How to Add and Subtract Fractions (Step-by-Step Guide)

Adding and subtracting fractions trips up a lot of people — but once you understand the key rule, it becomes straightforward. The trick: you can only add or subtract fractions with the same denominator.

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Same Denominator — The Easy Case

When the bottom numbers are the same, just add or subtract the top numbers:

3/8 + 2/8 = (3+2)/8 = 5/8

7/9 − 4/9 = (7−4)/9 = 3/9 = 1/3 (simplified)

Different Denominators — Finding the LCD

When denominators differ, find the Least Common Denominator (LCD) — the smallest number both denominators divide into evenly.

Method 1: Multiply the denominators

Works for any two fractions (may not give the lowest LCD but always works).

1/3 + 1/4
LCD = 3 × 4 = 12
1/3 = 4/12 (multiply top and bottom by 4)
1/4 = 3/12 (multiply top and bottom by 3)
4/12 + 3/12 = 7/12

Method 2: LCM Method (more efficient)

Find the Least Common Multiple of the denominators.

5/6 + 3/8
Multiples of 6: 6, 12, 18, 24, 30…
Multiples of 8: 8, 16, 24, 32…
LCD = 24
5/6 = 20/24 | 3/8 = 9/24
20/24 + 9/24 = 29/24 = 1 and 5/24

Step-by-Step Process

Find the LCD of both denominators
Convert each fraction to have the LCD as denominator
Add or subtract the numerators
Keep the denominator the same
Simplify if possible (divide by GCF)

Worked Examples

2/3 + 3/5
LCD = 15
2/3 = 10/15 | 3/5 = 9/15
10/15 + 9/15 = 19/15 = 1 and 4/15

7/8 − 1/3
LCD = 24
7/8 = 21/24 | 1/3 = 8/24
21/24 − 8/24 = 13/24

Adding Mixed Numbers

A mixed number has a whole part and a fraction part (e.g. 2 and 1/3).

Add the whole numbers separately
Add the fractions using the LCD method
If the fraction result is improper (top > bottom), convert and add to whole number

2 and 3/4 + 1 and 2/3
Whole: 2 + 1 = 3
Fractions: 3/4 + 2/3, LCD = 12 → 9/12 + 8/12 = 17/12 = 1 and 5/12
Total: 3 + 1 and 5/12 = 4 and 5/12