Fraction Subtraction With Unlike Denominators

Fraction subtraction with unlike denominators

When two fractions have different denominators, you cannot subtract them directly. First, rewrite them so they share a common denominator.

1) Find a common denominator

Choose a number both denominators divide into evenly. The least common denominator is often the easiest choice, because it keeps the numbers smaller.

2) Rewrite each fraction

Multiply the numerator and denominator of each fraction by the same number so both fractions have the common denominator. This does not change the value of the fraction.

3) Subtract the numerators

Once the denominators match, subtract only the numerators and keep the denominator the same.

4) Simplify the result

Reduce the fraction if possible by dividing the numerator and denominator by their greatest common factor. If the fraction is improper, you may also convert it to a mixed number if needed.

Check your work

You can verify by estimating whether the answer should be close to zero, to one-half, or to another simple benchmark. Also, make sure both original fractions were rewritten correctly before subtracting.

Example idea: If you see (\frac{a}{b} - \frac{c}{d}), first make the denominators match, then compute (\frac{ad'}{bd'} - \frac{cb'}{db'}) only after rewriting both fractions with the same denominator.