Adding Fractions Calculator
Type two fractions or mixed numbers to add them, with the common denominator found and every step written out, then simplified.
3/4 + 1/6 =
11/12
3/4 + 1/6 = 11/12, about 0.9167 as a decimal.
- As a decimal
- ≈ 0.916667
- Repeating
- 0.91(6)
How to add fractions
Fractions can only be added when they count pieces of the same size, so the first job is a common denominator. The best one is the least common multiple of the two denominators (the least common denominator, LCD). For 3/4 + 1/6 the multiples of 4 are 4, 8, 12 … and of 6 are 6, 12 …, so the LCD is 12.
Rewrite each fraction over the LCD by multiplying its top and bottom by the same number: 3/4 = 9/12 and 1/6 = 2/12. Now add the numerators and keep the denominator: 9/12 + 2/12 = 11/12. Finish by simplifying, and turn an improper answer into a mixed number if you want one.
With mixed numbers you can add the whole numbers and the fractions separately (1 1/2 + 2 2/3 = 3 + 7/6 = 4 1/6), or turn both into improper fractions first, which is what the working here does because it never needs a carry.
a/b + c/d = (a × (L ÷ b) + c × (L ÷ d)) / L, where L = lcm(b, d)
- US students learn to add fractions with unlike denominators in grade 5 by replacing them with equivalent fractions that have a common denominator (5.NF.A.1). Source: Common Core State Standards, Grade 5 Number and Operations: Fractions.
Common fraction sums
Each sum with its least common denominator, the fractions rewritten over it, and the answer in simplest form.
| Sum | LCD | Rewritten | Answer |
|---|---|---|---|
| 1/2 + 1/3 | 6 | 3/6 + 2/6 | 5/6 |
| 1/2 + 1/4 | 4 | 2/4 + 1/4 | 3/4 |
| 1/3 + 1/4 | 12 | 4/12 + 3/12 | 7/12 |
| 1/3 + 1/6 | 6 | 2/6 + 1/6 | 1/2 |
| 1/4 + 1/8 | 8 | 2/8 + 1/8 | 3/8 |
| 2/3 + 3/4 | 12 | 8/12 + 9/12 | 1 5/12 |
| 3/8 + 1/6 | 24 | 9/24 + 4/24 | 13/24 |
| 1/5 + 1/10 | 10 | 2/10 + 1/10 | 3/10 |
| 2/5 + 1/3 | 15 | 6/15 + 5/15 | 11/15 |
| 5/6 + 7/10 | 30 | 25/30 + 21/30 | 1 8/15 |
Show all 15 rowsShow fewer
| 3/4 + 5/12 | 12 | 9/12 + 5/12 | 1 1/6 |
| 7/8 + 5/6 | 24 | 21/24 + 20/24 | 1 17/24 |
| 1/2 + 1/2 | 2 | 1/2 + 1/2 | 1 |
| 1 1/2 + 2 3/4 | 4 | 6/4 + 11/4 | 4 1/4 |
| 2 1/3 + 1 5/6 | 6 | 14/6 + 11/6 | 4 1/6 |
Frequently Asked Questions
Do I have to use the least common denominator?
No. Any common denominator works, such as the product of the two denominators (4 × 6 = 24 for 3/4 + 1/6), but you will have a bigger fraction to simplify at the end: 18/24 + 4/24 = 22/24 = 11/12.
Why can’t I just add the tops and the bottoms?
Because 1/2 + 1/2 would then be 2/4, which is a half, not a whole. The denominator names the size of the pieces; adding fractions adds the number of pieces, so the size must stay the same.
How do I add three or more fractions?
Find a denominator that all of them divide into (the LCD of all of them), rewrite each one over it, and add all the numerators at once. Or add two at a time with this calculator, feeding each answer back in.