Use this fractions calculator to easily perform arithmetic calculations with fractions. Add, subtract, multiply, and divide fractions, as well as raise a fraction to power (fraction or not). Supports evaluation of mixed fractions (e.g. "2 1/3") and negative fractions (e.g. "-2/3"). Use "pi" or "π" for the number Pi. Powerful advanced mode for evaluating whole expressions with fractions.
Quick navigation:
- Using the fraction calculator
- How to do fractions math
- Practical Examples
Using the fraction calculator
The fraction calculator offers two modes: basic and advanced. Basic mode supports a single operation (addition, subtraction, multiplication, division, exponentiation) with two fractions only, e.g. 1/2 + 2 2/3. In advanced mode you can evaluate very complex expressions such as ((2 x 2/5 / 13.5) + 1/3 + 2/3 x (pi / 2))^1/2.
The calculator supports:
- Simple fractions: - e.g. 1/2, 3/4, 13/5 in both modes.
- Mixed fractions: - e.g. 1 1/2, 2 3/4, 10 3/5 in both modes. Make sure you leave one space between the whole part and the fraction part.
- Decimal fractions: - e.g. 1.5, 3.45, 10.01 in both modes. You can also input things like 1.5/2.5 . Make sure you use dot (.) as a decimal separator.
- Thousand separators: you can enter big numbers using commas as thousand separators, e.g. 1,000, 1,200,550 in both modes.
- Operators: in basic mode, use the drop-down. In advanced mode use "+" for addition, "-" for subtraction, "x" or "*" for multiplication, "/" or ":" for division, "^" for power (x^y).
- Groupings/Parenthesis: in advanced mode you can use parenthesis to group items and force the calculation order. Calculations are carried in the usual order otherwise.
- Number Pi (π): you can input "pi" or "π" in both modes, e.g. pi/2 in basic mode, (pi + 5)/2 in advanced mode. It will be converted automatically to the correct value of approximately 3.14159.
- Negative fractions: both modes support negative fractions, decimals and numbers.
In advanced mode, the order of calculations in the tool is: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction (PEMDAS).
The result is presented as a decimal number (precision 12 positions after the decimal point) and as a simplified mixed fraction.
How to do fractions math
The principles of fractions mathematics are the same whether you code them into a calculator or do the math by hand. First, when adding or subtracting fractions you need to start by finding the least common denominator, also known as lowest common denominator or smallest common denominator of the fractions you need to work with. It is by definition the smallest positive integer that is divisible by each denominator. The LCD is the least common multiple (LCM) of the fractions' denominators. This operation is not necessary when doing multiplication, division, or exponentiation.
Then you need to convert mixed fractions to simple fractions, to make it easier to work with. To find the numerator of the simple fraction multiply the whole part by the denominator and add the numerator of the fraction part to it. The denominator stays the same.
Finally, do the operations required (add, subtract, multiply, divide) by working with the numerators. You then get the result of the calculation. Of course, it is much easier to use a powerful fraction calculator as ours above.
Illustrating the process step by step, it is:
- if adding or subtracting fractions, find the least common denominator
- convert mixed fractions to simple fractions
- perform the arithmetic with the numerators
It is not that hard, but it can be difficult to do by hand in certain scenarios which would not be an issue for an online calculator.
Practical Examples
Example task #1: Add the fractions 1/2 and 3/4.
Solution: The least common denominator of 2 and 4 is 4, so 1/2 = 2/4 and 3/4 remains 3/4. Adding 2 + 3 = 5, so the answer is 5/4. As a mixed fraction that is 1 1/4, in decimal: 1.25.
Example task #2: Subtract the fractions 1 1/5 and 2/3.
Solution: First, convert 1 1/5 to a simple fraction by (1 x 5 + 1)/5 = 6/5. The least common denominator of 5 and 3 is 15, so 6/5 = 18/15 and 2/3 = 10/15. Subtracting 10 from 18 = 8, so the answer is 8/15. It cannot be simplified further. In decimal it is 0.53(3). You can verify the result using our tool.
Example task #3: Multiply the fractions 1/3 and 5/8
Solution: To evaluate this expression, simply multiply the numerators together and then the denominators together. Multiplying 1 by 5 we get 5, multiplying 3 by 8 we get 24, so the answer is 5/24, or 0.2083(3).
