The four fraction rules
Every fraction problem comes down to four rules. Adding and subtracting need a common denominator, because you can only add parts of the same size. Multiplying and dividing do not: you multiply straight across, and for division you flip the second fraction first.
Adding and subtracting fractions
Take 1 1/2 + 2/3. First turn the mixed number into an improper fraction: 1 1/2 = (1 × 2 + 1)/2 = 3/2. The denominators are 2 and 3, and the least common denominator, the smallest number both divide into, is 6. So 3/2 = 9/6 and 2/3 = 4/6. Now add the numerators and keep the denominator: 9/6 + 4/6 = 13/6. As a mixed number that is 2 1/6, because 6 goes into 13 twice with 1 left over.
You can always use the product of the two denominators as a common denominator, as in the formula above. The least common denominator keeps the numbers small, so there is less to simplify at the end.
Multiplying and dividing fractions
To multiply, multiply the numerators and the denominators: 3/4 × 2/5 = 6/20, which simplifies to 3/10. To divide, flip the second fraction to get its reciprocal and multiply: 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8 = 1 7/8. Dividing by a fraction smaller than 1 makes the result bigger, which is a quick way to check your answer. Dividing by 0 is not defined, because no number times 0 gives anything but 0.
Simplifying fractions
A fraction is in lowest terms when the numerator and denominator share no factor other than 1. To simplify, find their greatest common divisor (GCD) and divide both by it. For 18/24 the GCD is 6, so 18/24 = 3/4. If the numerator is larger than the denominator, you can also write the answer as a mixed number: 13/6 = 2 1/6.
Fractions as decimals
Divide the numerator by the denominator to get the decimal. Some fractions end, like 3/8 = 0.375. Others repeat forever, like 1/3 = 0.333…, which the calculator marks with a bar over the repeating digits.
| Fraction | Decimal | Percent |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.333… | 33.33% |
| 2/3 | 0.666… | 66.67% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 1/6 | 0.1666… | 16.67% |
| 1/8 | 0.125 | 12.5% |
| 3/8 | 0.375 | 37.5% |
| 5/8 | 0.625 | 62.5% |
| 1/10 | 0.1 | 10% |
| 1/12 | 0.08333… | 8.33% |
How to use the fraction calculator
- 1Type the first number as a fraction, mixed number, whole number or decimal.
- 2Pick add, subtract, multiply or divide, and type the second number.
- 3Read the simplified fraction, the mixed number and the decimal, and follow the steps to see how the answer comes together. To simplify one fraction or convert a decimal, use the two small tools below the calculator.
Frequently asked questions
How do I add fractions with different denominators?
Find the least common denominator, the smallest number both denominators divide into. Rewrite each fraction with it, add the numerators and keep the denominator. For 1/4 + 1/6 the common denominator is 12, so 3/12 + 2/12 = 5/12.
How do I turn a mixed number into an improper fraction?
Multiply the whole number by the denominator and add the numerator. That is the new numerator, and the denominator stays the same. 2 3/5 becomes (2 × 5 + 3)/5 = 13/5.
How do I convert a decimal to a fraction?
Write the digits after the point over 10, 100 or 1000, one zero per decimal place, and simplify. 0.625 has three places, so it is 625/1000. Both numbers divide by 125, which gives 5/8.
Why does 1/3 show as 0.333…?
Some fractions never end as a decimal. A fraction in lowest terms only has a finite decimal when its denominator has no prime factors other than 2 and 5. Thirds, sixths, sevenths and ninths repeat forever, so the calculator rounds to 6 places and shows the repeating digits with a bar.
Can I use negative fractions?
Yes. Type a minus sign in front, like -3/4 or -2 3/5. A negative mixed number means the whole value is negative, so -2 3/5 is -(2 + 3/5) = -13/5, not -2 + 3/5.