Fraction Calculator

Below are multiple fraction calculators that can perform addition, subtraction, multiplication, division, simplification, and conversions between fractions and decimals. Fields above the solid black line represent the numerator, and fields below represent the denominator.

Addition:

Unlike adding and subtracting integers such as 2 and 8, fractions require a common denominator to undergo these operations. One method for finding a common denominator involves multiplying the numerators and denominators of all of the fractions involved by the product of the denominators of each fraction. Multiplying all of the denominators ensures that the new denominator is certain to be a multiple of each individual denominator. The numerators also need to be multiplied by the appropriate factors to preserve the value of the fraction as a whole. This is arguably the simplest way to ensure that the fractions have a common denominator. However, in most cases, the solutions to these equations will not appear in simplified form (the provided calculator computes the simplification automatically). Below is an example using this method.

$ab+cd=a×db×d+c×bd×b=ad+bcbd\frac{a}{b} + \frac{c}{d} = \frac{a \times d}{b \times d} + \frac{c \times b}{d \times b} = \frac{ad + bc}{bd}$

Example:

$34+16=3×64×6+1×46×4=2224=1112\frac{3}{4} + \frac{1}{6} = \frac{3 \times 6}{4 \times 6} + \frac{1 \times 4}{6 \times 4} = \frac{22}{24} = \frac{11}{12}$

This process can be used for any number of fractions. Just multiply the numerators and denominators of each fraction in the problem by the product of the denominators of all the other fractions (not including its own respective denominator) in the problem.

Example:

$14+16+12=1×6×24×6×2+1×4×26×4×2+1×4×62×4×6\frac{1}{4} + \frac{1}{6} + \frac{1}{2} = \frac{1 \times 6 \times 2}{4 \times 6 \times 2} + \frac{1 \times 4 \times 2}{6 \times 4 \times 2} + \frac{1 \times 4 \times 6}{2 \times 4 \times 6}$

An alternative method for finding a common denominator is to determine the least common multiple (LCM) for the denominators, then add or subtract the numerators as one would an integer. Using the least common multiple can be more efficient and is more likely to result in a fraction in simplified form. In the example above, the denominators were 4, 6, and 2. The least common multiple is the first shared multiple of these three numbers.

Multiples of 2: 2, 4, 6, 8, 10, 12
Multiples of 4: 4, 8, 12
Multiples of 6: 6, 12

The first multiple they all share is 12, so this is the least common multiple. To complete an addition (or subtraction) problem, multiply the numerators and denominators of each fraction in the problem by whatever value will make the denominators 12, then add the numerators.

Example:

$14+16+12=1×34×3+1×26×2+1×62×6\frac{1}{4} + \frac{1}{6} + \frac{1}{2} = \frac{1 \times 3}{4 \times 3} + \frac{1 \times 2}{6 \times 2} + \frac{1 \times 6}{2 \times 6}$