Add fractions - Same denominator
Theory
To add fractions with the same denominator, add the numerators and keep the denominator. Then write the answer in its simplest form if the top and bottom share a factor.
The denominator tells the size of each part. When it is the same, the parts match.
Add the numerators and write the total over the same denominator: \(\dfrac{1}{5}+\dfrac{2}{5}=\dfrac{3}{5}\).
Then write the answer in its simplest form if the top and bottom share a common factor.
Add the numerators over the shared denominator, then simplify if you can.
| Sum | Add tops | Simplest form |
|---|---|---|
| \(\dfrac{1}{5}+\dfrac{2}{5}\) | \(\dfrac{3}{5}\) | \(\dfrac{3}{5}\) |
| \(\dfrac{2}{6}+\dfrac{2}{6}\) | \(\dfrac{4}{6}\) | \(\dfrac{2}{3}\) |
| \(\dfrac{3}{8}+\dfrac{5}{8}\) | \(\dfrac{8}{8}\) | \(1\) |
How to add fractions with the same denominator
- Add the numerators.
- Keep the denominator the same.
- Simplify the answer if the top and bottom share a factor.
Add the numerators, keep the denominator.
| \(\dfrac{1}{5}+\dfrac{2}{5}\) | \(=\) | \(\dfrac{3}{5}\) |
| \(\dfrac{2}{6}+\dfrac{2}{6}\) | \(=\) | \(\dfrac{4}{6}\) |
| \(=\) | \(\dfrac{2}{3}\) |
| \(\dfrac{3}{8}+\dfrac{5}{8}\) | \(=\) | \(\dfrac{8}{8}\) |
| \(=\) | \(1\) |
| \(\dfrac{3}{10}+\dfrac{4}{10}\) | \(=\) | \(\dfrac{7}{10}\) |
Common pitfalls
Frequently asked questions
How do you add fractions with the same denominator?
Add the numerators and keep the denominator the same. \(\dfrac{1}{5}+\dfrac{2}{5}=\dfrac{3}{5}\).
Do you add the denominators?
No. The denominator is the size of the parts and stays the same; only the numerators are added.
When is the answer one whole?
When the numerator adds up to the denominator, like \(\dfrac{8}{8}\), which equals \(1\).
Do you have to simplify the answer?
Yes, write it in simplest form when the top and bottom share a common factor, such as \(\dfrac{4}{6}=\dfrac{2}{3}\).