How to Add Fractions — 1/2 + 1/3 = 5/6 Step‑by‑Step

Guides · Calculator · Updated 2026

Adding fractions is one of those skills that looks easy — until you actually have to do it without a calculator. The rule is simple: find a common denominator, add the numerators, and simplify. But when mixed numbers, improper fractions, or three fractions appear, mistakes creep in. In this article we’ll add 1/2 + 1/3 the old‑fashioned way, show how GCD simplification works, and introduce a tool that handles everything — including mixed numbers and step‑by‑step working — instantly.

The common‑denominator method

Every fraction addition follows the same logic:

a/b + c/d = (a×d + b×c) / (b×d)
Then simplify the result by dividing numerator and denominator by their greatest common divisor (GCD).

For 1/2 + 1/3, b=2, d=3. So the new numerator = 1×3 + 2×1 = 5, and denominator = 2×3 = 6. The fraction is 5/6 — already simplified because GCD(5,6) = 1.

Step‑by‑step: add any two fractions

Open the Fraction Calculator tool.
Enter the numerators and denominators for both fractions. If you have mixed numbers (e.g., 2 1/2), type the whole‑number part in the optional “Whole” field.
Select the operation (+, −, ×, ÷) and click Calculate.
The tool displays the simplified fraction, the mixed‑number form, and the decimal equivalent. Below that, a muted block shows the working steps — including the common denominator and GCD reduction.

💡 Tip: Always reduce your answer. Leaving 10/12 instead of 5/6 is technically correct but will lose marks on a test. The calculator automatically reduces to the simplest form.

Worked example: 1/2 + 1/3

Step 1: Find a common denominator. The least common multiple of 2 and 3 is 6. Step 2: Convert each fraction: 1/2 = 3/6, 1/3 = 2/6. Step 3: Add numerators: 3 + 2 = 5. Result: 5/6. Step 4: Simplify — GCD(5,6)=1, so the answer stays 5/6. The whole process is done automatically by the tool, but seeing it written out builds understanding for tests where you can’t use a calculator.

Frequently Asked Questions

What if I have a negative fraction?

Enter the negative sign in the numerator field. The tool handles negative fractions correctly, including when simplifying (the denominator stays positive).

How does the GCD simplification work?

The tool finds the greatest common divisor of the numerator and denominator using the Euclidean algorithm, then divides both by that number. It ensures the fraction is in its lowest terms.

Can I add more than two fractions at once?

The current version works with two fractions at a time. To add three fractions, add the first two, then add the result to the third. Or use our Average Calculator if you need the mean of several fractions.

What if the denominator is zero?

The tool will reject a zero denominator with an alert. Division by zero is undefined, so the fraction is invalid.

Is it free and private?

Yes — the tool runs entirely in your browser, free, with no sign‑up and nothing uploaded to a server.

Try the Fraction Calculator