Subtracting Fractions — Step by Step with Examples

To subtract fractions, make the denominators match, then subtract the numerators. The whole method rests on one idea: fractions combine directly only when they are measured in the same-sized parts, and most wrong answers come from skipping that step.

When Each Case Applies

If the denominators already match, you can subtract right away and keep the denominator. If they differ, you must rewrite first. Knowing which case you are in is the first decision.

When two fractions share a denominator,

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,

The denominator does not change because the unit has not changed; you are still working in elevenths.

When the denominators differ, such as $\frac{a}{b} - \frac{c}{d}$, do not subtract the numerators yet. Take $\frac{3}{4}$ and $\frac{1}{2}$: 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, and then

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

The Steps

1. Check the denominators. If they already match, subtract the numerators and keep the denominator.
2. Find a common denominator. If they differ, rewrite both fractions as equivalent fractions with the same denominator.
3. Subtract and simplify. Subtract the numerators, keep the denominator, and reduce the result if possible.

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

Check the denominators. They are $6$ and $4$, so they differ. Find a common denominator; the least common denominator is $12$.

Find a common denominator and rewrite.

Subtract and simplify.

Since $7$ and $12$ share no common factor greater than $1$, the final answer is

That is the full pattern for unlike denominators: rewrite, subtract, then simplify.

Practice And Self-Check

Try

Work the steps in order. Self-check at each step: the denominators differ, so the common denominator is $24$; rewritten, the fractions become $\frac{21}{24}$ and $\frac{8}{24}$; subtracting gives $\frac{13}{24}$, which is already in lowest terms. If both fractions are not in twenty-fourths before you subtract, your common denominator step went wrong.

Where Each Step Goes Wrong

The biggest trap, at the subtract step, is subtracting the denominators too. In general, $\frac{a}{b} - \frac{c}{d} \ne \frac{a-c}{b-d}$.

At the rewrite step, students often convert one fraction incorrectly after choosing a common denominator. Recheck that each new numerator was scaled by the same factor as its denominator.

At the simplify step, it is easy to forget to reduce the final fraction when a common factor remains.

And watch the sign: when the second fraction is larger, the answer is negative. For example, $\frac{1}{3} - \frac{3}{4}$ should come out negative.

Subtracting fractions appears in measurement, cooking, time intervals, probability, and algebra, and supports later topics such as rational expressions and equation solving, where tracking common denominators matters.