Calculate fractions
Add, subtract, multiply or divide two fractions.
Set up the fraction problem
Enter the numerator and denominator for each fraction, then choose the operation. The numerator is the top number. The denominator is the bottom number. Keep each fraction in its own fields so the calculator can apply the correct rule.
Use this page for adding, subtracting, multiplying and dividing fractions. If the problem includes whole numbers, convert them to fractions first or use a mixed number calculator. If your class expects exact answers, keep the result as a fraction rather than a rounded decimal.
Reading the simplified answer
The result is simplified when possible. That means the numerator and denominator have no common factor left except 1. A result of 4/8 becomes 1/2 because both numbers can be divided by 4.
A fraction result may also be shown as a decimal, but the fraction is usually the exact answer. Decimals can be easier to compare, while fractions are often better for school work, recipes and exact ratios.
Fraction rules behind the calculator
Addition and subtraction need a common denominator. Once the denominators match, add or subtract only the numerators. Multiplication is different. Multiply numerator by numerator and denominator by denominator. For division, multiply by the reciprocal of the second fraction.
These rules are not interchangeable. Adding denominators is the classic mistake. The denominator names the size of the pieces, so the pieces must match before you add or subtract them.
Adding unlike denominators
To add 1/2 and 1/3, use a common denominator of 6. One half becomes 3/6. One third becomes 2/6. Add the numerators to get 5/6. The denominator stays 6 because the pieces are sixths.
For multiplication, 1/2 x 1/3 is 1/6. No common denominator is needed. For division, 1/2 divided by 1/3 becomes 1/2 x 3/1, which equals 3/2.
Denominators and signs to check
The biggest mistake is adding denominators. For 1/2 + 1/3, the answer is not 2/5. The fractions first need the same denominator. Also check whether the expected answer should be a fraction or a decimal.
Another mistake is forgetting to flip the second fraction in division. Only the second fraction becomes its reciprocal. The first fraction stays the same.
Fraction Calculator FAQ
How do I add fractions with different denominators?
Find a common denominator first. Convert each fraction to an equivalent fraction with that denominator. Then add the numerators and keep the denominator the same.
For 1/2 + 1/3, use sixths. The fractions become 3/6 and 2/6. The answer is 5/6.
Why do you not add the denominators?
The denominator describes the size of the pieces. If one fraction is in halves and the other is in thirds, the pieces are not the same size yet.
After converting both fractions to the same denominator, the pieces match. Then you can add or subtract the numerators.
A quick way to check this is to draw the pieces. Halves and thirds cannot be counted together until they are renamed as equal sized parts.
How do I divide fractions?
Keep the first fraction, change division to multiplication and flip the second fraction. This is often called multiplying by the reciprocal.
For example, 2/3 divided by 4/5 becomes 2/3 x 5/4. Multiply across to get 10/12, then simplify to 5/6.
Should the answer be a fraction or a decimal?
Use the format your problem asks for. Fractions are exact and are usually preferred in school fraction work. Decimals are helpful when comparing sizes or using money and measurements.
If a decimal repeats, the fraction form is often cleaner and more accurate.
What does simplifying a fraction mean?
Simplifying means dividing the numerator and denominator by the same common factor until no common factor remains. The value does not change.
For example, 12/18 simplifies to 2/3 because both 12 and 18 can be divided by 6.