Addition needs matching pieces
You can add counts only when the pieces are the same size. To add or subtract fractions, rewrite them with a common denominator. The product of the denominators always works, though the least common multiple may give smaller numbers.
Once the denominators match, add or subtract the numerators and retain that denominator. Do not add denominators: one half plus one half is two halves, not two quarters.
Products and quotients use a different rule
Multiply numerators together and denominators together for a product. You may cancel common factors across the numerator and denominator before multiplying, which keeps the arithmetic manageable.
To divide by a fraction, multiply by its reciprocal. The divisor must not be zero. A negative sign can sit in the numerator, denominator or in front of the fraction, but use just one consistent representation.
Simplify and check the size
Divide numerator and denominator by their greatest common divisor. A negative denominator is conventionally moved into the numerator. An improper fraction can be a perfectly valid final answer.
Estimate the size: multiplying two positive proper fractions should produce a smaller value than either factor. Dividing by a positive number below one makes a positive quantity larger.
LET’S WORK IT THROUGH
Add 2/5 and 1/6.
- Use the common denominator 30.
- 2/5 = 12/30 and 1/6 = 5/30.
- 12/30 + 5/30 = 17/30.
THE ANSWER17/30, already in simplest form.
YOUR TURN
A small check for understanding.
Divide 3/4 by 2/5.
Reveal the answer
15/8. Multiply 3/4 by the reciprocal 5/2.
Now try your own numbers.
The fraction calculator includes input guidance and the limits of its supported calculations. Use it alongside the method above.
Open Fraction calculator ↗A note on precision: preserve exact fractions where possible and round numerical results at the end. Found an unclear step? Prepare a correction report.