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
How we build and check this calculator
This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
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