Fraction Calculator
Add, subtract, multiply and divide fractions and mixed numbers, simplify any fraction, or turn a decimal into a fraction. Every answer comes with the steps, a mixed-number form, a decimal and a percentage.
Your result
Enter your fractions above to see the result.
Step by step
Equivalent fractions
Exact whole-number arithmetic, so there is no rounding. Repeating decimals are shown with the repeating digits in brackets.
Fractions in plain words
A fraction describes part of a whole. The bottom number, the denominator, says how many equal pieces the whole is cut into. The top number, the numerator, says how many of those pieces you have. So 3/4 means three of four equal pieces, which is three quarters of a pizza.
Fractions look fiddly because each operation has its own rule, and mixed numbers add another layer. The good news is that there are only a few rules, and once you see why they work they stop feeling arbitrary.
How to use this calculator
- Calculate: enter two fractions, or mixed numbers using the Whole box, pick +, −, × or ÷, and read the answer.
- Simplify: enter one fraction and get it in its lowest terms, with the greatest common divisor shown.
- Decimal to fraction: type a decimal such as 0.375 and get 3/8.
Each answer is given as a simplified fraction, a mixed number, a decimal and a percentage, and the steps below explain how it was reached.
The four rules
Adding and subtracting
You can only add or subtract pieces of the same size, so first rewrite both fractions over a common denominator. Then add or subtract the numerators and keep the denominator. For 1/4 + 1/6, use 12: 3/12 + 2/12 = 5/12.
Multiplying
Multiply the tops and multiply the bottoms. A half of a third is 1/2 × 1/3 = 1/6. There is no need for a common denominator.
Dividing
Dividing by a fraction means multiplying by its reciprocal, the same fraction turned upside down. How many quarters fit into 3/4? 3/4 ÷ 1/4 = 3/4 × 4/1 = 3.
Simplifying
Divide the top and bottom by the same number until nothing but 1 divides both. The greatest common divisor gets you there in one step. 18/24 divided through by 6 is 3/4.
Worked examples
Adding mixed numbers
2 1/3 + 1 3/4. Convert to improper fractions: 7/3 and 7/4. The common denominator is 12, so these become 28/12 and 21/12. Add them to get 49/12, which is 4 1/12 as a mixed number.
Dividing fractions
3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8 = 1 7/8. The answer is bigger than 3/4 because 2/5 is a small amount, and dividing by a small amount gives a larger result.
A decimal to a fraction
0.375 has three decimal places, so write it as 375/1000. The greatest common divisor of 375 and 1000 is 125, which gives 3/8.
Mixed numbers and improper fractions
A mixed number such as 2 1/3 is a whole number and a fraction together. An improper fraction such as 7/3 says the same thing with a single fraction. To convert a mixed number, multiply the whole part by the denominator, add the numerator, and keep the denominator: 2 × 3 + 1 = 7, so 7/3. To go back, divide the numerator by the denominator: 7 ÷ 3 is 2 remainder 1, so 2 1/3. Calculations are easiest on improper fractions, which is what the calculator uses behind the scenes.
Fractions, decimals and percentages
A fraction is a division in disguise, so dividing the top by the bottom gives its decimal. 1/8 is 0.125 and 5/8 is 0.625. Some fractions never end: 1/3 is 0.3333… and 1/7 is 0.142857142857… with a block of digits repeating. The calculator shows these in brackets, such as 0.(3) for 1/3, so you see the exact value rather than a rounded one. Multiply a decimal by 100 for the percentage.
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.(3) | 33.(3)% |
| 1/4 | 0.25 | 25% |
| 1/5 | 0.2 | 20% |
| 1/8 | 0.125 | 12.5% |
| 2/3 | 0.(6) | 66.(6)% |
| 3/4 | 0.75 | 75% |
| 7/8 | 0.875 | 87.5% |
Common mistakes
- Adding the numerators and the denominators separately, so 1/2 + 1/3 becomes 2/5. The correct answer is 5/6.
- Forgetting to find a common denominator before adding or subtracting.
- Flipping the wrong fraction when dividing. Only the second fraction is inverted.
- Not simplifying the answer, so 6/12 is left when 1/2 is expected.
- Adding the whole numbers of mixed numbers and the fractions separately but forgetting to carry when the fraction part reaches 1 or more.
Frequently asked questions
How do I add fractions with different denominators?
Find a common denominator, which is a number both denominators divide into evenly, usually the lowest common multiple. Rewrite each fraction with that denominator, add the numerators and keep the denominator. For 1/4 + 1/6 the common denominator is 12, so you add 3/12 + 2/12 to get 5/12. The calculator shows these steps for any pair.
How do I subtract fractions?
The method is the same as adding. Convert both fractions to a common denominator, then subtract the second numerator from the first and keep the denominator. For 3/4 minus 1/3, use 12 as the denominator: 9/12 minus 4/12 equals 5/12.
How do I multiply fractions?
Multiply the numerators together and multiply the denominators together, then simplify. For 2/3 times 3/4 you get 6/12, which simplifies to 1/2. You do not need a common denominator for multiplication.
How do I divide fractions?
Flip the second fraction upside down (its reciprocal) and multiply. Dividing by 2/5 is the same as multiplying by 5/2. So 3/4 divided by 2/5 becomes 3/4 times 5/2, which is 15/8, or 1 and 7/8 as a mixed number.
How do I simplify a fraction?
Divide the numerator and the denominator by their greatest common divisor, the largest whole number that divides both exactly. For 18/24 the greatest common divisor is 6, so the simplified fraction is 3/4. A fraction is fully simplified when the only number that divides both parts is 1.
How do I work with mixed numbers?
A mixed number such as 2 1/3 is a whole number plus a fraction. To calculate with it, first turn it into an improper fraction by multiplying the whole number by the denominator and adding the numerator: 2 x 3 + 1 = 7, so 2 1/3 is 7/3. The calculator does this for you and shows the answer as both an improper fraction and a mixed number.
What is the difference between a proper and an improper fraction?
In a proper fraction the numerator is smaller than the denominator, so its value is less than 1, such as 3/5. In an improper fraction the numerator is equal to or larger than the denominator, so the value is 1 or more, such as 9/4. An improper fraction can be rewritten as a mixed number: 9/4 is 2 1/4.
How do I convert a fraction to a decimal or percentage?
Divide the numerator by the denominator. 3/8 gives 0.375, and multiplying by 100 gives 37.5 percent. Some fractions produce a repeating decimal, for example 1/3 is 0.333 with the 3 repeating forever. The calculator marks the repeating part in brackets, so 1/3 appears as 0.(3).
How do I turn a decimal into a fraction?
Write the decimal over a power of ten with as many zeros as it has decimal places, then simplify. 0.375 is 375/1000, which simplifies to 3/8. Use the Decimal to fraction tab and type any terminating decimal.
Can I enter negative fractions?
Yes. Put a minus sign in front of the whole number, or in front of the numerator if there is no whole number. A negative mixed number such as -2 1/3 means minus (2 + 1/3), so it equals -7/3.
Why does the calculator say I cannot divide by zero?
A fraction with a zero denominator is undefined, and dividing by a fraction whose value is zero is also undefined, because it would mean multiplying by a reciprocal that does not exist. Change the denominator or the second fraction and the calculation will go through.
Is anything I type saved or sent anywhere?
No. The sums run in your browser and nothing you enter is uploaded or stored on our servers.
Related calculators
For percentages and fraction-to-percent conversions try the percentage calculator. To find the mean of a list of values use the average calculator, and to measure how spread out values are, see the standard deviation calculator.