Adding Fractions Calculator
Add two fractions with unlike denominators instantly: enter the numerators and denominators and get the simplified sum, mixed number, and decimal — plus a complete step-by-step solution.
Denominators of the two fractions
Least Common Denominator (LCD)
Convert first fraction: multiply top and bottom by 4
Convert second fraction: multiply top and bottom by 5
Add the numerators (denominators are now equal)
Already in lowest terms (GCD = 1)
Result
How does this calculator work?
To add fractions with different denominators: find the LCD, scale each fraction up to that denominator, add the numerators, then simplify by dividing by the GCD. For example, 2/5 + 3/4: LCD = 20 → 8/20 + 15/20 = 23/20 (already in lowest terms, mixed number = 1 3/20).
Formula
How this is calculated
You cannot add fractions directly when their denominators differ, because the fractions represent parts of different-sized wholes. The standard method is to find the Least Common Denominator (LCD) — the smallest number both denominators divide into evenly — and rewrite each fraction with that denominator before adding the numerators.
The LCD is the Least Common Multiple of the two denominators, calculated as LCM(b, d) = b × d ÷ GCD(b, d). Each fraction is then scaled up: multiply numerator and denominator by the factor that brings the denominator to the LCD. For example, to add 2/5 + 3/4, the LCD is 20; 2/5 becomes 8/20 and 3/4 becomes 15/20, giving 23/20.
The resulting numerator and denominator are reduced to lowest terms by dividing both by their GCD. If the GCD is 1, the fraction is already fully simplified. The calculator also converts the result to a mixed number (for improper fractions) and shows the decimal equivalent.
Frequently asked questions
If both denominators are already the same (e.g. 1/5 + 2/5), the LCD equals that common denominator and both "conversion" multipliers equal 1. You just add the numerators directly: 1/5 + 2/5 = 3/5.
Express the whole number as a fraction over 1 (e.g. 3 = 3/1), then enter numerator 3 and denominator 1 for the second fraction. The calculator will find LCD(d, 1) = d and combine normally.
Yes — enter a negative numerator. For example, to add 3/4 and −1/3, enter numerator2 = −1 and denominator2 = 3. The sign is carried through the arithmetic correctly.
Also known as
TG we-Calculate Editorial Team. (2026). Adding Fractions Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/adding-fractions-calculator
TG we-Calculate Editorial Team. "Adding Fractions Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/adding-fractions-calculator.
TG we-Calculate Editorial Team, "Adding Fractions Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/adding-fractions-calculator
@misc{wecalculate_adding_fractions_calculator, title = {Adding Fractions Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/adding-fractions-calculator}}, year = {2026}, note = {TG we-Calculate} }
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