Fraction Calculator
Perform arithmetic on two fractions and see the simplified answer.
Operation
Formula
How this is calculated
Each fraction is entered as an integer numerator over an integer denominator: the first as a/b and the second as c/d. The numerator is the count of parts and the denominator is how many equal parts make a whole, so a denominator of 0 is undefined and rejected. Non-integer or non-numeric entries are also flagged as invalid.
The chosen operation sets the raw result before simplifying. Addition and subtraction use the common denominator b·d, giving (a·d ± c·b) / (b·d). Multiplication goes straight across as (a·c) / (b·d). Division multiplies by the reciprocal of the second fraction, yielding (a·d) / (b·c), which is undefined when c is 0.
The raw numerator and denominator are then reduced to lowest terms by dividing both by their greatest common divisor, and any negative sign is moved to the numerator so the denominator stays positive. The decimal value is the reduced numerator divided by the denominator, shown to six places. Results are exact rational arithmetic, but very large numerators or denominators can exceed integer precision.
Examples
| Input | Result |
|---|---|
| 1/2 + 1/3 | 3/6 + 2/6 = 5/6 |
| 3/4 - 1/6 | 9/12 - 2/12 = 7/12 |
| 2/3 x 3/5 | 6/15 = 2/5 |
| 1/2 / 1/4 | 1/2 x 4/1 = 2 |
About this calculator
A fraction represents a part of a whole, written as a numerator over a denominator, such as 3/4. The numerator counts how many parts you have, and the denominator tells you how many equal parts make up one whole. This Fraction Calculator lets you add, subtract, multiply, and divide fractions and then automatically reduces the answer to its simplest form, so you do not have to hunt for common factors by hand.
Each operation follows its own rule. To multiply, you multiply the numerators together and the denominators together, so 2/3 x 3/5 = 6/15. To divide, you flip the second fraction and multiply, turning 1/2 / 1/4 into 1/2 x 4/1 = 2. Addition and subtraction require a common denominator first: you rewrite both fractions over the same bottom number, then add or subtract the numerators. For 1/2 + 1/3 you convert to 3/6 + 2/6 = 5/6. Simplifying means dividing the top and bottom by their greatest common divisor, which is how 6/15 becomes 2/5.
To use the calculator, type the numerator and denominator of your first fraction, choose the operation from the plus, minus, times, or divide options, and enter your second fraction. Press calculate and the tool returns the exact result in lowest terms, along with the decimal equivalent so you can sanity-check the size of the answer.
Interpreting results is easy once you remember a few cues. A proper fraction has a numerator smaller than its denominator and represents less than one whole, like 5/6. An improper fraction such as 7/4 is larger than one and can also be written as the mixed number 1 3/4. If the denominator divides the numerator evenly, the answer is a whole number, which is why 1/2 / 1/4 simplifies all the way to 2.
The classic mistake is adding fractions straight across, which incorrectly turns 1/2 + 1/3 into 2/5 instead of the correct 5/6; you must find a common denominator first. Another error is forgetting to flip the divisor during division, and a third is leaving an answer unsimplified. Always reduce your final fraction and double-check it against its decimal value.
Frequently asked questions
You can only add parts that are the same size. A common denominator rewrites both fractions into equal-sized pieces so the numerators can be combined. Without it, you would be adding pieces of different sizes, which has no meaning.
Keep the first fraction, flip the second (swap its numerator and denominator), and multiply. So 1/2 / 1/4 becomes 1/2 x 4/1 = 4/2 = 2. The flipped fraction is called the reciprocal.
Simplifying divides the numerator and denominator by their greatest common factor until no common factor remains. For example, 6/15 both share a factor of 3, so it reduces to 2/5. The value is unchanged, just written more cleanly.
A proper fraction has a numerator smaller than its denominator and is less than one, like 3/4. An improper fraction has a numerator equal to or larger than its denominator and is one or greater, like 7/4, which equals the mixed number 1 3/4.
Divide the numerator by the denominator. For 5/6 you compute 5 / 6 = 0.8333, and for 3/4 you get 0.75. Some fractions produce repeating decimals, which is why the exact fraction form is often preferred.
Convert a mixed number to an improper fraction first by multiplying the whole part by the denominator and adding the numerator. The number 1 3/4 becomes (1 x 4 + 3) / 4 = 7/4, which you then enter normally.
Also known as
TG we-Calculate Editorial Team. (2026). Fraction Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/fraction-calculator
TG we-Calculate Editorial Team. "Fraction Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/fraction-calculator.
TG we-Calculate Editorial Team, "Fraction Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/fraction-calculator
@misc{wecalculate_fraction_calculator, title = {Fraction Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/fraction-calculator}}, year = {2026}, note = {TG we-Calculate} }
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