Fraction Calculator
Add, subtract, multiply, divide, simplify, and convert fractions with step by step explanations.
Why Use a Fraction Calculator?
Fractions show up everywhere. Cooking measurements, woodworking cuts, school math, and even splitting bills. But fraction math is easy to mess up when you are doing it by hand. You need common denominators, you need to simplify at the end, and one small mistake throws the whole answer off.
This calculator handles all of that. Add, subtract, multiply, or divide two fractions and get the answer instantly, already simplified, with a step by step explanation so you understand how it was done.
What This Calculator Can Do
- Add fractions - Find the least common denominator and add
- Subtract fractions - Find the least common denominator and subtract
- Multiply fractions - Multiply across the top and bottom
- Divide fractions - Flip the second fraction and multiply
- Simplify fractions - Reduce to lowest terms using the greatest common divisor
- Fraction to decimal - Calculate decimal expansions using exact integer long division
- Decimal to fraction - Convert terminating and repeating decimals exactly
- Mixed numbers - Show an equivalent mixed-number form for improper fractions
Example
Add 1/2 and 1/3: Find the least common denominator (6). 1/2 becomes 3/6 and 1/3 becomes 2/6. Add them together and you get 5/6.
Frequently Asked Questions
What is a common denominator?
A common denominator is a shared bottom number that both original denominators can divide into evenly. For example, to add 1/2 and 1/3, we convert them to 3/6 and 2/6 so they share the denominator 6. Then we just add the top numbers (3 + 2 = 5) to get 5/6. The calculator automatically finds the smallest common denominator.
How do you simplify a fraction?
Find the greatest common divisor (GCD) of the numerator and denominator, then divide both by that number. For example, 6/8 simplifies to 3/4 because the GCD of 6 and 8 is 2.
How do you divide fractions?
Flip the second fraction by swapping its numerator and denominator, then multiply by the reciprocal. For example, 1/2 divided by 1/4 becomes 1/2 times 4/1, which equals 4/2 or 2.
Can this handle improper fractions?
Yes. An improper fraction is one where the numerator is larger than the denominator, like 7/4. The calculator handles these fine. The result is simplified and, when appropriate, also shown as a mixed number such as 1 3/4.
How do you convert a decimal to a fraction?
For a terminating decimal, count the decimal places and place the number over 10, 100, 1,000, or the appropriate power of 10, then simplify. For repeating decimals, enter the repeating portion followed by three dots, such as 0.333... or 1.1666....
Can I enter repeating decimals?
Yes. Type the digits that repeat, then add three dots (...). The calculator will figure out the shortest repeating pattern automatically. For example, 0.333... → 1/3, 0.121212... → 4/33, and 1.1666... → 7/6.
Are there limits on very large numbers?
This calculator uses exact integer arithmetic and can handle numbers up to 1,000 digits long for fraction inputs and decimal inputs. If a decimal expansion is extremely long or repeating forever, it will be shown with parentheses to indicate the repeating part, or cut off with an ellipsis (…) when it exceeds the display limit.