Adding and Subtracting Fractions Calculator
Add or subtract any two fractions: enter the numerators, denominators, and operation — the calculator finds the least common denominator, converts both fractions, computes the result, and simplifies it to lowest terms.
Operation
Denominators of the two fractions
Least Common Denominator (LCD)
Convert first fraction to LCD
Convert second fraction to LCD
Add numerators
Already in lowest terms (GCD = 1)
Result
How does this calculator work?
To add or subtract fractions, find the LCD of both denominators, convert each fraction to that denominator, then add or subtract the numerators. Finally, simplify by dividing numerator and denominator by their GCD. For example, 1/3 + 1/4: LCD = 12 → 4/12 + 3/12 = 7/12.
Formula
How this is calculated
Fractions with different denominators cannot be added or subtracted directly — they first need a common denominator. This calculator uses the Least Common Denominator (LCD), which is the smallest number both denominators divide into evenly. The LCD equals the Least Common Multiple of the two denominators: LCD = (b × d) ÷ GCD(b, d).
Once the LCD is found, each fraction is converted by multiplying its numerator and denominator by the factor that brings its denominator up to the LCD. For example, to convert 1/3 to a denominator of 12, multiply top and bottom by 4 to get 4/12. Now both fractions share the same denominator and the numerators can be added or subtracted directly.
The raw result is then reduced to its simplest form by dividing both numerator and denominator by their Greatest Common Divisor (GCD). If the GCD is 1 the fraction is already in lowest terms. The calculator also shows the mixed-number form for improper fractions and the decimal equivalent.
Frequently asked questions
A denominator tells you how many equal parts make a whole. Adding 1/3 and 1/4 directly would mean adding thirds and quarters together, which are different sized pieces. Converting to the same denominator (twelfths) makes the pieces the same size, so the numerators can be added normally: 4/12 + 3/12 = 7/12.
The LCD (Least Common Denominator) is the smallest denominator that both fractions can share. Using it keeps the numbers as small as possible and avoids the extra simplification step you would need with a larger common denominator.
After adding or subtracting, the numerator and denominator are divided by their Greatest Common Divisor (GCD). For example, 6/8 simplifies to 3/4 because GCD(6,8) = 2. If the GCD is 1, the fraction is already in lowest terms.
Also known as
TG we-Calculate Editorial Team. (2026). Adding and Subtracting Fractions Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/adding-and-subtracting-fractions-calculator
TG we-Calculate Editorial Team. "Adding and Subtracting Fractions Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/adding-and-subtracting-fractions-calculator.
TG we-Calculate Editorial Team, "Adding and Subtracting Fractions Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/adding-and-subtracting-fractions-calculator
@misc{wecalculate_adding_and_subtracting_fractions_calculator, title = {Adding and Subtracting Fractions Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/adding-and-subtracting-fractions-calculator}}, year = {2026}, note = {TG we-Calculate} }
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