Solverly

Fraction Calculator

Add, subtract, multiply, divide, simplify, and convert fractions. Works with mixed numbers and very large integers.

Fraction Calculator

Steps to calculate Fractions

Enter values…

Fractions — Final result

Enter values…

Mixed Numbers Calculator

Steps to calculate Mixed Numbers

Enter values…

Mixed Numbers — Final result

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Simplify Fractions Calculator

Steps to simplify a Mixed Fraction

Enter values…

Simplify — Final result

Enter values…

Decimal to Fraction Calculator

Steps to convert Decimal to Fraction

Enter a valid decimal…

Decimal → Fraction — Final result

Enter a valid decimal…

Fraction to Decimal Calculator

Steps to convert Fraction to Decimal

Enter numerator & denominator…

Fraction → Decimal — Final result

Enter numerator & denominator…

Big Number Fraction Calculator

Use when numerators/denominators are very large. Uses BigInt integer arithmetic.

Steps to calculate Big-Number Fractions

Enter valid big integers…

Big-Number Fractions — Final result

Enter valid big integers…

Results interpretation

  • Improper vs. mixed — we reduce to simplest form and also show a mixed number when helpful.
  • Decimal line — decimals are rounded for display; the fraction is exact.
  • Who it’s for — students checking steps, cooks scaling recipes, DIYers combining measurements.
  • Norms — denominators are kept positive and we always reduce by the greatest common divisor.

How this calculator works

Show the math
  • Add/Subtract: convert to a common denominator (LCM), combine numerators, reduce by GCD.
  • Multiply: multiply numerators and denominators; reduce by GCD.
  • Divide: multiply by the reciprocal of the second fraction; reduce by GCD.
  • Mixed numbers: convert to improper, compute, convert back if desired.
  • Decimal → Fraction: write as integer over \(10^k\) where \(k\) is the number of decimal places; then reduce.
  • Big numbers: integer-exact BigInt arithmetic plus BigInt GCD.

Assumptions: denominators ≠ 0, whole numbers may be negative, and inputs are unit-less.

What this Fraction Calculator does

Fractions are the language of exact quantities. This calculator treats every entry as a rational number and keeps it exact from input to output. Start on the Two Fractions tab to combine two simple ratios; switch to Mixed Numbers to work with everyday forms like 2 3/5; use Simplify to reduce any fraction to lowest terms; convert back and forth between decimals and fractions; and reach for Big Number mode when numerators or denominators stretch far beyond normal size.

Each operation uses the standard rules of rational arithmetic and then reduces the result by dividing top and bottom by their greatest common divisor. If a result is at least one in magnitude, you’ll see a mixed number view alongside the improper fraction so you can read it quickly without losing precision. The decimal view is there for context, but the core of the calculation stays exact.

Why would you choose one tab over another? Two Fractions is perfect for homework, ratios, and recipes. Mixed Numbers mirrors how people write portions in the real world (think carpentry and cooking). Simplify is a finishing step—use it to make answers neat or to compare fractions quickly. Decimal ↔ Fraction helps translate between measurement systems and spreadsheet outputs. Big Number handles edge cases like probability calculations with combinatoric counts that don’t fit in 64-bit integers.

Assumptions & limits: denominators must be non-zero; repeating decimals are not inferred automatically; mixed numbers require an integer part, a space, then a proper fraction. If you see an error, it will be explicit—no silent rounding or hidden state.

Whether you’re checking a school problem, reconciling recipe quantities, or validating a symbolic result from elsewhere, this tool emphasizes clarity: inputs on one side, a green results banner with exact output on the other, and well-labeled sections that explain the math when you want the details.

How to work with fractions (add, subtract, multiply, divide, and simplify)

A fraction has a numerator (top) and a denominator (bottom). The calculator handles addition, subtraction, multiplication, division, simplification, mixed numbers, and decimal ↔ fraction conversion.

Core rules

  • Add/Subtract: Use a common denominator. If denominators differ, use the LCM (least common multiple).
  • Multiply: Multiply numerators together and denominators together, then reduce.
  • Divide: Multiply by the reciprocal of the second fraction.
  • Simplify: Divide top and bottom by their GCD (greatest common divisor).
  • Mixed ↔ Improper: a b/c = (a×c+b)/c; reverse by dividing and taking remainder.
LCM, GCD, and reducing steps

To add a/b + c/d, use LCM(b,d) as the common denominator. Scale each numerator:a×(LCM/b) and c×(LCM/d), then combine and simplify by GCD(numerator, denominator).

To reduce n/d, compute g = GCD(n,d) and write (n/g)/(d/g). Mixed number: divide n ÷ d = q remainder r; result q r/d.

Use cases & examples

Example 1 — Add unlike denominators: 2/3 + 5/8

  1. LCM(3,8) = 24 → rewrite as 16/24 + 15/24
  2. Add numerators: 31/24 = 1 7/24

Example 2 — Multiply and simplify: 9/14 × 7/6

  1. Cross-reduce: 7 cancels with 14 → 1/2; 9 cancels with 6 → 3/2
  2. Multiply: (3/2) × (1/2) = 3/4 → 3/4

Example 3 — Divide mixed numbers: 2 1/5 ÷ 3/10

  1. Convert: 2 1/5 = 11/5
  2. Divide: (11/5) ÷ (3/10) = (11/5) × (10/3) = 110/15
  3. Simplify: divide by 5 → 22/3 = 7 1/3

Fraction Calculator — FAQ

How do I add or subtract fractions with different denominators?

Find the LCM of the denominators, convert both fractions to that denominator, combine numerators, and reduce.

What’s the fastest way to simplify a fraction?

Divide top and bottom by their GCD. Using prime factors (or the calculator’s auto-reduce) is quickest.

How do I multiply and divide fractions?

Multiply: top×top and bottom×bottom. Divide: multiply by the reciprocal of the second fraction, then reduce.

How do I convert a mixed number to an improper fraction?

Compute whole×denominator + numerator over the denominator. Example: 3 2/5 → (3×5+2)/5 = 17/5.

How do I turn a decimal into a fraction?

Write the decimal over a power of 10 and reduce. Example: 0.375 = 375/1000 = 3/8.

What’s the difference between simplest form and lowest terms?

They’re the same idea: a fraction whose numerator and denominator share no common factor > 1.

How do I compare two fractions quickly?

Cross-multiply: compare a×d with c×b for a/b vs c/d. Larger product → larger fraction.

What is an improper fraction and when should I use mixed numbers?

Improper means numerator ≥ denominator. Use mixed numbers for readability; use improper form when calculating.