Add fractions - Related denominators
Theory
To add fractions with related denominators, rename one fraction so both share the larger denominator, then add the numerators and simplify. \(\dfrac{1}{2}+\dfrac{1}{4}=\dfrac{2}{4}+\dfrac{1}{4}=\dfrac{3}{4}\).
Denominators are related when the larger is a multiple of the smaller, like \(2\) and \(4\).
Rename the smaller-denominator fraction to the larger denominator so the parts match.
Add the numerators, keep that denominator, and simplify: \(\dfrac{1}{2}+\dfrac{1}{4}=\dfrac{3}{4}\).
Rename to the larger denominator, then add the numerators over that denominator.
| Sum | Rename and add | Simplest form |
|---|---|---|
| \(\dfrac{1}{2}+\dfrac{1}{4}\) | \(\dfrac{2}{4}+\dfrac{1}{4}\) | \(\dfrac{3}{4}\) |
| \(\dfrac{1}{3}+\dfrac{1}{6}\) | \(\dfrac{2}{6}+\dfrac{1}{6}\) | \(\dfrac{1}{2}\) |
| \(\dfrac{1}{4}+\dfrac{3}{8}\) | \(\dfrac{2}{8}+\dfrac{3}{8}\) | \(\dfrac{5}{8}\) |
How to add fractions with related denominators
- Rename the smaller-denominator fraction to the larger denominator.
- Add the numerators and keep that denominator.
- Simplify the answer if you can.
| \(\dfrac{1}{2}+\dfrac{1}{4}\) | \(=\) | \(\dfrac{2}{4}+\dfrac{1}{4}\) |
| \(=\) | \(\dfrac{3}{4}\) |
| \(\dfrac{1}{3}+\dfrac{1}{6}\) | \(=\) | \(\dfrac{2}{6}+\dfrac{1}{6}\) |
| \(=\) | \(\dfrac{3}{6}=\dfrac{1}{2}\) |
| \(\dfrac{1}{4}+\dfrac{3}{8}\) | \(=\) | \(\dfrac{2}{8}+\dfrac{3}{8}\) |
| \(=\) | \(\dfrac{5}{8}\) |
| \(\dfrac{1}{2}+\dfrac{2}{4}\) | \(=\) | \(\dfrac{2}{4}+\dfrac{2}{4}\) |
| \(=\) | \(\dfrac{4}{4}=1\) |
Common pitfalls
Frequently asked questions
How do you add fractions with related denominators?
Rename one fraction to the larger denominator so the parts match, then add the numerators. \(\dfrac{1}{2}+\dfrac{1}{4}=\dfrac{3}{4}\).
Which denominator do you use?
The larger one, because it is a multiple of the smaller, so only one fraction needs to be renamed.
Why rename before adding?
Fractions can only be added when the parts are the same size, which means the denominators must match.
Do you simplify the answer?
Yes, write the sum in simplest form when the top and bottom share a factor, such as \(\dfrac{3}{6}=\dfrac{1}{2}\).