Adding & Subtracting Common Fractions

About this video

How to add and subtract fractions with different denominators by finding a common denominator first. A core skill that shows up everywhere, from algebra to financial maths.

What it covers

Why the denominators must match before you can add or subtract
Finding the LCM (lowest common multiple) of the two denominators
The long division line: how many times does each denominator go into the LCM
Answers bigger than 1, negative answers, and answers of zero

Worksheet for this video

📄 Printable worksheet ✅ Memo

These are the questions worked through in the video. Pause after each one, do it yourself, then check against the video.

The method used in this video

Find the LCM of the two denominators.
Draw one long division line and write the LCM underneath.
Ask: how many times does each denominator go into the LCM? Multiply that answer by its numerator, above the line.
Bring the + or − down and work out the top.

SECTION A — ADDING

1
Calculate:3/8 + 1/4(2)
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LCM of 8 and 4 is 8
8 goes into 8 1 time → 1 × 3 = 3 | 4 goes into 8 2 times → 2 × 1 = 2
= (3 + 2)/8 = 5/8
2
Calculate:5/6 + 2/9(2)
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LCM of 6 and 9 is 18
6 goes into 18 3 times → 3 × 5 = 15 | 9 goes into 18 2 times → 2 × 2 = 4
= (15 + 4)/18 = 19/18
3
Calculate:2/5 + 3/10(2)
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LCM of 5 and 10 is 10
5 goes into 10 2 times → 2 × 2 = 4 | 10 goes into 10 1 time → 1 × 3 = 3
= (4 + 3)/10 = 7/10
4
Calculate:4/7 + 13/14TRY IT YOURSELF(3)
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LCM of 7 and 14 is 14
7 goes into 14 2 times → 2 × 4 = 8 | 14 goes into 14 1 time → 1 × 13 = 13
= (8 + 13)/14 = 21/14

SECTION B — SUBTRACTING

5
Calculate:2/3 − 6/4(2)
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LCM of 3 and 4 is 12
3 goes into 12 4 times → 4 × 2 = 8 | 4 goes into 12 3 times → 3 × 6 = 18
= (8 − 18)/12 = −10/12
6
Calculate:3/2 − 6/4(2)
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LCM of 2 and 4 is 4
2 goes into 4 2 times → 2 × 3 = 6 | 4 goes into 4 1 time → 1 × 6 = 6
= (6 − 6)/4 = 0/4 = 0
7
Calculate:9/18 − 2/9(2)
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LCM of 18 and 9 is 18
18 goes into 18 1 time → 1 × 9 = 9 | 9 goes into 18 2 times → 2 × 2 = 4
= (9 − 4)/18 = 5/18
8
Calculate:2/4 − 3/6TRY IT YOURSELF(3)
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LCM of 4 and 6 is 12
4 goes into 12 3 times → 3 × 2 = 6 | 6 goes into 12 2 times → 2 × 3 = 6
= (6 − 6)/12 = 0/12 = 0

Extra worked examples

✍️ Extra example: ⅔ + ¼

1
Find the LCM of 3 and 4, which is 12.
12 is the smallest number both 3 and 4 go into.
2
Write one long division line with 12 underneath.
Everything now goes over the LCM.
3
3 goes into 12 four times, so 4 × 2 = 8. 4 goes into 12 three times, so 3 × 1 = 3.
Multiply each numerator by how many times its denominator goes in.
4
Bring the + down: (8 + 3)/12 = 11/12.
Work out the top only — the denominator stays 12.

✍️ Extra example: 2/5 − 5/6

1
The LCM of 5 and 6 is 30.
30 is the smallest number both go into.
2
5 goes into 30 six times: 6 × 2 = 12. 6 goes into 30 five times: 5 × 5 = 25.
How many times each denominator goes into the LCM, times its numerator.
3
(12 − 25)/30 = (−13)/30
Carry the − sign down. A negative answer is fine.

Exercises to try

Work each one out, then click to reveal the answer.

1
½ + ⅓
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LCM of 2 and 3 is 6 → 3/6 + 2/6 = 5/6
2
¾ − ⅖
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LCM of 4 and 5 is 20 → 15/20 − 8/20 = 7/20
3
⅚ − ⅓
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LCM of 6 and 3 is 6 → 5/6 − 2/6 = 3/6
4
5/8 + 5/6
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LCM of 8 and 6 is 24 → (15 + 20)/24 = 35/24 (bigger than 1 — that is fine)
5
3/4 − 6/8
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LCM of 4 and 8 is 8 → (6 − 6)/8 = 0