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Fraction Calculator

Calculate, simplify and convert fractions online with full step-by-step details.

Fraction 1
Op.
Fraction 2
Examples: ½ + ⅓ ¾ − ¼ ⅔ × ¾ ⅚ ÷ ⅔ ½ + ¼ 1½ + 2⅓ ⅞ − ⅚
Optional integer part
Examples: 12/18 36/48 100/75 7/13 (irréd.) 144/60 3 2/4
⇄
Enter decimal → fraction auto
Examples: 1/3 1/4 2/3 5/8 7/4 0.125 0.6
↵ Enter to calculate
Choose a mode and enter your fractions.

How to calculate with fractions?

An online fraction calculator quickly performs the four arithmetic operations on fractions: addition, subtraction, multiplication and division. It also simplifies fractions by reducing to the lowest common denominator using GCD, and converts fractions to decimal numbers and percentages.

Adding and subtracting fractions

To add or subtract two fractions, first find a common denominator (the LCM of both denominators). Multiply each numerator by the appropriate factor, then add or subtract the numerators. The result is then simplified by dividing by the GCD. Example: 1/2 + 1/3 = 3/6 + 2/6 = 5/6.

Multiplying and dividing fractions

Fraction multiplication is straightforward: multiply the numerators together and the denominators together, then simplify. Division becomes multiplication: a/b ÷ c/d = a/b × d/c (multiply by the reciprocal). Example: 2/3 × 3/4 = 6/12 = 1/2.

Simplifying a fraction

A fraction is irreducible when its numerator and denominator are coprime (GCD = 1). To simplify, divide both terms by their GCD. Example: 12/18 → GCD(12,18) = 6 → 12÷6 / 18÷6 = 2/3.

Frequently asked questions

To add two fractions with different denominators, first find the LCM (Least Common Multiple) of both denominators. This LCM becomes the common denominator. Then... To add two fractions with different denominators, first find the LCM (Least Common Multiple) of both denominators. This LCM becomes the common denominator. Then multiply each numerator by the quotient of the LCM divided by its denominator, and add the new numerators. Example: 1/2 + 1/3. LCM(2,3) = 6. We get 3/6 + 2/6 = 5/6.

To simplify a fraction, divide the numerator and denominator by their GCD (Greatest Common Divisor). The result is an irreducible fraction, meaning the numerato... To simplify a fraction, divide the numerator and denominator by their GCD (Greatest Common Divisor). The result is an irreducible fraction, meaning the numerator and denominator have no common divisor other than 1. Example: 12/18 → GCD(12,18) = 6 → 12÷6 = 2 and 18÷6 = 3 → 2/3.

To convert a fraction to a decimal, simply divide the numerator by the denominator. Example: 3/4 = 3 ÷ 4 = 0.75. Some fractions produce terminating decimals (1/... To convert a fraction to a decimal, simply divide the numerator by the denominator. Example: 3/4 = 3 ÷ 4 = 0.75. Some fractions produce terminating decimals (1/4 = 0.25), others repeating decimals (1/3 = 0.333...). To convert a decimal to a fraction, our tool uses the continued fractions algorithm to find the exact fraction.

To divide one fraction by another, multiply the first fraction by the reciprocal (flipped fraction) of the second. In other words: a/b ÷ c/d = a/b × d/c = (a×d)... To divide one fraction by another, multiply the first fraction by the reciprocal (flipped fraction) of the second. In other words: a/b ÷ c/d = a/b × d/c = (a×d) / (b×c). Example: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6 after simplification.

A mixed number combines an integer and a proper fraction, like 1 2/3 (read 'one and two thirds'). To calculate with mixed numbers, first convert them to imprope... A mixed number combines an integer and a proper fraction, like 1 2/3 (read 'one and two thirds'). To calculate with mixed numbers, first convert them to improper fractions: 1 2/3 = (1×3 + 2)/3 = 5/3. Our calculator automatically handles mixed numbers via the optional 'integer part' field to the left of each fraction.

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