LazyTools

🔒 Every tool runs in your browser — the files and values you enter are never uploaded to any server. How it works

➗ Fraction Calculator

1 1/2 + 3/4 = 9/4 = 2 1/4 — exactly, with the steps shown. Fractions, mixed numbers and decimals in; simplified fraction, mixed number and decimal out.

Accepts fractions (3/4), mixed numbers (1 2/3), integers and decimals (2.5).

9/4

exact fraction

2 1/4

mixed number

2.25

decimal (exact)

Working

  1. Write both fractions over the common denominator 4: 3/2 = 6/4 and 3/4 = 3/4
  2. Add the numerators: 6 + 3 = 9, giving 9/4
  3. Simplify to lowest terms: 9/4

Computed with exact integer arithmetic — no floating-point rounding, ever. Runs locally.

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How the fraction calculator works

Every input — a fraction like 3/4, a mixed number like 1 2/3, an integer or a decimal — is converted to an exact rational number (a pair of arbitrary-precision integers), and the arithmetic happens on those. Addition and subtraction go through the least common denominator, multiplication multiplies straight across, division multiplies by the reciprocal — and each route shows its working as numbered steps, the way it's taught. The result appears three ways at once: simplified fraction, mixed number, and decimal (marked exact when it terminates, rounded when it doesn't).

Why exact matters: a floating-point calculator answering 1/3 + 1/3 + 1/3 gets 0.9999999999999999 — close, but wrong, and visibly wrong when the numbers feed a recipe scale-up or a homework answer. Rational arithmetic has no such drift: thirds stay thirds. The steps display doubles as a checking aid for schoolwork — the answer alone teaches nothing; the working is the point.

Frequently asked questions

What input formats are accepted?

Proper and improper fractions (3/4, 7/2), mixed numbers with a space (1 2/3), negative values (-5/6), whole numbers, and decimals (2.5 becomes 5/2 exactly). Both operands accept any of these, mixed freely.

How do you add fractions with different denominators?

Rewrite both over the least common denominator, then add numerators. 1/2 + 1/3 → 3/6 + 2/6 = 5/6. The tool shows exactly this working for your numbers.

Why does my calculator show 0.9999999999 for 1/3 + 2/3?

Because it computes in binary floating point, which cannot represent 1/3 exactly, so tiny errors accumulate. This tool keeps numbers as exact fractions — 1/3 + 2/3 is exactly 1.

Does it simplify to lowest terms?

Always — results are reduced by the greatest common divisor and shown as a fraction, a mixed number (when the value exceeds 1), and a decimal marked exact or rounded.

Is my input sent anywhere?

No — all arithmetic runs in your browser and the page works offline.

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