Adding fractions
To add fractions, make the denominators the same, add the numerators, and simplify. The calculator below does it with the steps shown; the guide explains each move.
Working
- Find the least common denominator of 3 and 4: LCD = 12.
- Rewrite each fraction over 12.
2/3 = 8/12, 1/4 = 3/12 - Add the numerators and keep the denominator.
8 + 3 = 11 → 11/12 - 11/12 is already in lowest terms.
How to add fractions, step by step
- Check the denominators. If they already match (2/7 + 3/7), skip to step 3.
- Find a common denominator. Use the least common denominator — the smallest number both denominators divide into. For 2/3 + 1/4 that is 12.
- Rewrite each fraction. Multiply top and bottom by whatever turns the old denominator into the new one: 2/3 = 8/12 and 1/4 = 3/12.
- Add the numerators. Keep the denominator: 8/12 + 3/12 = 11/12. Never add the denominators.
- Simplify. Divide by the greatest common factor and convert an improper result to a mixed number if your teacher wants one.
Why fractions need a common denominator
The denominator names the size of the pieces. You can only add pieces of the same size — so first we re-cut the bars. Step through it:
Step 1 of 3 — Here are 1/2 and 1/3. The pieces are different sizes, so "1 piece plus 1 piece" means nothing yet.
Adding fractions with like denominators
When the bottoms match, the pieces are already the same size, so you only count them: 3/8 + 4/8 = 7/8. The denominator stays 8 because the size of each piece has not changed.
Adding fractions with unlike denominators
Different denominators mean different-sized pieces. 1/2 + 1/3 is not 2/5 — that would be smaller than the 1/2 you started with. Re-cut both into sixths: 3/6 + 2/6 = 5/6.
Any common multiple works (you could use 12 or 18), but the least one keeps the numbers small and means less simplifying at the end. The LCD calculator finds it for longer lists.
Adding mixed numbers
Method 1: add the whole numbers and the fractions separately, then carry. 2 3/4 + 1 1/2 = 3 + (3/4 + 2/4) = 3 + 5/4 = 4 1/4.
Method 2: convert to improper fractions first. 11/4 + 3/2 = 11/4 + 6/4 = 17/4 = 4 1/4. Method 2 is slower by hand but never needs carrying, and it is what the calculator shows.
Adding a fraction and a whole number
Write the whole number over 1, or simply attach it: 3 + 2/5 = 3 2/5. As an improper fraction that is 17/5.
Common mistakes
- Adding the denominators: 1/2 + 1/4 ≠ 2/6.
- Changing the denominator but forgetting to scale the numerator: 2/3 is 8/12, not 2/12.
- Leaving the answer unsimplified: 6/8 should be 3/4.
Questions people ask
Do you add the denominators when adding fractions?
No. The denominator describes the size of the pieces, which does not change when you add. Make the denominators equal, then add only the numerators.
What is 1/2 + 1/4?
1/2 = 2/4, so 2/4 + 1/4 = 3/4.
What is 2/3 + 3/4?
The LCD of 3 and 4 is 12: 8/12 + 9/12 = 17/12 = 1 5/12.
How do you add three fractions?
Find one common denominator for all three (the LCD of the list), rewrite each, then add all the numerators. For example 1/2 + 1/3 + 1/6 = 3/6 + 2/6 + 1/6 = 6/6 = 1.