Adding Fractions — the 80/20
To add fractions, make denominators match (use the LCD), add the numerators, then simplify. The calculator automates this without changing your numbers.
How it works
- Find LCD of denominators.
- Convert each a/b → (a×k)/(b×k) so all denominators equal LCD.
- Add numerators; keep the common denominator.
- Simplify; convert to mixed number if improper.
Sanity checks
- If denominators already match, only numerators should change.
- Result should lie between min and max of inputs when both are positive.
- 1/2 + 1/2 must equal 1; 1/3 + 1/6 must equal 1/2.
Shortcuts
- Same denominator: add numerators directly.
- One denominator divides the other: use the larger as LCD.
- Mixed numbers: either add whole parts + fractional parts or convert to improper first.
Pitfalls
- Adding denominators (wrong).
- Forgetting to simplify the final result.
- Sign errors with negative fractions or mixed numbers.
Micro‑examples
- 3/4 + 1/6 → LCD 12 → 9/12 + 2/12 = 11/12.
- 2/7 + 3/7 = 5/7 (same denominator).
- −2/5 + 3/10 → LCD 10 → −4/10 + 3/10 = −1/10.
Mini‑FAQ
- Can I add without a common denominator? No—create one first.
- Do I have to use the LCD? Any common denominator works; LCD keeps numbers small.
- Improper result? You can keep it improper or convert to a mixed number.
Action tip
Enter your fractions above and the tool finds the LCD, adds, simplifies, and optionally shows a mixed number—step by step.