Fraction Calculator: Add, Simplify, Mixed Numbers
Add, subtract, multiply and divide fractions, mixed numbers and decimals exactly, with the least common denominator and every step shown. Get the simplified fraction, mixed number and repeating decimal, or create Unicode fractions like ½ and ²²⁄₇. Nothing is uploaded.
About the Fraction Calculator
The Fraction Calculator adds, subtracts, multiplies and divides fractions, mixed numbers, whole numbers and decimals in one expression, such as 1 1/2 + 3/4 - 2/5. It gives the answer as a simplified fraction, a mixed number and a decimal, and it shows the working: the improper fractions, the least common denominator, each term rewritten over that denominator, and the final simplification. Every step is exact. The calculator uses whole-number arithmetic of unlimited size rather than floating point, so 1/3 stays 1/3 and never turns into 0.333333. A second mode writes fractions as Unicode characters, such as ½ or ²²⁄₇, ready to paste into a document, a chat or a web page. Everything is calculated in your browser, and nothing is sent to a server.
How to use it
Calculator
- Type an expression in the Fractions box. Write a fraction as
3/4, a mixed number as1 1/2with a space between the whole part and the fraction, a whole number as3, and a decimal as1.25. - Use
+and-to add and subtract, and*,xor×to multiply. To divide, use÷,:or a slash between two fractions, as in1/2 / 1/4. - Read the answer in its four forms and follow the working underneath. The results update as you type.
Unicode fractions
Choose Unicode fractions, then type one fraction or mixed number per line. Each line gets its own result with a Copy button, and Copy all copies every valid result, one per line.
How the answer is worked out
Order of operations
Multiplication and division are done first, from left to right, then addition and subtraction. So 1/2 + 1/3 × 3/4 multiplies 1/3 by 3/4 to get 1/4 before adding 1/2, which gives 3/4. Division is shown as multiplication by the reciprocal: 3/4 ÷ 3/8 becomes 3/4 × 8/3.
Least common denominator
To add or subtract, every fraction is rewritten over the least common denominator (LCD), the smallest number that every denominator divides. For 3/2 + 3/4 − 2/5 the LCD of 2, 4 and 5 is 20, so the sum becomes 30/20 + 15/20 − 8/20, and the numerators combine to 37/20.
Simplifying
A fraction is in lowest terms when its numerator and denominator share no factor other than 1. The calculator divides both by their greatest common divisor, found with Euclid's algorithm, and says which number it divided by, as in 6/8 = 3/4 (divide both by 2). To see the divisor worked out step by step, use the GCD and LCM Calculator.
Decimals and repeating decimals
Terminating decimals are read exactly: 1.25 is 125/100, which simplifies to 5/4. A repeating decimal is written with its repeating block in brackets, so 0.(3) is 1/3 and 0.1(6) is 1/6. The decimal answer marks the repeating block the same way and also with a bar over the repeating digits, so 22/7 is 3.(142857). Every fraction has a decimal that either ends or repeats. When the repeating block is longer than 1,000 digits, as it is for 1/1019, only the first 1,000 digits are shown and the page says so.
Unicode fraction characters
Unicode has single characters for the common vulgar fractions: ½, ⅓, ⅔, ¼, ¾, the fifths, ⅙, ⅚, ⅐, the eighths, ⅑, ⅒ and ↉ (zero thirds). These are used where they exist. Any other fraction is built from superscript digits for the numerator, the fraction slash U+2044, and subscript digits for the denominator, so 22/7 becomes ²²⁄₇. Fonts that support the fraction slash draw it as a neat diagonal fraction. Fractions are written as you typed them and are not simplified first.
Limits
An expression may be up to 2,000 characters long, and the Unicode mode accepts up to 1,000 lines. Brackets for grouping are not supported; split a long calculation into parts instead. Numerators and denominators can be any size.
Related tools
To change a whole number between bases, use the Number Base Converter. To break a numerator or denominator into primes, use the Prime Factorization Calculator. For percentages, use the Percentage Calculator.
Open-source credits
- The calculator is written for this site and uses no third-party library. Arithmetic uses the browser's built-in
BigInt, specified in ECMA-262, the ECMAScript language specification. - Fractions are reduced with Euclid's algorithm from the Elements, Book VII, Propositions 1 and 2. Repeating decimals are found by long division, stopping at the first remainder that repeats, and the long-period test uses 1019, a full reptend prime listed in OEIS A001913.
- The Unicode characters come from the Number Forms and Latin-1 Supplement blocks of The Unicode Standard, and composed fractions follow its guidance on U+2044 FRACTION SLASH.
Frequently asked questions
How do I enter a mixed number?
Type the whole part, a space, then the fraction, for example 2 3/4 for two and three quarters. A minus sign in front applies to the whole mixed number, so -2 3/4 means minus eleven quarters. Whole numbers and decimals can be mixed into the same expression.
How does the calculator find the least common denominator?
It takes the least common multiple of every denominator in the sum, one pair at a time, using the greatest common divisor from Euclid's algorithm. Each fraction is then scaled up to that denominator, and the working lists the rewritten fractions before their numerators are combined.
Can I convert a repeating decimal to a fraction?
Yes. Put the repeating digits in brackets: 0.(3) is one third, 0.1(6) is one sixth and 0.(142857) is one seventh. The calculator turns the digits into an exact fraction and reduces it to lowest terms, so there is no rounding at any point.
Why are my Unicode fractions not simplified?
The Unicode mode writes each fraction exactly as you typed it, so 2/4 becomes ²⁄₄ rather than ½. That keeps recipe quantities and measurements in the form you chose. To reduce a fraction first, enter it in the calculator mode and copy the simplified fraction it gives you.
Will the composed Unicode fractions display everywhere?
The single-character fractions such as ½ and ¾ display in almost every font. Composed ones such as ²²⁄₇ rely on superscript and subscript digits and the fraction slash, which most modern fonts include, although a few older fonts may draw them with uneven heights or a plain slash.