How do you add fractions with different denominators?

Find a common denominator (multiply the two denominators together, or use the LCM). Convert each fraction to the common denominator, then add the numerators. Simplify the result by dividing by the GCD.

How do you multiply fractions?

Multiply the numerators together and the denominators together, then simplify: (a/b) × (c/d) = (a×c)/(b×d).

How do you divide fractions?

Multiply the first fraction by the reciprocal of the second: (a/b) ÷ (c/d) = (a/b) × (d/c) = (a×d)/(b×c).

How do you convert a mixed number to an improper fraction?

Multiply the whole part by the denominator, add the numerator, and place the result over the original denominator. For example, 2 3/4 = (2×4+3)/4 = 11/4.

Fraction Calculator

Fraction arithmetic rules

Operation	Rule
Addition (a/b + c/d)	(a×d + c×b) / (b×d), then simplify
Subtraction (a/b − c/d)	(a×d − c×b) / (b×d), then simplify
Multiplication (a/b × c/d)	(a×c) / (b×d), then simplify
Division (a/b ÷ c/d)	(a/b) × (d/c) = (a×d) / (b×c), then simplify

Simplifying fractions

A fraction a/b is in its simplest (lowest) form when the greatest common divisor (GCD) of a and b is 1. To simplify, divide both numerator and denominator by their GCD.

The GCD is found using the Euclidean algorithm: repeatedly replace the larger number with the remainder of dividing the larger by the smaller until the remainder is zero.

Mixed numbers and improper fractions

A mixed number like 2 3/4 is equivalent to the improper fraction 11/4. Convert by multiplying the whole part by the denominator and adding the numerator: (2 × 4) + 3 = 11.

To convert an improper fraction back to a mixed number, divide the numerator by the denominator. The quotient is the whole part and the remainder is the new numerator: 11 ÷ 4 = 2 remainder 3, so 11/4 = 2 3/4.

Least common denominator

When adding or subtracting fractions with different denominators, always use the least common multiple (LCM) of the denominators as the common denominator. While any common denominator works mathematically, using the LCD keeps numbers smaller and reduces the simplification step. Example: 1/4 + 1/6 - LCD is 12 (not 24), giving 3/12 + 2/12 = 5/12.

Complex fractions

A complex fraction has a fraction in its numerator, denominator, or both - for example (1/2) / (3/4). Simplify by multiplying the numerator fraction by the reciprocal of the denominator fraction: (1/2) × (4/3) = 4/6 = 2/3. This is equivalent to "invert and multiply" applied to compound fractions.