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Education & Math

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.

Education & MathBy

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

  1. 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.
  2. 2Enter the numerator and denominator for the second fraction. Denominators cannot be zero because a fraction with zero on the bottom is undefined.
  3. 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.
  4. 4Click Calculate to see the simplified fraction result right away. The tool also shows the decimal equivalent so you can compare sizes more easily.
  5. 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

Fraction11/2
Fraction21/3
Operationadd
Result5/6 (0.833333)

Subtract 5/6 - 1/4

Fraction15/6
Fraction21/4
Operationsubtract
Result7/12 (0.583333)

Multiply 3/5 x 10/9

Fraction13/5
Fraction210/9
Operationmultiply
Result2/3 (0.666667)

Divide 7/8 by 14/5

Fraction17/8
Fraction214/5
Operationdivide
Result5/16 (0.3125)

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.

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Frequently Asked Questions

Yes. After the selected operation is completed, the calculator reduces the numerator and denominator by their greatest common divisor. That means a result like 18/24 is shown as 3/4 rather than left in a larger equivalent form.
Fractions describe parts of a whole, and the denominator tells you the size of each part. You cannot combine 1/2 and 1/3 by just adding top and bottom because halves and thirds are different-sized pieces. Converting both to sixths makes them comparable, which is why 1/2 becomes 3/6 and 1/3 becomes 2/6 before adding.
Division asks how many times one quantity fits into another. Mathematically, dividing by a fraction is the same as multiplying by its reciprocal. So 2/3 ÷ 5/7 becomes 2/3 x 7/5. That rewrite keeps the value correct and turns division into multiplication, which is easier to compute.
Yes. You can enter fractions like 9/4 or -11/6 directly. The tool performs the arithmetic, simplifies the result, and shows the decimal value. If you need the answer as a mixed number such as 2 1/4, you will need to convert that from the improper fraction yourself.
Yes. A value like 3/-4 is mathematically valid and equal to -3/4. The calculator normalizes the final result so the negative sign appears in the numerator, which is the more standard written form.
Use the fraction when exactness matters, especially for repeating values like 1/3, 2/11, or 7/9. The decimal display is helpful for quick comparison and estimation, but it is rounded for readability. The simplified fraction preserves the exact relationship between numerator and denominator.
Fractions show up anywhere measurements and ratios matter. Cooks scale recipes, carpenters cut lumber to fractional inches, students solve worksheet problems, sewists measure fabric allowances, and shoppers compare discounts or package sizes. Even when the final answer is estimated in decimals, the work often starts in fractions.
First confirm that both denominators are non-zero. Then verify the operation, because subtract instead of add is a common slip. After that, check the signs and the second fraction in division problems. In most cases, a strange result traces back to one input error rather than to the simplification step.
It estimates fraction calculator outputs using the visible inputs and formula assumptions on this page.

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