Fraction Calculator

What This Calculator Really Does

This calculator performs the four basic operations on fractions — addition, subtraction, multiplication and division — and shows the intermediate steps: common denominators, cross-multiplication where applicable, and full simplification of the result. It also handles mixed numbers, so 2 1/2 can be entered the way you would write it on paper.

Fraction arithmetic is one of the most common homework sticking points because each operation has a different rule. The step display is the point: you should be able to reproduce the answer yourself, not just copy it.

Everything runs locally in your browser — no upload, no tracking, exact rational arithmetic.

The Rules, Explained Plainly

• Add / subtract: convert both fractions to a common denominator (the LCM of the denominators is the smallest safe choice), then add or subtract numerators.
• Multiply: numerator × numerator, denominator × denominator — no common denominator needed.
• Divide: multiply by the reciprocal — a/b ÷ c/d = a×d / (b×c).
• Simplify: divide numerator and denominator by their GCD.

Mixed numbers are converted to improper fractions first (2 1/2 → 5/2), the operation runs, and the result converts back if it is improper.

How to Use It — In Order

1. Enter the first fraction — numerator and denominator, or a mixed number.
2. Choose the operation — +, −, × or ÷.
3. Enter the second fraction.
4. Read the steps — common denominator or reciprocal, shown explicitly.
5. Check the simplified result — both as a fraction and as a mixed number when improper.

Worked Example, Verified by Hand

3/4 + 5/6:

1. LCM of 4 and 6 = 12.
2. 3/4 = 9/12 (×3); 5/6 = 10/12 (×2).
3. 9/12 + 10/12 = 19/12.
4. GCD(19,12) = 1, so it is already fully simplified: 19/12 = 1 7/12.

Division check — 3/4 ÷ 2/5: multiply by the reciprocal: 3/4 × 5/2 = 15/8 = 1 7/8.

Common Mistakes to Avoid

• Adding denominators — 3/4 + 5/6 is not 8/10; denominators never add.
• Cross-multiplying in addition — that trick is only for comparing fractions or solving proportions.
• Flipping the wrong fraction in division — flip the second one, and only the second one.
• Leaving results unsimplified — 10/16 and 5/8 are equal, but the simplified form is the expected answer.
• Entering zero denominators — division by zero has no defined result; the tool flags it.

Limitations

• Integers only — decimal inputs are converted to fractions where exact, otherwise rejected.
• Very large numerators can overflow display formatting, though the math stays exact.
• This tool covers arithmetic; solving equations with fractions needs an algebra solver.

Expected Accuracy

Results are computed as exact rational numbers — no floating-point rounding — then simplified. The answer is exactly correct arithmetic, always.

Privacy — Your Data Never Leaves This Device

All arithmetic runs in your browser. No account, no upload, no tracking.

Related Tools & Guides

Natural next steps from Fraction Calculator:

• All Math Calculators
• Percentage Calculator — fractions as percentages
• Ratio Calculator
• LCM & GCD Calculator
• Average Calculator

Sources & Standards

The operation rules follow standard school and college algebra conventions.

• Khan Academy — Fraction arithmetic (reference)
• NIST — rational number arithmetic references

Bottom Line

Fraction arithmetic has exactly four rules, and this calculator shows each one applied to your numbers. Master the patterns here and the homework stops being guesswork.

Frequently Asked Questions