Fraction Calculator
Adjust the inputs below. Results update as you type.
How it works
Addition/subtraction: find LCD, convert fractions, combine numerators. Multiplication: multiply numerators and denominators directly, then simplify. Division: multiply by the reciprocal of the divisor. Always simplify by dividing by the GCF. Mixed numbers convert to improper fractions first: a b/c = (a×c + b)/c. Results are given in simplest form with step-by-step detail.
Input guidance
- Check units and decimal placement before running calculations.
- For percentage and ratio tasks, define the baseline value clearly.
- Use rounded output carefully and keep full precision for intermediate steps.
The formula
Add or subtract fractions over a common denominator: a/b ± c/d = (ad ± cb)/bd. Multiply across: a/b × c/d = ac/bd. Divide by inverting: a/b ÷ c/d = ad/bc. Simplify by the greatest common divisor.
Worked example
1/2 + 1/3 = (3 + 2)/6 = 5/6. And 2/3 × 3/4 = 6/12, which simplifies to 1/2.
More examples to test
- Baseline example: solve with clean numbers first to verify formula direction.
- Edge-case example: test near-zero or boundary values to avoid interpretation errors.
How to interpret results
Use outputs as quick checks, then verify with step-by-step work for graded or high-stakes use.
When this can be inaccurate
Errors usually come from unit mismatch, wrong baseline assumptions, or rounding too early in multistep problems.
Change history
- July 2026: Published fraction arithmetic path with simplification guidance.
Site-wide corrections also appear on the corrections log.
Build math and logic skills with guided lessons
Educational platform recommendation.
Frequently asked questions
How do I add fractions with different denominators?+
Convert to a common denominator first, add the numerators, then simplify. For 1/2 + 1/3, use sixths: 3/6 + 2/6 = 5/6.
How do I simplify a fraction?+
Divide the numerator and denominator by their greatest common divisor. 6/12 ÷ 6 = 1/2 in lowest terms.
How do I divide fractions?+
Multiply by the reciprocal of the divisor: a/b ÷ c/d = a/b × d/c. Flip the second fraction and multiply.
Why do my classroom and calculator results differ?+
Differences usually come from rounding conventions, order-of-operations handling, or different baseline assumptions.
What is the safest way to validate an answer?+
Recompute with units shown and check against a second method or manual arithmetic for critical problems.
Guided next steps
Want the full workflow? Use this calculator inside a step-by-step guide.