How to use the fraction calculator
- Enter the first fraction. For a mixed number such as 2 1/3, fill the whole number, numerator and denominator. For a plain fraction, leave the whole number blank.
- Choose add, subtract, multiply or divide.
- Enter the second fraction the same way. Negative values go on the whole number, or on the numerator when there is no whole part.
- Read the simplest form, the mixed number and the decimal. The steps show the common denominator, any reciprocal and the simplification.
Formula
a/b + c/d = (a x d + c x b) / (b x d)
a/b x c/d = (a x c) / (b x d)
a/b / c/d = (a x d) / (b x c), with c not 0
Simplify by dividing top and bottom by their greatest common divisor
All arithmetic uses exact whole numbers, so there is no rounding until the decimal is shown. Subtraction is addition of the negative.
Worked examples
3/4 + 1/2: the common denominator is lcm(4, 2) = 4, so 1/2 = 2/4. Then 3/4 + 2/4 = 5/4, which is 1 1/4 or 1.25.
1/2 + 1/3: lcm(2, 3) = 6, so 3/6 + 2/6 = 5/6, which is 0.8(3), meaning 0.8333... repeating.
2/3 x 3/4: 2 x 3 = 6 and 3 x 4 = 12, so 6/12. The greatest common divisor is 6, so the answer is 1/2.
2 1/3 x 1 1/2: convert to 7/3 x 3/2 = 21/6 = 7/2, or 3 1/2.
3/4 / 2/3: multiply by the reciprocal, 3/4 x 3/2 = 9/8, or 1 1/8.
Mixed numbers and negative values
A mixed number such as 2 1/3 is the whole number plus the fraction, so it equals 7/3. A negative mixed number such as -2 1/3 means negative (2 + 1/3), which is -7/3. That is why the minus sign belongs on the whole number. If you type a negative numerator after a whole number, the tool asks you to move the sign.
Repeating decimals
Some fractions never end as decimals. The tool finds the repeating block by long division and shows it in parentheses, so 1/7 is 0.(142857) and 7/12 is 0.58(3). To convert a single fraction or round it to inch fractions, use the fraction to decimal converter.
Errors the tool catches
A denominator of zero has no meaning, and dividing by a fraction equal to zero is undefined. The tool stops and explains the problem rather than printing infinity. Decimals in the boxes are rejected, since this tool is for whole-number fractions. For a ratio view of two numbers, try the ratio calculator.
Assumptions and limits
- Numerators, denominators and whole parts must be whole numbers of up to 40 digits.
- Results are always reduced to lowest terms, and the unsimplified fraction is shown when it differs.
- The decimal is computed exactly by long division and is cut off at 40 digits if the repeating block is longer, with three dots shown.
- Division by zero and zero denominators are reported as errors.
- Everything is calculated in your browser, and nothing is sent to a server.
Frequently asked questions
How do you add fractions with different denominators?
Rewrite both fractions over a shared denominator, usually the least common multiple of the two denominators, then add the numerators and keep the denominator. Finish by reducing the result.
How do you divide by a fraction?
Flip the second fraction to get its reciprocal and multiply. Dividing by 2/3 is the same as multiplying by 3/2. This is why dividing by a fraction less than 1 makes the number larger.
What is the simplest form of a fraction?
It is the version where the numerator and denominator share no common factor except 1. You get there by dividing both by their greatest common divisor, for example 6/12 becomes 1/2.
How do I turn an improper fraction into a mixed number?
Divide the numerator by the denominator. The whole part of the quotient is the whole number and the remainder becomes the new numerator over the same denominator, so 9/4 is 2 1/4.
Can the calculator handle negative fractions?
Yes. Put the minus sign on the numerator of a plain fraction or on the whole number of a mixed number, and the result keeps the correct sign.