Fraction Calculator
This free fraction calculator can add, subtract, multiply and divide fractions and mixed numbers. Type in two fractions, pick an operation, and get a simplified answer with the decimal value and every step of the working shown. Students use it to check homework, parents use it to help with school maths, and cooks use it to scale recipes up or down. Everything runs in your browser, so your numbers never leave your device.
How fractions are worked out
The calculator follows the standard rules for fraction arithmetic. Mixed numbers are first turned into improper fractions. Then:
- Addition: a/b + c/d = (a x d + b x c) / (b x d)
- Subtraction: a/b – c/d = (a x d – b x c) / (b x d)
- Multiplication: a/b x c/d = (a x c) / (b x d)
- Division: a/b / c/d = (a x d) / (b x c)
Finally, the answer is simplified by dividing the top and bottom by their greatest common divisor (GCD).
Worked example: 1 1/2 + 2/3
Here is how the calculator works through 1 1/2 + 2/3:
- Convert to improper fractions: 1 1/2 = 3/2, and 2/3 stays as 2/3.
- Find a common denominator. The lowest common multiple of 2 and 3 is 6, so 3/2 = 9/6 and 2/3 = 4/6.
- Add the top numbers: 9 + 4 = 13, giving 13/6.
- Simplify: the GCD of 13 and 6 is 1, so 13/6 is already in its simplest form. As a mixed number that is 2 1/6, and as a decimal it is about 2.16666667.
How to use this calculator
- Type each fraction into the labelled boxes: the whole-number part (leave it blank for a simple fraction), the numerator and the denominator.
- Choose +, -, x or / from the operation menu and press Calculate.
- Read the simplified answer. Use the toggle to switch between improper fraction and mixed number form, and check the decimal value and the step-by-step working underneath.
Ordering fractions
The ordering mode below sorts a list of fractions from least to greatest and from greatest to least. Type each value separated by commas: fractions like 3/4, mixed numbers like 3 5/8, decimals and whole numbers all work. The tool finds a common denominator and shows each value as an equivalent fraction before ordering them.
Fractions like 3/4, mixed numbers like 3 5/8, decimals and whole numbers all work.
How does the ordering tool use a common denominator?
You can only compare fractions fairly when they share the same denominator. The tool finds the lowest common denominator, rewrites every value with it, and then orders them by their top numbers. Equal values are shown with an equals sign, so 3/4 = 9/12.
Limits of this tool
- The boxes accept whole numbers only. Decimals, letters and symbols are rejected with a clear message.
- A denominator cannot be zero. The calculator will ask you to change it instead of giving a wrong answer.
- The tool works with two fractions at a time. For a longer chain, work through it in pairs.
- The fraction arithmetic is exact, but very large results show the decimal rounded to eight places.
The parts of a fraction
Every fraction has two parts. The top number, the numerator, counts how many pieces you have. The bottom number, the denominator, says how many equal pieces the whole was cut into. So 3/4 means three pieces, where each piece is a quarter of the whole. A fraction is also a division in disguise: 3/4 is exactly 3 ÷ 4, which is why its decimal value is 0.75. When the numerator is smaller than the denominator, the fraction is called proper and is worth less than 1. When it is bigger, the fraction is improper and is worth more than 1, like 11/4. A fraction worth exactly 1, such as 5/5, has equal top and bottom numbers.
Adding and subtracting fractions, step by step
Adding and subtracting are the two operations where the bottom numbers (the denominators) matter most. You can only add or subtract pieces that are the same size, so the denominators have to match before you start.
When the denominators already match
If both fractions share a denominator, just add or subtract the top numbers and keep the denominator as it is. For example, 3/8 + 2/8 = 5/8, and 7/10 − 3/10 = 4/10, which simplifies to 2/5.
When the denominators are different
Rewrite both fractions over a common denominator first. The calculator uses the lowest common denominator, which keeps the numbers small. Take 3/4 − 1/6: the lowest common multiple of 4 and 6 is 12, so 3/4 becomes 9/12 and 1/6 becomes 2/12. Then 9/12 − 2/12 = 7/12. The GCD of 7 and 12 is 1, so 7/12 is already in its simplest form.
Mixed numbers work the same way once they are converted. For 2 1/3 − 3/4, convert 2 1/3 to 7/3, rewrite both over 12 (28/12 − 9/12), and the answer is 19/12, which is 1 7/12 as a mixed number.
Multiplying and dividing fractions, step by step
Multiplication is the most direct of the four operations: multiply the top numbers together and the bottom numbers together. No common denominator is needed. So 2/3 × 4/5 = 8/15.
A shortcut worth knowing is cancelling before you multiply. In 2/3 × 9/4, the 2 and the 4 share a factor of 2, and the 3 and the 9 share a factor of 3, so the problem shrinks to 1/1 × 3/2 = 3/2 before you multiply anything. The calculator’s steps do this automatically by simplifying with the GCD at the end, which gives the same answer.
Division works by flipping the second fraction and multiplying: dividing by a fraction is the same as multiplying by its reciprocal. So 3/5 ÷ 2/7 becomes 3/5 × 7/2 = 21/10, which is 2 1/10 as a mixed number. A common way to remember it is “keep, change, flip”: keep the first fraction, change the sign to multiply, flip the second fraction.
Mixed numbers and improper fractions
A mixed number such as 2 3/4 combines a whole number with a fraction. An improper fraction such as 11/4 has a top number bigger than the bottom number. They are two ways of writing the same value, and the calculator’s toggle lets you see the answer in whichever form you prefer.
To turn a mixed number into an improper fraction, multiply the whole number by the denominator and add the numerator: 3 2/5 becomes (3 × 5 + 2)/5 = 17/5. To go back, divide the numerator by the denominator: 17 ÷ 5 is 3 with a remainder of 2, so 17/5 = 3 2/5. Improper fractions are easier to calculate with; mixed numbers are easier to picture. That is why the calculator works in improper form and then offers the answer both ways.
Simplifying fractions
An answer is in its simplest form when the top and bottom share no factor other than 1. To simplify, divide both by their greatest common divisor (GCD). For 24/36, the GCD is 12, so dividing top and bottom by 12 gives 2/3. Every answer from this calculator is simplified this way, and the steps show the GCD that was used. If you want to practise finding factors and common divisors yourself, try the Factors Calculator and the LCM Calculator.
Common fractions as decimals and percents
The same value can be written three ways. The calculator shows the decimal and the percent under every answer; here are the common ones worth recognising on sight.
| Fraction | Decimal | Percent |
|---|---|---|
| 1/10 | 0.1 | 10% |
| 1/8 | 0.125 | 12.5% |
| 1/5 | 0.2 | 20% |
| 1/4 | 0.25 | 25% |
| 1/3 | 0.333… | 33.33% |
| 3/8 | 0.375 | 37.5% |
| 2/5 | 0.4 | 40% |
| 1/2 | 0.5 | 50% |
| 3/5 | 0.6 | 60% |
| 5/8 | 0.625 | 62.5% |
| 2/3 | 0.667… | 66.67% |
| 3/4 | 0.75 | 75% |
| 4/5 | 0.8 | 80% |
| 7/8 | 0.875 | 87.5% |
For percent problems beyond simple conversions — discounts, tax, percent change — use the Percentage Calculator.
Fractions in everyday life
Fractions turn up constantly outside the classroom. Recipes are the classic case: halving a recipe that calls for 3/4 of a cup means working out 3/4 ÷ 2 = 3/8 of a cup. Measurements are full of them too, from 5/8 of an inch on a tape measure to 1/4 of an hour, which is 15 minutes. Money and sharing problems are fractions in disguise as well: splitting a bill three ways gives everyone 1/3, and a 1/4 discount is the same as paying 3/4 of the price. When a problem like these lands in front of you, type it into the calculator above and follow the steps to see how the answer is built.
Frequently asked questions
Can this fraction calculator add, subtract, multiply and divide mixed numbers too?
Yes. Put the whole-number part in the whole-number box and the fraction part in the numerator and denominator boxes. The tool converts each mixed number to an improper fraction before it calculates, then offers the answer back as a mixed number if you prefer.
Why does the working show a common denominator?
You can only add or subtract fractions when the bottom numbers match. The calculator finds the lowest common multiple of the two denominators, rewrites both fractions with it, and then adds or subtracts the top numbers. Showing this step makes it easier to follow and to learn the method.
What does the GCD simplification step do?
GCD stands for greatest common divisor: the largest whole number that divides both the top and bottom of the answer. Dividing by it gives the simplest form, so 6/12 becomes 1/2. The steps show the GCD used each time.
What happens if I enter 0 as a denominator?
You get a clear error message: “A denominator cannot be zero. Please change the denominator.” Nothing is calculated, because division by zero has no defined answer.
Related tools
- Browse all CalcNova calculators to see every free tool on the site.
- Percentage Calculator to turn fractions into percentages and work out percent change.
- Equation Solver to solve linear and quadratic equations with the steps shown.