Fraction Calculator
Add, subtract, multiply and divide fractions, mixed numbers and decimals or whole expressions, with simplified results, repeating decimals and steps.
The interactive tool loads here when JavaScript runs.
About this toolWhat is the Fraction Calculator?
Type two fractions and pick an operation, or switch to Expression and type something longer such as 1/2 + 2/3 × 3/4 − 1 1/4. Mixed numbers are written with a space (2 1/3), negatives with a minus sign, and decimals like 0.75 are turned into exact fractions before anything else happens.
The answer comes back in lowest terms, as a mixed number, and as a decimal. When the decimal never ends, the repeating block is shown in parentheses, so 13/6 reads 2.1(6) instead of a rounded 2.1666667. Below the result, each operation is written out: the least common denominator for addition and subtraction, the reciprocal for division, and the greatest common factor used to simplify.
All arithmetic uses exact whole-number maths (JavaScript BigInt), so even fractions with 18-digit denominators come out exactly right. Nothing leaves your browser.
- Fractions, mixed numbers, negatives and decimals in one input
- Multi-term expressions with correct order of operations and parentheses
- Exact BigInt arithmetic with lowest-terms results
- Mixed number and repeating-decimal output
- Step-by-step LCM, reciprocal and GCF working
How to use the Fraction Calculator
- Choose Two fractions for a single operation or Expression for several terms.
- Type each fraction as 3/4, a mixed number as 1 1/2 (with a space), or a decimal as 0.75.
- In two-fraction mode, choose add, subtract, multiply or divide. In expression mode, use + − × ÷ (or * and /) and parentheses.
- Read the simplified fraction, mixed number and decimal. A block in parentheses repeats forever.
- Follow the step list to see the common denominator, the multiplication and the simplification for each operation.
Worked examples
Mixed number plus a fraction
Input
1 1/2 + 2/3
Output
13/6 = 2 1/6 = 2.1(6)
1 1/2 becomes 3/2, the LCM of 2 and 3 is 6, and 9/6 + 4/6 = 13/6. The 6 after the decimal point repeats forever.
Order of operations
Input
1/2 + 2/3 × 3/4 − 1 1/4
Output
−1/4 = −0.25
The product 2/3 × 3/4 = 1/2 is done first, then 1/2 + 1/2 = 1, then 1 − 5/4 = −1/4.
Division of a bracket
Input
(3/4 − 1/8) ÷ 5/16
Output
2
The bracket gives 5/8, and dividing by 5/16 means multiplying by 16/5: 80/40 simplifies to 2.
Decimal and fraction together
Input
0.6 + 2/3
Output
19/15 = 1 4/15 = 1.2(6)
0.6 is read exactly as 3/5, so the sum is exact rather than a rounded 1.2666667.
Background and insight
To add or subtract, fractions need a common denominator. Any common multiple works, but the least common multiple (LCM) of the denominators keeps the numbers small. For 1/4 + 1/6 the LCM is 12, so the sum is 3/12 + 2/12 = 5/12. Multiplying is simpler: multiply the tops and the bottoms. Dividing means multiplying by the reciprocal, which is why 1/2 ÷ 3/4 = 1/2 × 4/3 = 2/3.
A fraction is in lowest terms when the numerator and denominator share no factor other than 1. Dividing both by their greatest common factor (GCF), found with Euclid's algorithm, gets there in one step. A fraction in lowest terms has a terminating decimal only when its denominator has no prime factors other than 2 and 5; anything else, such as 1/3, 1/7 or 1/12, repeats forever.
In an expression, multiplication and division are done before addition and subtraction, left to right, and parentheses override that order. That is the same convention used by scientific calculators and programming languages.
Common use cases
Homework and checking working
See each stage of a fraction sum laid out the way teachers expect, then compare it with your own.
Recipes and scaling
Add 2/3 cup and 3/4 cup, or work out 1 1/2 times a 3/4 teaspoon measure, without decimal rounding.
Woodwork and measurements
Combine inch fractions such as 5 3/8 + 2 7/16 and get the answer back as a mixed number you can mark on a tape.
Exact results for programmers
Check rational arithmetic where floating point would drift, for example sums of many small fractions.
Tips and limitations
- Write mixed numbers with a single space between the whole number and the fraction; 2 1/3 means two and one third, while 21/3 means seven.
- A minus sign in front of a mixed number applies to all of it: −1 1/2 is −3/2, not −1 + 1/2.
- In expression mode, a slash between two plain numbers (3/4) is read as a fraction, and ÷ is division, so 1/2 ÷ 3/4 behaves the way it looks.
- Simplifying at the end gives the same answer as simplifying as you go; the tool simplifies once and shows the GCF it used.
- Very long repeating decimals (1/97 repeats every 96 digits) are shown cut short in the summary card but are exact in the copy.
Frequently asked questions
How do you add fractions with different denominators?
Rewrite both over a common denominator, ideally the least common multiple of the two denominators, then add the numerators. For 1/4 + 1/6, the LCM is 12, so 3/12 + 2/12 = 5/12.
How do you divide fractions?
Flip the second fraction and multiply. 1/2 ÷ 3/4 becomes 1/2 × 4/3 = 4/6, which simplifies to 2/3. This works because dividing by a number is the same as multiplying by its reciprocal.
How do I enter a mixed number?
Type the whole number, a space, then the fraction: 2 1/3. The calculator converts it to an improper fraction (7/3) before working and shows that conversion in the steps.
How do I simplify a fraction to lowest terms?
Divide the numerator and denominator by their greatest common factor. 18/24 has GCF 6, so it simplifies to 3/4. Every result here is already in lowest terms, and the GCF used is shown.
Why does my fraction give a repeating decimal?
A fraction in lowest terms only terminates if its denominator has no prime factors other than 2 and 5. 3/8 = 0.375 terminates; 1/6 = 0.1(6) and 1/7 = 0.(142857) repeat. The digits in parentheses repeat forever.
Can I calculate with more than two fractions at once?
Yes. Switch to Expression and type as many terms as you like, with parentheses where needed, for example (1/2 + 1/3) × 3/4. Multiplication and division are done before addition and subtraction.
How do I turn a decimal into a fraction?
Type the decimal on its own in expression mode. 0.375 becomes 375/1000, which simplifies to 3/8. A finite decimal always has an exact fraction with a power of ten underneath.
Is there an in-depth guide to the Fraction Calculator?
Yes. “Percentages, Fractions and Ratios: How the Arithmetic Fits Together” covers the background, how it works, common pitfalls and worked examples. Read the full guide.
Related Tools You May Like
Free, in-browser tools that pair well with this one.