How to use the Fraction Calculator
- Enter the first fraction: numerator on top, denominator underneath, and a whole number in the small box for a mixed number.
- Choose +, −, × or ÷.
- Enter the second fraction the same way. The answer appears as you type.
- Read the simplified fraction, mixed number and decimal, and follow the step-by-step working to see how it was done.
Features
- Add, subtract, multiply and divide fractions
- Mixed numbers, whole numbers, negatives and decimals
- Answer in simplest form, as a mixed number and as a decimal
- Exact repeating decimals marked with a bar
- Step-by-step working with LCD and GCD shown
- Exact arithmetic with no rounding errors, even for big numbers
How fraction arithmetic works
Adding and subtracting
Fractions can only be added or subtracted when they share a denominator. Find the least common denominator (LCD), the smallest number both denominators divide into, rewrite each fraction over it, then add or subtract the numerators. For 1/2 + 1/3, the LCD of 2 and 3 is 6, so 1/2 = 3/6 and 1/3 = 2/6, and 3/6 + 2/6 = 5/6.
The LCD is the least common multiple of the denominators: LCD = a × b ÷ GCD(a, b). Any common denominator gives the same final answer after simplifying, but the smallest one keeps the numbers manageable.
Multiplying
Multiply straight across, numerator by numerator and denominator by denominator: 2/3 × 3/4 = 6/12 = 1/2. No common denominator is needed.
Dividing
To divide, multiply by the reciprocal of the second fraction, that is, flip it upside down: 3/4 ÷ 1/8 = 3/4 × 8/1 = 24/4 = 6. Dividing by zero is undefined, so a second fraction equal to 0 is rejected.
Mixed numbers
A mixed number such as 2 1/4 combines a whole number and a fraction. Convert it to an improper fraction before calculating: multiply the whole number by the denominator, add the numerator and keep the denominator, so 2 1/4 = (2 × 4 + 1)/4 = 9/4. To turn an answer back into a mixed number, divide the numerator by the denominator. The quotient is the whole part and the remainder is the new numerator: 15 ÷ 8 = 1 remainder 7, so 15/8 = 1 7/8.
Negative mixed numbers keep the sign on the whole value: −2 1/4 means −(2 + 1/4) = −9/4, not −2 + 1/4. In this calculator, type the minus sign in the whole-number box.
Simplifying
A fraction is in simplest form when its numerator and denominator share no factor other than 1. Divide both by their greatest common divisor (GCD): for 18/24 the GCD is 6, giving 3/4. The calculator finds the GCD with Euclid's algorithm, which repeatedly replaces the larger number with the remainder of dividing the two until the remainder is zero. It works with whole numbers of any size, so there is never a rounding error.
Fractions as decimals
Every fraction becomes either a terminating or a repeating decimal. If the simplified denominator has no prime factors other than 2 and 5, the decimal ends, as with 3/8 = 0.375. Otherwise it repeats forever: 1/3 = 0.333…, 5/6 = 0.8333… and 1/7 = 0.142857142857…. The calculator does exact long division and marks the repeating block with a bar, so 5/6 appears as 0.83 rather than a rounded value.
Worked example with mixed numbers
To work out 1 1/2 × 2 2/3, convert both to improper fractions, 3/2 and 8/3, then multiply to get 24/6. The GCD of 24 and 6 is 6, so the answer simplifies to 4. Enter it above to see each step laid out.
Working with percentages instead? The Percentage Calculator covers them, and the Scientific Calculator handles powers, roots and trig.
Frequently asked questions
How do I add fractions with different denominators?
Rewrite both fractions over their least common denominator, then add the numerators. For 1/2 + 1/3 the LCD is 6, so you get 3/6 + 2/6 = 5/6.
How do I enter a mixed number?
Type the whole number in the small box to the left of the fraction, then the numerator and denominator. For 2 ¾, enter 2, 3 and 4.
How do I simplify a fraction?
Divide the numerator and denominator by their greatest common divisor. The calculator always shows the answer in simplest form and lists the divisor it used.
How do I divide fractions?
Flip the second fraction and multiply. For example, 3/4 ÷ 1/8 = 3/4 × 8/1 = 6.
Why is there a line over some decimal digits?
The line marks digits that repeat forever. For example, 5/6 = 0.8333…, so the 3 is shown with a bar over it.