Fractions with unlike denominators · Usually met around P5
Common denominators: comparing unlike fractions
Common denominator first, then compare tops.
How to do it
Method
Common denominator first, then compare tops
34 and 56: 912 < 1012, so 34 < 56
Another way
Compare with 1/2
49 < 12 < 58
In full
With different denominators the pieces are different sizes, so you can't just compare the tops: first make the bottoms the same. Easiest is when one bottom is a multiple of the other: 12 and 38 — multiply the top and bottom of 12 by 4 to get 48, and 48 > 38, so 12 is greater. Way 1: give them a common denominator (the L.C.M. of the bottoms) and compare the tops: 34 and 56 become 912 and 1012, so 34 is smaller. Way 2: with the same top, a bigger bottom means smaller pieces: 34 > 35. Way 3: compare each with 12 or 1 first to sort them roughly: 49 is under 12, 58 is over. With whole and mixed numbers, compare the whole parts first, then the fractions; change an improper fraction to a mixed number first.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
To compare 13 and 29, the smallest common denominator is □.
Show the answer and working
Answer: 9
The common denominator is the L.C.M. of 3 and 9: 9.
Example 2
Which is greater, 13 or 16?
- A. Different bottoms: they can't be compared
- B. 13
- C. They are equal
- D. 16
Choose the right answer
Show the answer and working
Answer: B. 13
6 is 2 times 3: multiply the top and bottom of 13 by 2 to get 26, then compare its top with 16's.
Example 3
34 < □/8, and □ is a whole number. What is the smallest it can be?
Show the answer and working
Answer: 7
34 is 3 × 8 ÷ 4 lots of 18; the smallest whole number above that is 7.
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