1/4 + 1/2 Answer in simplest form

1/4 + 1/2 = 3/4. 1/4 + 1/2: a common denominator, the L.C.M. of 4 and 2, 4: 1/2 = 2/4; add the numerators, 1 + 2 = 3 → 3/4, already in simplest form

3/5 − 1/2 Answer in simplest form

3/5 − 1/2 = 1/10. 3/5 − 1/2: a common denominator, the L.C.M. of 5 and 2, 10: 3/5 = 6/10, 1/2 = 5/10; subtract the numerators, 6 − 5 = 1 → 1/10, already in simplest form

7/8 − 1/3 Answer in simplest form

7/8 − 1/3 = 13/24. 7/8 − 1/3: a common denominator, the L.C.M. of 8 and 3, 24: 7/8 = 21/24, 1/3 = 8/24; subtract the numerators, 21 − 8 = 13 → 13/24, already in simplest form

2/3 − 1/6 Answer in simplest form

2/3 − 1/6 = 1/2. 2/3 − 1/6: a common denominator, the L.C.M. of 3 and 6, 6: 2/3 = 4/6; subtract the numerators, 4 − 1 = 3 → 3/6; simplify by their H.C.F., 3: 3 ÷ 3 = 1, 6 ÷ 3 = 2 → 1/2

中文

Stage 8 · Fractions & decimals

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 pieces of 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: 34 − 16, common denominator 12, 912 − 212 = 712. Give the answer in simplest form. Multiplying the two denominators also works, with bigger numbers to simplify at the end — the same answer.

Worked examples

Have a go first, then open each one for the answer and the working.

Example 1
14 + 12
Answer in simplest form
Show the answer and working
Answer: 14 + 12 = 34
14 + 12: a common denominator, the L.C.M. of 4 and 2, 4: 12 = 24; add the numerators, 1 + 2 = 3 → 34, already in simplest form
Example 2
35 − 12
Answer in simplest form
Show the answer and working
Answer: 35 − 12 = 110
35 − 12: a common denominator, the L.C.M. of 5 and 2, 10: 35 = 610, 12 = 510; subtract the numerators, 6 − 5 = 1 → 110, already in simplest form
Example 3
78 − 13
Answer in simplest form
Show the answer and working
Answer: 78 − 13 = 1324
78 − 13: a common denominator, the L.C.M. of 8 and 3, 24: 78 = 2124, 13 = 824; subtract the numerators, 21 − 8 = 13 → 1324, already in simplest form
Example 4
23 − 16
Answer in simplest form
Show the answer and working
Answer: 23 − 16 = 12
23 − 16: a common denominator, the L.C.M. of 3 and 6, 6: 23 = 46; subtract the numerators, 4 − 1 = 3 → 36; simplify by their H.C.F., 3: 3 ÷ 3 = 1, 6 ÷ 3 = 2 → 12

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