Subtracting Fractions — Step by Step with Examples

To subtract fractions, make the denominators match, then subtract the numerators. If the denominators already match, you can subtract right away and keep the denominator.

That rule works because fractions can only be combined directly when they are measured in the same-sized parts. Most wrong answers come from skipping that step.

Subtract Fractions With The Same Denominator

If two fractions have the same denominator,

$$\frac{a}{b} - \frac{c}{b} = \frac{a-c}{b}$$

as long as $b \ne 0$. Both fractions are built from parts of size $\frac{1}{b}$, so you are subtracting how many of those parts remain.

For example,

$$\frac{9}{11} - \frac{4}{11} = \frac{5}{11}.$$

Nothing happens to the denominator because the unit has not changed. You are still working in elevenths.

Unlike Denominators: Rewrite First

If the denominators are different, such as

$$\frac{a}{b} - \frac{c}{d},$$

you should not subtract the numerators yet. The fractions are written in different-sized parts.

$\frac{3}{4}$ and $\frac{1}{2}$ show why. Fourths and halves are not the same unit, so $\frac{3}{4} - \frac{1}{2}$ is not a valid numerator-only subtraction.

Rewrite $\frac{1}{2}$ as $\frac{2}{4}$ first. Then both fractions are in fourths:

$$\frac{3}{4} - \frac{2}{4} = \frac{1}{4}.$$

The value did not change. Only the form changed so the subtraction became valid.

Worked Example: $\frac{5}{6} - \frac{1}{4}$

Solve

$$\frac{5}{6} - \frac{1}{4}.$$

Step 1: Find a common denominator

The denominators are $6$ and $4$, so start by finding a common denominator. The least common denominator is $12$.

Step 2: Rewrite both fractions

$$\frac{5}{6} = \frac{10}{12} \quad \text{and} \quad \frac{1}{4} = \frac{3}{12}$$

Step 3: Subtract the numerators

$$\frac{10}{12} - \frac{3}{12} = \frac{7}{12}$$

Step 4: Simplify if possible

$7$ and $12$ have no common factor greater than $1$, so the final answer is

$$\frac{7}{12}.$$

This is the full pattern for subtracting fractions with unlike denominators: rewrite, subtract, then simplify.

Common Mistakes In Fraction Subtraction

1. Subtracting the denominators too. In general, $\frac{a}{b} - \frac{c}{d} \ne \frac{a-c}{b-d}$.
2. Rewriting one fraction incorrectly after choosing a common denominator.
3. Forgetting to simplify the final fraction when a common factor remains.
4. Dropping the sign when the second fraction is larger. For example, $\frac{1}{3} - \frac{3}{4}$ should be negative.

Where Subtracting Fractions Is Used

Subtracting fractions appears in measurement, cooking, time intervals, probability, and algebra. Any time you remove one part of a whole from another part of a whole, fraction subtraction can appear.

It also supports later topics such as rational expressions and equation solving, where keeping track of common denominators matters.

Try A Similar Problem

Try

$$\frac{7}{8} - \frac{1}{3}.$$

Find the common denominator before you subtract anything. If your setup is correct, both fractions should be rewritten in twenty-fourths before the final subtraction.