 parts like the bottom one: 15 = 210. Compare the numerators, 2 and 5.

4. 8. A. 1318

   18 is a multiple of 6. Rewrite 16 over 18, then compare the numerators.

   18 is 3 times 6: multiply the numerator and denominator of 16 by 3 to get 318, then compare its numerator with 1318's.

5. 9. D. 524

   Put 14 and 16 over a common denominator first, then check whether each choice lies between them.

   With a common denominator, a number between them has a numerator in between: 524.

6. 10. False

   The denominators 3 and 5 differ: find their L.C.M., rewrite both fractions over it, then compare the numerators.

   Common denominator: 13 = 515 and 25 = 615; compare 5 and 6.

7. 11. D. 56

   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: 18 = 324, 13 = 824, 56 = 2024, 23 = 1624. The one with the biggest numerator is 56.

8. 12. False

   The denominators 4 and 2 differ: find their L.C.M., rewrite both fractions over it, then compare the numerators.

   Common denominator: 14 = 14 and 12 = 24; compare 1 and 2.

Part C: Word problems

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

1. 13. A. May

   167 is an improper fraction. Change it to a mixed number, then compare with 3 km.

   3 is 3 × 7 over 7; compare numerators with 167, or change 167 to a mixed number.

2. 14. 5

   Rewrite 914 and 1114 over a multiple of 7, then see which fraction with denominator 7 fits between them.

   Put 914 and 1114 over a multiple of 7: only 57 fits between.

3. 15. B. Ming

   The bottles are the same size, so just compare 23, 29 and 14: 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 23.

4. 16. 115

   Put 16 and 110 over a common denominator first, and see which team did more.

   Compare over a common denominator, then take the smaller from the bigger: 115.

5. 17. 6

   Rewrite 1114 and 1314 over a multiple of 7, then see which fraction with denominator 7 fits between them.

   Put 1114 and 1314 over a multiple of 7: only 67 fits between.

6. 18. B. Ming

   The bottles are the same size, so just compare 14, 12 and 1112: 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 1112.