Fraction calculator with worked steps
Enter two fractions and choose an operation. The calculator reduces the answer to its simplest form and displays a worked line. Use whole-number numerators and denominators; denominators cannot be zero.
Calculate
The four operations
- Addition and subtraction: find a common denominator, then add or subtract the numerators. Example: 1/2 + 1/3 = 3/6 + 2/6 = 5/6.
- Multiplication: multiply the numerators and multiply the denominators. Example: 2/3 × 3/4 = 6/12 = 1/2.
- Division: multiply by the reciprocal of the second fraction. Example: 1/2 ÷ 1/4 = 1/2 × 4/1 = 2.
- Simplify by dividing the numerator and denominator by their greatest common divisor. Example: 12/18 = 2/3.
Simplify before multiplying
You can reduce across the diagonal before multiplying. In 4/9 × 3/8, reduce 4 with 8 to 1 and 2, and 3 with 9 to 1 and 3. Then 1/3 × 1/2 = 1/6. This can keep intermediate numbers smaller.
Where fractions are useful
- Cooking: doubling 3/4 cup gives 1 1/2 cups.
- Woodworking and construction: inch-based drill bits and fasteners often use fractions such as 1/8 and 3/16.
- Music: note durations can be described as fractions of a beat; a 4/4 bar contains four quarter-note beats.
- Medication: follow the exact dose and instructions from a qualified professional; this calculator is not a dosing guide.
Frequently asked questions
Why does dividing by a fraction mean multiplying by its reciprocal?
Division asks how many groups of a given size fit into a value. There are four quarters in one whole, so dividing by 1/4 is equivalent to multiplying by 4. In general, divide by a/b by multiplying by b/a, as long as the divisor is not zero.
What are an improper fraction and a mixed number?
An improper fraction has a numerator whose absolute value is at least the denominator, such as 7/4. A mixed number writes it as a whole part and a fraction: 1 3/4. The calculator shows this form when the result is greater than one in magnitude.
Does every fraction have an exact decimal?
A reduced fraction has a terminating decimal only when its denominator has no prime factors other than 2 and 5. For example, 3/8 = 0.375; 1/3 repeats as 0.333… and 5/6 as 0.8333….
How can I compare 5/7 and 7/10 without a calculator?
Cross-multiply: 5 × 10 = 50 and 7 × 7 = 49. Since 50 is greater, 5/7 is greater than 7/10.
Can I enter negative fractions?
Yes. Put the negative sign in either numerator. The result is normalized so that the denominator is positive.
Related tools
For percentage calculations, use the percentage calculator.