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Fraction Calculator
To add 1 1/2 and 2 2/3, turn them into 3/2 and 8/3, rewrite both over the lowest common denominator 6 as 9/6 and 16/6, add the tops to get 25/6, and write it as the mixed number 4 1/6. This calculator does that for any two fractions, shows each step, and gives the decimal and percent too.
Add, subtract, multiply or divide.
- The first entry 1 1/2 is 3/2 as an improper fraction.
- The second entry 2 2/3 is 8/3 as an improper fraction.
- The lowest common denominator of 2 and 3 is 6.
- Rewrite over 6: 3/2 = 9/6 and 8/3 = 16/6.
- Add the numerators: 9 + 16 = 25, so the result is 25/6.
- 25/6 is in lowest terms: the greatest common divisor of 25 and 6 is 1.
- 25/6 is more than a whole, so as a mixed number it is 4 1/6.
| Form | Value |
|---|---|
| Lowest-terms fraction | 25/6 |
| Mixed number | 4 1/6 |
| Decimal | 4.1(6) (repeating) |
| Percent | about 416.67% |
The figures above are an example: put in your own. Type 3/4, a mixed number such as 1 1/2, a decimal or a whole number. Worked out in this browser and kept there; nothing is sent anywhere. Turning a count into a fraction? Try the tally percentage calculator.
Type two fractions, mixed numbers or decimals, choose an operation, and read the answer with its working. Leave the second box blank to simplify one fraction. The arithmetic is exact, so nothing is rounded until you see the decimal.
A fraction calculator does arithmetic on fractions: it adds, subtracts, multiplies and divides them and reduces the answer to lowest terms. A good one also shows how it got there.
- No sign-up
- Nothing uploaded
- Shows every step
- Works offline
- Exact, no rounding
Key facts
| Detail | Answer |
|---|---|
| Price | Free, no sign-up, nothing to install |
| Accepts | 3/4, 1 1/2, -2 3/5, 0.75, 5 |
| Operations | Add, subtract, multiply, divide, and simplify one fraction |
| Example | 1 1/2 + 2 2/3 = 25/6 = 4 1/6 = 4.1(6) |
| Arithmetic | Exact integers, so no rounding until the decimal is shown |
| Refuses | A denominator of 0 and division by 0, with a message |
| Where your numbers are kept | This browser only |
How to add fractions with different denominators
Enter both fractions and read the working; the same steps apply by hand.
Enter the first fraction
As 3/4, a mixed number such as 1 1/2, a decimal or a whole number.
Choose the operation
Add, subtract, multiply or divide.
Enter the second fraction
Leave it blank to simplify the first one instead.
Read the working
Each step is numbered: improper fractions, common denominator, the sum, then reducing.
Check the other forms
The table gives the mixed number, decimal and percent.
Copy it if you need the steps
The working copies as plain text.
Who uses a fraction calculator
Anyone who has a fraction to work out and wants to see why the answer is what it is.
Pupils checking homework
The answer, plus the steps to compare with their own.
Parents helping with maths
The method laid out in the order it is taught.
Cooks scaling a recipe
1 1/2 cups plus 2/3 of a cup, without guessing.
Woodworkers and crafters
Inch fractions added and subtracted exactly.
Teachers
A worked example for any pair of fractions in seconds.
People with counts
18 of 24 reduced to 3/4 and 75%.
Why 1/2 + 1/3 is not 2/5
Most wrong fraction answers come from one of three habits, and a calculator that only prints the answer hides which one you have. Adding the tops and the bottoms is the commonest: 1/2 + 1/3 is not 2/5, because a half is bigger than 2/5 on its own, so the sum of a half and something positive cannot be smaller than a half. Fractions can only be added when they are cut into the same size of piece, which is what a common denominator does.
| Sum | The slip | Right answer | Why |
|---|---|---|---|
| 1/2 + 1/3 | 2/5 | 5/6 | Rewrite as 3/6 + 2/6, then add the tops only |
| 3/4 ÷ 1/2 | 3/8 | 3/2 | Dividing by 1/2 is multiplying by its flip, 2: 3/4 × 2 = 6/4 |
| 1 1/2 − 3/4 | 1 1/4 (the smaller part taken from the larger in each column) | 3/4 | Use 3/2 − 3/4 = 6/4 − 3/4, so nothing is borrowed |
Try each one in the calculator above and read the numbered working. Turning mixed numbers into improper fractions first is the method the calculator uses, because it never needs to borrow or carry a whole number.
How each operation works
Each operation is the same few moves. The calculator uses them in this order, and names each in its working.
| Operation | Rule | Example |
|---|---|---|
| Add or subtract | Rewrite over the lowest common denominator, then add or subtract the tops | 3/8 + 5/12 = 9/24 + 10/24 = 19/24 |
| Multiply | Multiply the tops, multiply the bottoms, then reduce | 2/3 × 3/4 = 6/12 = 1/2 |
| Divide | Multiply by the flip of the second fraction | 3/4 ÷ 1/2 = 3/4 × 2/1 = 3/2 |
| Simplify | Divide top and bottom by their greatest common divisor | 18/24 = 3/4 (divide by 6) |
This is the order school curricula teach it in. The US Common Core State Standards for Grade 5 ask pupils to add and subtract fractions with unlike denominators, including mixed numbers, by using equivalent fractions, and to extend multiplication and division to fractions in the same grade. The “lowest common denominator” step is just the smallest number both denominators divide into: for 4 and 6 it is 12, not 24, and using the smaller one keeps the numbers small and the answer nearly reduced already.
The greatest common divisor that reduces a fraction is found with a method more than two thousand years old. Euclid’s Elements, Book VII, Proposition 2, gives a way to find the greatest common measure of two numbers by repeated subtraction. The calculator uses the modern form: replace the larger number by its remainder after dividing by the smaller, and repeat until the remainder is 0. For 18 and 24, the remainders go 6, then 0, so the divisor is 6.
Fractions as decimals: which repeat
Many fractions have no finite decimal, and a calculator that works in floating point rounds them without saying so: 1/3 appears as 0.3333333333 and then adds up wrongly. This calculator keeps every number as an exact fraction and only converts at the end, writing the repeating part in brackets, so 1/6 is 0.1(6): a 1, then 6 forever.
| Fraction | Decimal | Repeats? |
|---|---|---|
| 1/8 | 0.125 | No |
| 1/3 | 0.(3) | Yes, 1 digit |
| 1/6 | 0.1(6) | Yes, after one digit |
| 1/7 | 0.(142857) | Yes, 6 digits |
| 1/9 | 0.(1) | Yes, 1 digit |
| 1/11 | 0.(09) | Yes, 2 digits |
| 1/12 | 0.08(3) | Yes, after two digits |
The rule: a fraction in lowest terms ends as a decimal only when its denominator has no prime factors other than 2 and 5. That is why 1/8 (2 × 2 × 2) and 3/20 end, and why 1/3, 1/7 and 1/12 (which has a 3) do not. Very long repeats are cut off after 30 digits and marked with an ellipsis, and the percent is rounded to two places and labelled “about” unless it is exact.
Fractions from a count
On a counting site the fractions that come up most are made from counts: 18 of 24 pupils present, 45 of 60 shots on target, 7 of 12 jars sold. Enter the count over the total, such as 18/24, with the second box blank, and the calculator reduces it: 3/4, which is 0.75 or 75%. Two counts from different sessions can be combined the same way, by adding 18/24 and 12/20 to see them over a common denominator, though to combine them as one overall rate you should add the counts and the totals separately: 30/44, not the sum of the two fractions.
For a whole tally turned into percentages that add to 100, the tally percentage calculator does the arrangement for you, and the average calculator’s section on averaging averages explains why fractions of different totals should not simply be added.
What this calculator does not do
This is a calculator for fractions, not a homework answer key. It shows the standard method so you can check your own working, and it does not handle algebraic fractions (those with letters), exponents or roots. Entries are limited to 40 characters; numbers can be very large because the arithmetic uses exact integers. Dividing by zero, and a denominator of 0, are refused with a message instead of an answer.
| It does | It does not |
|---|---|
| Add, subtract, multiply and divide two fractions, mixed numbers or decimals | Handle letters, powers or roots |
| Show the working step by step | Skip to a rounded answer only |
| Give the result as a fraction, mixed number, decimal and percent | Round fractions through floating point |
| Keep your entries in this browser | Send anything anywhere |
This calculator or an answer-only one
What this page adds to a typical answer-only fraction calculator.
| This calculator | A typical calculator | |
|---|---|---|
| Cost | Free, no sign-up | Free, often with ads over the result |
| Shows the working | Every step, numbered | Often the answer alone |
| Mixed numbers and decimals in | Yes, both | Fractions only, or separate boxes |
| Exact arithmetic | Whole-number maths, no rounding | Sometimes floating point |
| Repeating decimals marked | 0.1(6) | Rounded |
| Your entries leave the browser | Never | Varies |
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Frequently asked questions
How do you add fractions with different denominators?
Find the lowest common denominator, the smallest number both denominators divide into. Rewrite each fraction over it, add the numerators and keep the denominator, then reduce. For 1/2 + 1/3 the denominator is 6, so it is 3/6 + 2/6 = 5/6. The calculator shows each of these steps.
How do you add mixed numbers?
Turn each mixed number into an improper fraction by multiplying the whole number by the denominator and adding the numerator, then add as usual. For 1 1/2 + 2 2/3 that gives 3/2 + 8/3 = 25/6, which is 4 1/6. The calculator accepts mixed numbers directly, typed with a space.
How do you simplify a fraction?
Divide the top and the bottom by their greatest common divisor. For 18/24 that divisor is 6, giving 3/4. If the divisor is 1 the fraction is already in lowest terms. Leave the second box blank in the calculator and it simplifies the first fraction and names the divisor.
How do you divide fractions?
Multiply by the flip, or reciprocal, of the second fraction. Dividing 3/4 by 1/2 is 3/4 times 2/1, which is 6/4 and reduces to 3/2. A common slip is multiplying 3/4 by 1/2 to get 3/8, which answers a different question. Dividing by a fraction that is 0 is not possible.
How do you multiply fractions?
Multiply the numerators together and the denominators together, then reduce. 2/3 times 3/4 is 6/12, which reduces to 1/2. No common denominator is needed for multiplication. A mixed number should be changed to an improper fraction first, which the calculator does for you.
How do you turn a fraction into a decimal?
Divide the numerator by the denominator. 3/8 is 0.375. Some fractions never end: 1/3 is 0.333 with the 3 repeating, written 0.(3), and 1/6 is 0.1(6). A fraction in lowest terms ends only if its denominator has no prime factors other than 2 and 5.
How do you turn a fraction into a percent?
Divide the top by the bottom and multiply by 100. 3/4 is 0.75, which is 75%. For 1/3 the answer repeats, 33.33…%, so this calculator rounds to two places and labels it “about”. A fraction over 100 is already a percent: 45/100 is 45%.
What is the lowest common denominator of two fractions?
It is the smallest number that both denominators divide into evenly, also called the least common multiple. For 4 and 6 it is 12, not 24. Using the smallest one keeps the working short, though any common denominator gives the right answer once you reduce.
Can a fraction calculator handle negative fractions and decimals?
Yes. Put a minus sign in front, as in -2 3/5, and type decimals such as 0.75 or a decimal comma such as 0,75. A decimal is first written as a fraction over a power of ten, so 0.75 is 75/100, then reduced to 3/4, and the calculator shows that step.
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