Subtract fractions - Related denominators
Theory
To subtract fractions with related denominators, rename one fraction so both share the larger denominator, then subtract the numerators and simplify. \(\dfrac{3}{4}-\dfrac{1}{2}=\dfrac{3}{4}-\dfrac{2}{4}=\dfrac{1}{4}\).
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.
Subtract the numerators, keep that denominator, and simplify: \(\dfrac{3}{4}-\dfrac{1}{2}=\dfrac{1}{4}\).
Rename to the larger denominator, then subtract the numerators over that denominator.
| Difference | Rename and subtract | Simplest form |
|---|---|---|
| \(\dfrac{3}{4}-\dfrac{1}{2}\) | \(\dfrac{3}{4}-\dfrac{2}{4}\) | \(\dfrac{1}{4}\) |
| \(\dfrac{5}{6}-\dfrac{1}{3}\) | \(\dfrac{5}{6}-\dfrac{2}{6}\) | \(\dfrac{1}{2}\) |
| \(\dfrac{7}{8}-\dfrac{1}{2}\) | \(\dfrac{7}{8}-\dfrac{4}{8}\) | \(\dfrac{3}{8}\) |
How to subtract fractions with related denominators
- Rename the smaller-denominator fraction to the larger denominator.
- Subtract the numerators and keep that denominator.
- Simplify the answer if you can.
| \(\dfrac{3}{4}-\dfrac{1}{2}\) | \(=\) | \(\dfrac{3}{4}-\dfrac{2}{4}\) |
| \(=\) | \(\dfrac{1}{4}\) |
| \(\dfrac{5}{6}-\dfrac{1}{3}\) | \(=\) | \(\dfrac{5}{6}-\dfrac{2}{6}\) |
| \(=\) | \(\dfrac{3}{6}=\dfrac{1}{2}\) |
| \(\dfrac{7}{8}-\dfrac{1}{2}\) | \(=\) | \(\dfrac{7}{8}-\dfrac{4}{8}\) |
| \(=\) | \(\dfrac{3}{8}\) |
| \(\dfrac{7}{8}-\dfrac{3}{4}\) | \(=\) | \(\dfrac{7}{8}-\dfrac{6}{8}\) |
| \(=\) | \(\dfrac{1}{8}\) |
Common pitfalls
Frequently asked questions
How do you subtract fractions with related denominators?
Rename one fraction to the larger denominator so the parts match, then subtract the numerators. \(\dfrac{3}{4}-\dfrac{1}{2}=\dfrac{1}{4}\).
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 subtracting?
Fractions can only be subtracted when the parts are the same size, which means the denominators must match.
Do you simplify the answer?
Yes, write the difference in simplest form when the top and bottom share a factor, such as \(\dfrac{3}{6}=\dfrac{1}{2}\).