Fraction Calculator
1/2 + 1/3 = 5/6. This fraction calculator handles the four fraction operations people actually need in school, cooking, budgeting, measurements, and quick homework checks. Enter two fractions, choose add, subtract, multiply, or divide, and the tool returns the simplified fraction plus its decimal value. That matters because many fraction problems are easier to understand once you can see both forms side by side. If you are comparing 7/8 to 0.875, scaling a recipe from 3/4 cup to a double batch, or checking whether 5/6 is larger than 4/5, the decimal view makes the answer easier to interpret while the fraction view preserves the exact math. The calculator also reduces improper fractions and normalizes signs, so you do not have to simplify the result by hand every time.
Quick answer
Addition and subtraction first convert both fractions to a common denominator, then combine the numerators.
What this tells you
- •Addition and subtraction first convert both fractions to a common denominator, then combine the numerators.
- •Multiplication is more direct. Multiply numerator by numerator and denominator by denominator, then reduce.
- •Division flips the second fraction and multiplies, which is why dividing by 2/3 means multiplying by 3/2.
- •Every result is simplified to lowest terms so 6/8 becomes 3/4 instead of staying unsimplified.
- •The decimal result is useful for comparison, but the simplified fraction is the exact answer when a repeating decimal would be rounded.
How to Use
- 1Enter the numerator and denominator for the first fraction. If the value is negative, place the minus sign in the numerator unless your class or worksheet says otherwise.
- 2Enter the numerator and denominator for the second fraction. Denominators cannot be zero because a fraction with zero on the bottom is undefined.
- 3Choose the operation you want to perform. Use add or subtract for combining quantities, multiply for finding a part of a part, and divide for splitting or comparing ratios.
- 4Click Calculate to see the simplified fraction result right away. The tool also shows the decimal equivalent so you can compare sizes more easily.
- 5If the answer surprises you, check the signs, denominators, and operation first. Most fraction errors come from one wrong input rather than from the simplification step.
How It Works
Formula
Use standard fraction arithmetic by operation, then reduce by greatest common divisor.For addition, use a/b + c/d = (ad + bc) / bd. For subtraction, use a/b - c/d = (ad - bc) / bd. For multiplication, use a/b x c/d = ac / bd. For division, use a/b ÷ c/d = ad / bc, which is the same as multiplying by the reciprocal of the second fraction. After the operation, the calculator finds the greatest common divisor of the numerator and denominator and divides both by that value to reduce the fraction to simplest terms. If the denominator ends up negative, the negative sign is moved to the numerator so the final form stays standard and easier to read.
Calculation note: values are processed in the order shown above, using the current input units.
Worked Examples
Add 1/2 + 1/3
Subtract 5/6 - 1/4
Multiply 3/5 x 10/9
Divide 7/8 by 14/5
Common mistakes
- Adding or subtracting denominators directly. 1/2 + 1/3 is not 2/5 because the pieces are different sizes until you convert to a common denominator.
- Forgetting to invert the second fraction during division. Dividing by 3/4 means multiplying by 4/3, not multiplying by 3/4 again.
- Leaving the answer unsimplified. 12/18 and 2/3 represent the same value, but many teachers, worksheets, and forms expect lowest terms.
- Missing a negative sign. A single minus sign changes the direction of the result, especially in subtraction problems like -1/2 - 1/3.
- Using a zero denominator or trying to divide by a zero-value fraction such as 0/5. Both cases are invalid because the math becomes undefined.
- Assuming the decimal is always the better answer. For repeating values like 1/3, the fraction is exact while the decimal must be rounded.
Embed this calculator on your site
Drop this single line where you want the calculator to appear. It is responsive, mobile-friendly, resizes automatically, and is free to use with attribution.
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