Fraction Calculator
Add, subtract, multiply and divide fractions with steps. Runs in your browser.
About this fraction calculator
This fraction calculator adds, subtracts, multiplies and divides fractions and mixed numbers, and shows every step of the working. It is for students checking homework, parents helping with it, and anyone scaling a recipe or cutting a board to 5/8 of an inch.
You can work with two fractions in stacked boxes, or type a whole expression such as 2 1/3 × (3/4 − 1/6) + 5/8. There are also modes to simplify a fraction with Euclid's algorithm and to turn a decimal, including a repeating one like 0.1666…, back into an exact fraction.
All arithmetic is exact. The calculator works with whole numbers of any size instead of floating point, so 1/3 + 1/6 is exactly 1/2 and never 0.49999.
Features
Mixed numbers everywhere
Use the whole-number box beside each fraction, or type 3 1/4 in an expression. Negative mixed numbers like −2 3/8 work too.
Steps you can follow
For two fractions, the working shows the improper fractions, the least common denominator, the rewritten fractions, the new numerator and the simplification.
Every answer format
Each result appears as a simplified fraction, a mixed number, a decimal with the repeating part marked by a bar, and a percent.
Expressions with brackets and powers
Combine as many fractions as you like with + − × ÷, brackets and whole-number powers such as (2/3)^3.
Repeating decimal to fraction
Type 0.(3) or 0.333… for one third, or 1.2(45) for 137/110. The brackets mark the digits that repeat forever.
Large numbers, no rounding
Numerators and denominators up to 60 digits each are handled exactly with arbitrary-precision integers.
How to use the fraction calculator
- 1Choose two fractions, an expression, simplify, or decimal to fraction.
- 2Type the whole number, numerator and denominator, or the full expression.
- 3Read the answer as a fraction, mixed number and decimal, with the steps.
When to use it
Homework checks
Solve the problem by hand first, then compare your steps with the working shown. A mismatch usually points to the LCD or a sign.
Recipes
Scaling a recipe by 1 1/2 means multiplying 3/4 cup by 3/2. The answer is 9/8, or 1 1/8 cups. For grams and millilitres, use the unit converter.
Woodwork and DIY
Add 2 5/8 in and 1 7/16 in to get 4 1/16 in without reaching for a decimal chart. For a whole floor or wall, the area calculator takes over.
Probability
Multiplying 1/6 by 1/6 gives the 1/36 chance of rolling double sixes, which you can test with the dice roller.
How do you add fractions with different denominators?
Find the least common denominator (LCD), rewrite each fraction over it, add the numerators, and simplify. The LCD is the least common multiple of the denominators.
Take 1 1/2 + 3/4, the example the calculator opens with. First turn 1 1/2 into 3/2. The LCD of 2 and 4 is 4, so 3/2 becomes 6/4. Now 6/4 + 3/4 = 9/4, which is 2 1/4 as a mixed number and 2.25 as a decimal.
You could also multiply the denominators (2 × 4 = 8) and simplify at the end. It works, but the numbers get bigger. The LCD keeps them small.
How do you multiply and divide fractions?
To multiply, multiply the numerators together and the denominators together: 2/3 × 3/4 = 6/12 = 1/2. No common denominator is needed.
To divide, flip the second fraction and multiply. 3 1/2 ÷ 1 3/4 is 7/2 ÷ 7/4, which becomes 7/2 × 4/7 = 28/14 = 2. Always convert mixed numbers first. Multiplying the whole parts and the fractions separately gives the wrong answer.
How do you simplify a fraction?
Divide the top and bottom by their greatest common divisor (GCD). The Simplify mode finds it with Euclid's algorithm, which repeats division with remainders until the remainder is 0.
For 84/126: 126 = 1 × 84 + 42, then 84 = 2 × 42 + 0. The last non-zero remainder, 42, is the GCD. 84 ÷ 42 = 2 and 126 ÷ 42 = 3, so 84/126 = 2/3.
How do I turn a repeating decimal into a fraction?
Put the repeating digits in brackets: 0.1(6) means 0.16666… The calculator uses the standard method. Shift the decimal so one copy of the repeat sits left of the point, subtract the unshifted version to cancel the endless tail, and divide.
For 0.1(6), the non-repeating part has 1 digit and the repeat has 1 digit, so the fraction is (16 − 1) ÷ 90 = 15/90 = 1/6. Every fraction has a decimal that either ends or repeats. A denominator whose only prime factors are 2 and 5 gives a decimal that ends, like 3/8 = 0.375. Any other prime factor makes it repeat, like 1/7 = 0.(142857).
Why use Mavros
| Mavros | Typical upload sites | |
|---|---|---|
| Input | Two stacked fractions or a full expression with brackets | Two fractions only |
| Mixed numbers | Supported in both modes, including negatives | Often a separate calculator |
| Working | LCD, rewritten fractions, GCD and mixed-number conversion | Answer only, or steps behind a paywall |
| Repeating decimals | Shown with a bar, and convertible back to a fraction | Rounded to a few decimal places |
| Precision | Exact integer arithmetic up to 60 digits | Floating point |
| Privacy | Runs in your browser | Ad-heavy pages |
Tips
- In an expression, a fraction typed without spaces, like 1/2, is treated as one number. So 2 ÷ 1/2 = 4, which matches what you would write on paper.
- To divide by a mixed number, use the ÷ key or a colon. Typing 2 / 1 1/2 with spaces works as well.
- A negative sign goes on the whole number or the numerator, never the denominator. −3/4 and 3/−4 are the same value, but the calculator keeps the sign on top.
- The bar over decimal digits marks the repeating block. 0.1 with a bar over the 6 is 0.1666… forever.
- Need a percent instead? Every result shows one, and the percentage calculator handles percent change and discounts.
Questions
How do you add fractions with unlike denominators?
Rewrite both fractions over the least common denominator, add the numerators, then simplify. For 1/4 + 1/6 the LCD is 12, so 3/12 + 2/12 = 5/12.
How do I enter a mixed number?
Put the whole number in the left box and the fraction in the stacked boxes. In Expression mode, type the whole number, a space, then the fraction, like 2 3/4.
How do you convert a mixed number to an improper fraction?
Multiply the whole number by the denominator and add the numerator, keeping the same denominator. 2 3/4 becomes (2 × 4 + 3)/4 = 11/4.
How do you divide fractions?
Keep the first fraction, flip the second, and multiply. 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8, which is 1 7/8. This is often remembered as keep, change, flip.
What is 0.375 as a fraction?
0.375 is 3/8. Write it as 375/1000, then divide the top and bottom by their GCD, 125. The Decimal to fraction mode does this for any decimal.
What is 0.333 repeating as a fraction?
It is exactly 1/3. Type 0.(3) or 0.333… in Decimal to fraction mode. Note that 0.333 without the repeat is 333/1000, which is slightly less than one third.
Why does the answer show a bar over some digits?
The bar marks digits that repeat forever. 5/6 is 0.8333…, shown as 0.8 with a bar over the 3. It is the exact decimal, not a rounded one.
Can it handle negative fractions?
Yes. Put a minus sign on the whole number or the numerator. −1 1/2 + 3/4 gives −3/4, and the steps show how the signs combine.