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Subtracting Fractions

When subtracting fractions, the first thing to check is if the denominators are the same.

Subtracting Fractions with Like Denominators

Fractions with the same denominators are called like fractions.

To subtract fractions with like denominators, subtract the numerators , and write the difference over the denominator.

$\frac{5}{7}-\frac{4}{7}=\frac{1}{7}$

You may get an answer which is not in lowest terms , even if the fractions you were adding and subtracting both were. In this case, you have to reduce the fraction .

$\frac{8}{9}-\frac{2}{9}=\frac{6}{9}=\frac{6÷3}{9÷3}=\frac{2}{3}$

Subtracting Fractions with Unlike Denominators

If the denominators are not the same, then you have to use equivalent fractions which do have a common denominator . To do this, you need to find the least common multiple (LCM) of the two denominators.

To subtract fractions with unlike denominators, rename the fractions with a common denominator. Then subtract and simplify.

For example, suppose you want to add:

$\frac{6}{7}-\frac{2}{3}$

The LCM of $3$ and $11$ is $33$ . So, we need to find fractions equivalent to $\frac{6}{7}$ and $\frac{2}{3}$ which have $21$ in the denominator. Multiply the numerator and denominator of $\frac{6}{7}$ by $3$ , and multiply the numerator and denominator of $\frac{2}{3}$ by $7$ .

$\frac{6\times 3}{7\times 3}-\frac{2\times 7}{3\times 7}=\frac{18}{21}-\frac{14}{21}$

Now we have like denominators, and we can subtract as described above.

$=\frac{4}{21}$