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How to Add Fractions?
Updated Math & Study Help
Case 1 — Same denominator (easy)
Add the numerators (top numbers) and keep the denominator (bottom number) the same.
- Example: 1/5 + 2/5 = 3/5
Case 2 — Different denominators
You first need a common denominator.
- Find a common denominator. Use the least common multiple of the two denominators (or just multiply them together).
- Convert each fraction to an equivalent fraction with that denominator by multiplying the top and bottom by the same number.
- Add the numerators, keep the common denominator.
- Simplify the result if possible.
Worked examples
| Problem | Common denominator | Converted | Result |
|---|---|---|---|
| 1/2 + 1/3 | 6 | 3/6 + 2/6 | 5/6 |
| 1/3 + 1/2 | 6 | 2/6 + 3/6 | 5/6 |
| 1/3 + 1/4 | 12 | 4/12 + 3/12 | 7/12 |
| 1/4 + 1/2 | 4 | 1/4 + 2/4 | 3/4 |
Walking through 1/2 + 1/3
- Common denominator of 2 and 3 is 6.
- Convert: 1/2 = 3/6, and 1/3 = 2/6.
- Add: 3/6 + 2/6 = 5/6.
Walking through 1/3 + 1/4
- Common denominator of 3 and 4 is 12.
- Convert: 1/3 = 4/12, and 1/4 = 3/12.
- Add: 4/12 + 3/12 = 7/12, which doesn't simplify further.
Mixed numbers (like 2 1/4): either add the whole numbers and fractions separately, or convert to improper fractions first, then add using the same steps above.
Tip: Always simplify your final answer. For example, 2/4 simplifies to 1/2. If the numerator ends up bigger than the denominator (an improper fraction like 7/6), you can rewrite it as a mixed number (1 1/6).
Subtracting fractions uses the same rule: just like addition, you need a common denominator before you can subtract — convert both fractions the same way as above, then subtract the numerators instead of adding them and keep the denominator.
Adding three or more fractions: the rule doesn't change, you just need a common denominator that all of the fractions share. For example, 1/2 + 1/3 + 1/6: the common denominator of 2, 3, and 6 is 6. Convert: 1/2 = 3/6, 1/3 = 2/6, and 1/6 stays 1/6. Add: 3/6 + 2/6 + 1/6 = 6/6 = 1.
Simplifying with the greatest common divisor: to simplify a result like 4/8, find the largest number that divides evenly into both the numerator and denominator (here, 4) and divide both by it: 4÷4 = 1, 8÷4 = 2, giving 1/2. This is the same idea as the earlier tip, just naming the specific number (the GCD) that tells you how far a fraction can be reduced.
Nearby questions in this topic include How to Do Division? and How to Find the Average?.
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