Adding & Subtracting Fractions Calculator
Add or subtract two fractions with full step-by-step working.
Finds the LCD, converts fractions, and simplifies the result to lowest terms.
Why you need a common denominator: You can only add or subtract fractions when they share the same denominator. Think of it like units — you can’t add apples and oranges directly. 1/3 means “1 out of 3 equal parts”; 1/4 means “1 out of 4 equal parts.” To combine them you need a common unit size.
Finding the LCD (Least Common Denominator): The LCD is the Least Common Multiple (LCM) of the two denominators.
LCD(a, b) = |a × b| / GCD(a, b)
Conversion step: Multiply each fraction’s numerator by (LCD ÷ its own denominator).
The formula:
a/b ± c/d = (a × LCD/b ± c × LCD/d) / LCD
Simplification: Divide both numerator and denominator by their GCD to reach lowest terms.
Mixed number form: If the result is an improper fraction (numerator > denominator), it can also be written as a whole number + fraction, e.g. 7/4 = 1 and 3/4.
Worked example: 1/3 + 1/4
Step 1 — Find LCD: LCM(3, 4) = 12 Step 2 — Convert: 1/3 → 4/12, 1/4 → 3/12 Step 3 — Add numerators: 4 + 3 = 7 Step 4 — Result: 7/12 Step 5 — Simplify: GCD(7, 12) = 1 → already in lowest terms → 7/12