Fractions with unlike denominators · Usually met around P5
Adding unlike fractions
Same denominator first: use the L.C.M.
How to do it
Method
Same denominator first: use the L.C.M.
12 + 13 = 36 + 26 = 56
One more example
34 − 16 = 912 − 212 = 712
In full
Different denominators mean the pieces are different sizes. So first give them a common denominator: the L.C.M. of the two. 12 + 13: the L.C.M. of 2 and 3 is 6, 12 = 36, 13 = 26, 36 + 26 = 56. If one denominator is a multiple of the other, use the bigger one: 12 + 14 = 24 + 14 = 34. Taking away works the same way: 34 − 16, common denominator 12, 912 − 212 = 712. Give the answer in its simplest form. Multiplying the two denominators together also works, but you'll have bigger numbers to simplify at the end.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
112 + 13
Answer in simplest form
Show the answer and working
Answer: 112 + 13 = 512
112 + 13: a common denominator, the L.C.M. of 12 and 3, 12: 13 = 412; add the numerators, 1 + 4 = 5 → 512, already in simplest form
Example 2
56 − 512
Answer in simplest form
Show the answer and working
Answer: 56 − 512 = 512
56 − 512: a common denominator, the L.C.M. of 6 and 12, 12: 56 = 1012; subtract the numerators, 10 − 5 = 5 → 512, already in simplest form
Example 3
12 − 37
Answer in simplest form
Show the answer and working
Answer: 12 − 37 = 114
12 − 37: a common denominator, the L.C.M. of 2 and 7, 14: 12 = 714, 37 = 614; subtract the numerators, 7 − 6 = 1 → 114, already in simplest form
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