About the fraction calculator
This fraction calculator adds, subtracts, multiplies and divides fractions and mixed numbers and always returns the answer in simplest form, as a mixed number and as a decimal. It can also simplify a single fraction, convert a fraction to a decimal, and turn a terminating decimal back into a fraction.
All arithmetic is done with exact whole numbers, so there is no rounding error, even for large numerators and denominators.
Who should use the fraction calculator
- Students learning or checking fraction arithmetic.
- Cooks and makers scaling recipes and measurements.
- Teachers who want worked steps to show on screen.
How to use the fraction calculator: what each input means
- Fraction 1 and 2
- Each has an optional whole-number part, a numerator and a denominator. Leave the whole number at 0 for a plain fraction.
- Operation
- Add, subtract, multiply or divide.
- Other modes
- Simplify a fraction, convert to decimal, or convert a decimal to a fraction.
How the fraction calculator works: method and formula
To add or subtract, the fractions are rewritten over a common denominator, then combined. To multiply, numerators are multiplied together and denominators are multiplied together. To divide, the second fraction is flipped (its reciprocal) and multiplied.
Every result is reduced by dividing the numerator and denominator by their greatest common factor. Mixed numbers are first converted to improper fractions.
- Add
- a/b + c/d = (a×d + c×b) ÷ (b×d)
- Multiply
- a/b × c/d = (a×c) ÷ (b×d)
- Divide
- a/b ÷ c/d = (a×d) ÷ (b×c)
How to read your fraction calculator result
The headline answer is the simplified fraction. The mixed-number form is useful for measurements, and the decimal form is shown for comparison; a repeating decimal is marked as such.
Division by a zero fraction is not defined and is reported as an error.
Fraction Calculator worked example
Work with 1/2 and 1/3.
- Add: 1/2 + 1/3 = 3/6 + 2/6 = 5/6.
- Multiply: 1/2 × 1/3 = 1/6.
- Divide: 1/2 ÷ 1/3 = 1/2 × 3/1 = 3/2 (1.5).
1/2 + 1/3 = 5/6, which is 0.8(3)… as a repeating decimal.
Practical uses of the fraction calculator
- Adding measurements such as 2 3/4 cups and 1 5/8 cups.
- Checking homework answers.
- Converting 0.375 to 3/8.
Assumptions and limitations of this calculator
- Decimal-to-fraction conversion handles terminating decimals only; for a repeating decimal such as 0.333… enter the fraction form.
- Numerators and denominators must be whole numbers, and denominators must be above zero.