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Fraction Calculator

Perform arithmetic on two fractions and see the result as a simplified fraction and decimal.

Input Information

Result

Enter fractions to calculate

Fraction Calculator performs arithmetic operations (+, -, ×, ÷) between two fractions and displays the result as both a simplified fraction and a decimal.

Fractions are used to express values that cannot be represented as whole numbers, where the denominator represents the whole and the numerator represents the part.

This calculator automatically simplifies the result to a reduced fraction (divided by the GCD of numerator and denominator) for the simplest form.

Term Glossary

Fraction
A number representing parts of a whole divided into equal pieces. E.g., 3/4 means 3 out of 4 parts.
Numerator
The top number in a fraction, indicating how many parts are taken.
Denominator
The bottom number in a fraction, indicating into how many equal parts the whole is divided. Cannot be zero.
Reduced Fraction
A fraction where the numerator and denominator have been divided by their GCD so it cannot be simplified further.

  1. 1

    Enter two fractions

    Enter the numerator and denominator for the first and second fractions. The denominator cannot be zero.

  2. 2

    Choose an operation

    Select the arithmetic operation to perform: addition (+), subtraction (−), multiplication (×), or division (÷).

  3. 3

    Calculate

    Press the calculate button to get the result of the operation. The calculator simplifies the result to a reduced fraction.

  4. 4

    Read the result

    Review the result in both fraction and decimal form. You can also check the improper or mixed fraction form if needed.

Example 1 — Addition

Compute 1/2 + 1/4. Using a common denominator: 2/4 + 1/4 = 3/4. So 1/2 + 1/4 = 3/4 = 0.75.

Example 2 — Multiplication

Compute 2/3 × 3/4. Multiply numerators and denominators: 6/12, which reduces to 1/2. So 2/3 × 3/4 = 1/2 = 0.5.

Example 3 — Division

Compute 3/4 ÷ 1/2. Multiply by the reciprocal: 3/4 × 2/1 = 6/4 = 3/2. So 3/4 ÷ 1/2 = 3/2 = 1.5.

Addition/Subtraction

ab+cd=ad+cbbd\dfrac{a}{b} + \dfrac{c}{d} = \dfrac{ad + cb}{bd}
ab−cd=ad−cbbd\dfrac{a}{b} - \dfrac{c}{d} = \dfrac{ad - cb}{bd}

When denominators differ: find LCM, then operate on numerators

Multiplication

ab×cd=acbd\dfrac{a}{b} \times \dfrac{c}{d} = \dfrac{ac}{bd}

Numerator × Numerator, Denominator × Denominator

Division

ab÷cd=ab×dc=adbc\dfrac{a}{b} \div \dfrac{c}{d} = \dfrac{a}{b} \times \dfrac{d}{c} = \dfrac{ad}{bc}

Division is converted to multiplication by the reciprocal

Simplification (GCD)

GCD(a,b): 유클리드 호제법\text{GCD}(a, b):\ \text{유클리드 호제법}

Divide by the Greatest Common Divisor (GCD) to get the reduced fraction

Examples

Addition Example

12+13=1×3+1×22×3=56\dfrac{1}{2} + \dfrac{1}{3} = \dfrac{1 \times 3 + 1 \times 2}{2 \times 3} = \dfrac{5}{6}

Multiplication Example

23×34=612=12\dfrac{2}{3} \times \dfrac{3}{4} = \dfrac{6}{12} = \dfrac{1}{2}

Division Example

35÷27=35×72=2110\dfrac{3}{5} \div \dfrac{2}{7} = \dfrac{3}{5} \times \dfrac{7}{2} = \dfrac{21}{10}

Useful Tips

  • A fraction with a denominator of 0 is undefined. Always check the denominator.
  • To convert a fraction to decimal, divide the numerator by the denominator.
  • To convert an improper fraction (e.g., 7/3) to a mixed number (e.g., 2 1/3): quotient is the whole part, remainder is the new numerator.
  • Finding a common denominator: multiply the numerator and denominator of each fraction by the other denominator.

QHow do you add fractions?

If the denominators are the same, add the numerators. If not, find a common denominator (LCM), then add the numerators. Example: 1/2 + 1/4 becomes 2/4 + 1/4 = 3/4. Simplify the result to a reduced fraction when possible.

QHow do you multiply fractions?

Multiply the numerators together and the denominators together: (a/b) × (c/d) = (a×c) / (b×d). Example: 2/3 × 3/4 = 6/12 = 1/2. Multiplication does not require a common denominator.

QHow do you divide fractions?

Division is converted to multiplication by the reciprocal (flip the divisor): (a/b) ÷ (c/d) = (a/b) × (d/c). Example: 3/4 ÷ 1/2 = 3/4 × 2/1 = 6/4 = 3/2 = 1.5.

QWhat is the difference between improper and mixed fractions?

An improper fraction has a numerator greater than or equal to its denominator (e.g., 7/3). A mixed fraction combines a whole number and a proper fraction (e.g., 2 1/3). To convert an improper fraction to a mixed number, divide the numerator by the denominator: the quotient is the whole part and the remainder is the new numerator. 7/3 = 2 with remainder 1, so 2 1/3.

QHow do you convert a fraction to a decimal?

Divide the numerator by the denominator to convert to a decimal. Example: 3/4 = 3 ÷ 4 = 0.75. Some fractions give a finite decimal (e.g., 1/2 = 0.5), while others repeat infinitely (e.g., 1/3 = 0.333...). This calculator shows both the reduced fraction and decimal result.

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