Fraction Calculator: Add, Subtract, Multiply & Divide

Calculate with fractions online without rewriting common denominators by hand. Enter a proper, improper, or mixed fraction, choose an operation, and see the simplified fraction, mixed-number form, decimal approximation, and the main calculation steps in one result panel.

Core rule
Simplify a fraction by dividing the numerator and denominator by their greatest common divisor.

Fraction calculator

Free browser tool
Use arithmetic for two fractions, or choose a conversion mode for one fraction or decimal.

First fraction

Leave Whole at 0 for a simple fraction such as 3/4. Use 1, 1, and 2 for 1 1/2.
The result is reduced after the selected operation.

Second fraction

Enter a second fraction for arithmetic. Its value cannot be zero when dividing.

This calculator runs in your browser. The numbers you enter are used to update the page and are not sent to a server by this tool.

Calculated result
17/12
Example result

Three-fourths plus two-thirds equals seventeen-twelfths. The result is already simplified, and it can also be read as 1 5/12 or about 1.4167.

17 12
Mixed number
1 5/12

A whole-number and remainder form when the result is improper.

Decimal
1.4167

A rounded decimal view of the fraction result.

GCD used
1

The greatest common divisor used to reduce the fraction.

Inputs
3/4 + 2/3

The fraction expression used for this calculation.

Quick check
17 / 12 = 1.4167

A compact decimal or reduction check for the result.

Fraction formula

3/4 + 2/3 = (9 + 8) / 12 = 17/12

Calculation steps

  1. The least common denominator for 4 and 3 is 12.
  2. Convert 3/4 to 9/12 and 2/3 to 8/12.
  3. Add the numerators: 9 + 8 = 17, so the result is 17/12.
  4. The greatest common divisor of 17 and 12 is 1, so no further reduction is needed.

Fraction Calculator Examples

Load a worked scenario to see how unlike denominators, multiplication, and mixed-number inputs behave. The examples are small enough to check by hand.

3/4 + 2/3

A common-denominator example. The calculator changes both fractions to twelfths and returns 17/12, or 1 5/12.

1 1/2 x 2/3

A mixed fraction calculator example. Convert 1 1/2 to 3/2, multiply, and simplify the result to 1.

0.625 to a fraction

A decimal-to-fraction example. 0.625 is 625/1000, which reduces to 5/8 after common factors are removed.

How to Use the Fraction Calculator

Enter the values as integers, then let the tool handle common denominators, signs, reduction, and decimal formatting.

1

Choose a mode

Select arithmetic for two fractions, fraction to decimal for one fraction, or decimal to fraction for a terminating decimal.

2

Enter each fraction

Use Whole = 0 for a simple fraction. For 2 3/5, enter Whole 2, Numerator 3, and Denominator 5. Denominators must not be zero.

3

Choose the operation

For arithmetic, select addition, subtraction, multiplication, or division. The operation stays visible in the result card for easy checking.

4

Review every form

Read the reduced fraction first, then compare the mixed number, decimal approximation, formula line, and steps with your original problem.

Fraction Calculator Formulas

The tool uses exact integer arithmetic for the fraction portion of each calculation, then reduces the result before displaying a decimal approximation.

Addition

a/b + c/d = (a x d + c x b) / (b x d)

Multiply across to create a common denominator, add the cross-products, then simplify the resulting fraction.

Subtraction

a/b - c/d = (a x d - c x b) / (b x d)

The denominator follows the same cross-product pattern; only the numerator changes from addition to subtraction.

Multiplication

a/b x c/d = (a x c) / (b x d)

Multiply numerators together and denominators together. Reduce common factors before or after multiplying.

Division

a/b / c/d = a/b x d/c

Invert the second fraction and multiply. Division is not valid when the second fraction has a value of zero.

Simplifying

simplified numerator = numerator / GCD; simplified denominator = denominator / GCD

The greatest common divisor is the largest positive integer that divides both parts evenly.

Mixed numbers

whole number plus numerator/denominator = (whole x denominator + numerator) / denominator

The calculator converts mixed inputs to an improper fraction for arithmetic, then converts the result back when useful.

How to Read a Fraction Result

The reduced fraction is the exact answer when the inputs are integers. A fraction such as 17/12 is improper because the numerator is larger than the denominator, but it is still a complete and correct result. The mixed-number view, 1 5/12, is often easier to read in a measurement, recipe, or classroom problem.

The decimal is a convenient approximation, not a replacement for the exact fraction. Terminating decimals such as 5/8 become 0.625 exactly. Fractions such as 1/3 repeat forever in decimal form, so the calculator rounds the displayed value. Keep the fraction when you need an exact value for another calculation.

The steps panel explains the main operation rather than pretending to reproduce every line of a textbook solution. It shows the common denominator for addition and subtraction, the cross-products used by the operation, and the greatest common divisor used for reduction. This makes the result easier to audit before you copy it into homework, a spreadsheet, or a project note.

Result format What it means Best for
Reduced fraction The exact numerator-over-denominator answer after common factors are removed. Further math and exact answers
Mixed number A whole number plus a proper fractional remainder. Measurements and everyday explanations
Decimal A readable approximation; repeating values are rounded. Quick comparison and calculators that accept decimals
GCD used The common factor that shows how the fraction was simplified. Checking reduction and learning the method

Fraction Calculator Edge Cases

A valid-looking fraction can still describe an impossible operation or an input that needs clarification. Check these boundaries before relying on the answer.

Zero denominator

A denominator of zero does not define a fraction. The calculator stops and asks you to enter a non-zero denominator rather than showing infinity or a misleading number.

Division by zero

Division requires a non-zero second fraction. A numerator of zero is valid for a fraction, but a whole fraction with value zero cannot be the divisor.

Negative fractions

Negative numerators and negative mixed values are accepted. A negative denominator is normalized so the final denominator is positive and the sign is easier to read.

Whole-number fractions

A fraction such as 4/1 is valid and simplifies to 4. The mixed-number display removes an unnecessary zero remainder when the result is a whole number.

Improper fractions

A numerator larger than the denominator is not an error. It represents a value above one and is shown as both an improper fraction and a mixed number.

Rounding

The fraction remains the exact result. Decimal output is limited to a readable number of places, so use the fraction or formula line when rounding matters.

Fraction Calculator FAQ

Answers to common questions about adding, simplifying, converting, and entering fractions.

Find a common denominator, rewrite both fractions with that denominator, add the numerators, and simplify. For example, 3/4 + 2/3 becomes 9/12 + 8/12 = 17/12.

Yes. Choose arithmetic mode, enter the two fractions, select add, subtract, multiply, or divide, and the result panel shows the reduced fraction, mixed number, decimal, and steps.

Use the Whole, Numerator, and Denominator fields. For 2 3/5, enter 2 as Whole, 3 as Numerator, and 5 as Denominator. The calculator converts it to 13/5 internally.

A fraction simplifier divides the numerator and denominator by their greatest common divisor. This calculator simplifies every arithmetic result and shows the GCD used so you can check the reduction.

Divide the numerator by the denominator. Use fraction-to-decimal mode for a direct conversion; for example, 5/8 becomes 0.625. Repeating decimals are rounded in the display.

Write the digits after the decimal over a power of ten, then simplify. For example, 0.625 is 625/1000, which reduces to 5/8. Use decimal-to-fraction mode for terminating decimals.

An improper fraction has a numerator larger than its denominator and represents a value greater than one. It is not wrong; the mixed-number field gives the equivalent whole-and-remainder form.

A negative denominator is mathematically valid, but the calculator moves the sign to the numerator and keeps the displayed denominator positive. This produces a consistent easier-to-read result.

The fraction result is exact for integer inputs. A terminating decimal can be exact, while a repeating decimal such as 1/3 must be rounded for display. Keep the reduced fraction when exactness is important.

Ready to calculate a fraction?

Enter the two fractions, choose an operation, and use the exact result plus the decimal view to check your work.

Jump to calculator