How to use the Fraction Calculator
- Enter the numerator and denominator of the first fraction.
- Choose add, subtract, multiply or divide.
- Enter the numerator and denominator of the second fraction.
- Read the simplified fraction, the mixed number and the decimal.
Formula used
a/b + c/d = (ad + bc) ÷ bd. a/b × c/d = ac ÷ bd. a/b ÷ c/d = ad ÷ bc. The result is divided by the greatest common divisor to simplify it.
Worked example
Here is the Fraction Calculator worked through with the example values shown above, so you can check each step by hand.
| Inputs | |
|---|---|
| First fraction: numerator | 3 |
| First fraction: denominator | 4 |
| Operation | Add (+) |
| Second fraction: numerator | 5 |
| Second fraction: denominator | 6 |
| Result | |
| Simplified fraction | 19/12 |
| Mixed number | 1 7/12 |
| Decimal | 1.5833333 |
Adding and subtracting fractions
To add fractions with different denominators, convert them to a common denominator. For 3/4 + 5/6, the common denominator is 12: 3/4 = 9/12 and 5/6 = 10/12, so the sum is 19/12, which is 1 7/12 as a mixed number and 1.5833 as a decimal. The calculator multiplies the denominators (4 × 6 = 24) to get 38/24, then simplifies by dividing by the greatest common divisor, 2.
Subtraction works the same way. 1/3 − 1/2 gives -1/6, a negative result, because 1/3 is smaller than 1/2.
Multiplying and dividing fractions
To multiply, multiply the numerators and the denominators: 2/3 × 3/4 = 6/12, which simplifies to 1/2. To divide, multiply by the reciprocal of the second fraction: 1/2 ÷ 1/4 = 1/2 × 4/1 = 2, because there are two quarters in a half.
You cannot divide by a fraction whose numerator is zero, since it equals zero, and no denominator may be zero.
Simplifying and mixed numbers
A fraction is simplified when the numerator and denominator share no common factor other than 1. The calculator divides both by their greatest common divisor, so 6/12 becomes 1/2. When the numerator is larger than the denominator, the fraction is improper and can be written as a mixed number, such as 19/12 = 1 7/12.
Negative results are shown with the sign on the numerator, as in -3/2, and the mixed form is -1 1/2.
Where fractions are used
Fractions appear in recipes, measurements, construction, probability and algebra. Doubling a recipe that calls for 3/4 cup of sugar and 1/3 cup of oil means multiplying fractions, and combining 5/8 inch and 3/16 inch boards means adding them. The decimal result helps when you need a number for a calculator or a spreadsheet.
This calculator works with whole-number numerators and denominators. To handle a mixed number such as 1 1/2, convert it to an improper fraction first: 3/2.
Mistakes to avoid, and common decimal equivalents
The most common mistake is adding numerators and denominators separately: 1/2 + 1/3 is not 2/5. The correct result is 3/6 + 2/6 = 5/6. Another is forgetting to flip the second fraction when dividing: 1/2 ÷ 1/4 is 1/2 × 4 = 2.
Useful decimal equivalents: 1/8 = 0.125, 1/4 = 0.25, 1/3 = 0.3333…, 3/8 = 0.375, 1/2 = 0.5, 5/8 = 0.625, 2/3 = 0.6667…, 3/4 = 0.75 and 7/8 = 0.875. Some fractions give repeating decimals, so the decimal shown is rounded. Prefer the fraction when you need an exact answer.
Frequently asked questions
How do I add fractions with different denominators?
Rewrite them over a common denominator, add the numerators and simplify. The calculator does this using the product of the denominators and then simplifies.
How do I divide fractions?
Multiply the first fraction by the reciprocal of the second.
How do I simplify a fraction?
Divide the numerator and the denominator by their greatest common divisor.
How do I enter a mixed number?
Convert it to an improper fraction first. For 2 1/3, enter 7 over 3.
Can I use negative numbers?
Yes, in the numerator. A negative denominator is also accepted and is moved to the numerator.
Why does it say the denominator cannot be zero?
Division by zero is undefined, so a fraction with a zero denominator has no value.
Why is 1/2 + 1/3 not 2/5?
Fractions with different denominators must be rewritten over a common denominator first. 1/2 + 1/3 = 3/6 + 2/6 = 5/6.
This calculator gives estimates for information only. Actual figures from a bank, employer, tax authority or doctor may differ. It is not financial, tax, legal or medical advice.