How to Add, Subtract, Multiply and Divide Fractions

Adds, subtracts, multiplies or divides two fractions and gives the answer in lowest terms. Addition and subtraction go over a common denominator, multiplication takes numerators and denominators in pairs, and division multiplies by the reciprocal. The mixed number and the decimal are also shown.

Two fractions are added, subtracted, multiplied or divided. Addition and subtraction go over a common denominator before the numerators are combined.

\dfrac{a}{b} \pm \dfrac{c}{d} = \dfrac{ad \pm cb}{bd}

Multiplication takes numerators and denominators in pairs.

\dfrac{a}{b} \times \dfrac{c}{d} = \dfrac{ac}{bd}

Division turns the second fraction over and multiplies.

\dfrac{a}{b} \div \dfrac{c}{d} = \dfrac{ad}{bc}

The answer is reduced to lowest terms, and the mixed number and the decimal are shown alongside it.

Example

For $\dfrac{1}{2} + \dfrac{1}{3}$ , a common denominator gives $\dfrac{3}{6} + \dfrac{2}{6}$ , and adding the numerators leaves $\dfrac{5}{6}$ , about 0.8333 as a decimal.

Why a common denominator is needed

The denominator says how big one piece is. A half and a third are pieces of different sizes, so their numerators cannot simply be added. Rewriting both over 6 makes each one a count of sixths, and counts of the same thing can be added.

Notes

Numerators and denominators must be whole numbers. To use a whole number as it stands, give it a denominator of 1.

No fraction has a denominator of 0, and dividing by a fraction whose numerator is 0 is not possible either.

Very large denominators overflow the range of integers that can be held exactly once the fractions are put over a common denominator. That case is refused rather than answered wrongly.