Fraction Calculator

Add, subtract, multiply, and divide fractions with step-by-step simplification using GCD.

Select Operation & Enter Fractions

First Fraction

13
+
14

Second Fraction

Result

Result
7/12
= 0.583333...
Unsimplified Result 7/12
GCD 1
Simplified Result 7/12
Decimal Value 0.583333...
Mixed Number 0 and 7/12

Step-by-Step Solution

1/3 + 1/4 = 4/12 + 3/12 = 7/12

How to Calculate with Fractions

A fraction represents a part of a whole and consists of a numerator (top number) and a denominator (bottom number). The four basic operations with fractions each have their own set of rules for finding the result.

Fraction Operations

Addition

Find a common denominator, convert both fractions, then add numerators.

a/b + c/d = (ad + bc) / bd

Subtraction

Find a common denominator, convert both fractions, then subtract numerators.

a/b - c/d = (ad - bc) / bd

Multiplication

Multiply numerators together and denominators together.

a/b × c/d = ac / bd

Division

Multiply by the reciprocal of the second fraction.

a/b ÷ c/d = a/b × d/c = ad / bc

Simplifying Fractions

After performing any operation, the resulting fraction should be simplified by dividing both the numerator and denominator by their Greatest Common Divisor (GCD). The GCD is the largest number that divides evenly into both numbers.

For example, to simplify 8/12: the GCD of 8 and 12 is 4, so 8/12 = (8÷4)/(12÷4) = 2/3.

Finding the Least Common Denominator (LCD)

When adding or subtracting fractions with different denominators, you need a common denominator. The Least Common Denominator is the smallest number that both denominators divide into evenly. The LCD equals the Least Common Multiple (LCM) of the two denominators.

  • Find the LCM of the two denominators.
  • Convert each fraction to an equivalent fraction with the LCD.
  • Perform the addition or subtraction on the numerators.
  • Simplify the result if possible.

Mixed Numbers

When the numerator is larger than the denominator (an improper fraction), the result can be expressed as a mixed number. Divide the numerator by the denominator: the quotient is the whole number part, and the remainder over the denominator is the fractional part.

Tips for Working with Fractions

  • Always simplify your final answer to lowest terms.
  • When multiplying, you can cross-cancel before multiplying to keep numbers smaller.
  • Remember: dividing by a fraction is the same as multiplying by its reciprocal.
  • A negative sign can be placed on the numerator, denominator, or in front of the fraction.