How to use the Fraction calculator
- 1Enter the first fraction. For a mixed number, fill in the whole-number part as well as the numerator and denominator.
- 2Choose add, subtract, multiply or divide, then enter the second fraction.
- 3Read the simplified fraction, the mixed-number form and the decimal value.
- 4To reduce one fraction on its own, switch to simplify and enter just that fraction.
How it works
Mixed numbers are first converted to improper fractions: 2 1/4 becomes (2 × 4 + 1)/4 = 9/4. That lets every operation follow a single rule.
For addition and subtraction, both fractions are rewritten over a common denominator, then the numerators are combined. Multiplication multiplies numerators together and denominators together. Division flips the second fraction and multiplies.
Finally, the result is divided top and bottom by the greatest common divisor to reach lowest terms. If the numerator is larger than the denominator, the whole-number part is split out to give a mixed number. A denominator of zero, or dividing by a zero fraction, is undefined and is reported as an error.
Formulas
a/b + c/d = (ad + bc) / bda/b − c/d = (ad − bc) / bda/b × c/d = ac / bda/b ÷ c/d = a/b × d/c = ad / bcc cannot be zero.
w n/d = (w × d + n) / dWorked examples
3/4 − 5/6
- 1Common denominator 12: 9/12 − 10/12
- 29 − 10 = −1
−1/12 ≈ −0.0833.
2 1/4 × 1 1/3
- 12 1/4 = 9/4 and 1 1/3 = 4/3
- 29/4 × 4/3 = 36/12
- 336/12 simplifies to 3
Exactly 3.
3/4 ÷ 2/5
- 1Flip the second fraction: 3/4 × 5/2
- 2= 15/8
- 315 ÷ 8 = 1 remainder 7
15/8 = 1 7/8 = 1.875.
Simplify 18/24
- 1gcd(18, 24) = 6
- 218 ÷ 6 = 3; 24 ÷ 6 = 4
18/24 = 3/4.
Why do you flip the second fraction when dividing?
Dividing by a number is the same as multiplying by its reciprocal. Asking "how many 2/5s fit into 3/4?" is equivalent to 3/4 × 5/2, because each whole contains 5/2 lots of 2/5. The result, 1 7/8, says one full 2/5 fits in, plus seven-eighths of another.
Do I need the lowest common denominator?
No. Any common denominator works; multiplying the two denominators is always valid. Using the lowest one just keeps the numbers smaller. The calculator simplifies the final answer either way, so you get the same result.
Frequently asked questions
How do I enter a negative fraction?
Put the minus sign on the whole number or the numerator. −1 1/2 means negative one and a half, which is −3/2.
How do I convert a fraction to a decimal?
Divide the numerator by the denominator. 7/8 = 7 ÷ 8 = 0.875. The calculator shows the decimal alongside every result, rounded where it repeats, as with 1/3 ≈ 0.3333.
What is an improper fraction?
A fraction whose numerator is equal to or larger than its denominator, such as 7/4. It equals the mixed number 1 3/4.
How do I know a fraction is fully simplified?
When the numerator and denominator share no common factor other than 1. 8/12 isn't, because both divide by 4; 2/3 is.
Can the denominator be zero?
No. Division by zero is undefined, so a fraction such as 5/0 has no value and the calculator shows an error instead.