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Fraction Calculator

This tool shows clean, exact results when you combine or compare fractional values, even with different denominators. It’s useful for homework checks, scaling recipes or plans, splitting costs, and any situation where decimals hide the true ratio.

The Fraction Calculator streamlines the hard parts-finding a common denominator, reducing to simplest form, and showing equivalent mixed numbers, decimals, and percentages. The goal is error-free math you can explain and reuse, so decisions and assignments are faster and clearer. Enter your values to get started.

Add, subtract, multiply, divide, simplify, and convert fractions-including mixed numbers and very large integers.

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Fraction Calculator

Steps to calculate Fractions

27 + 38
Start with the two fractions and the chosen operation.
2 × 87 × 8 + 3 × 78 × 7
Find a common denominator (LCM = 56) and scale each numerator/denominator.
3756
Combine numerators over the common denominator.
3756
Reduce to simplest terms by dividing both parts by the GCD.

Fractions - Final result

3756
Result in decimals: 0.660714285714

Mixed Numbers Calculator

Steps to calculate Mixed Numbers

-234 + 357
Start with the two mixed numbers.
-114 + 267
Convert mixed numbers to improper fractions.
2728
Use a common denominator, then combine numerators.

Mixed Numbers - Final result

2728
Result in decimals: 0.964285714286

Simplify Fractions Calculator

Steps to simplify a Mixed Fraction

22198
Start with a whole number plus a fractional part.
3114
Convert the mixed number to an improper fraction.
3114
Reduce by dividing numerator and denominator by their GCD.
2314
Optionally show the simplified fraction as a mixed number.

Simplify - Final result

3114
= 2314
Result in decimals: 2.214285714286

Decimal to Fraction Calculator

Steps to convert Decimal to Fraction

1.375
Start with the decimal value.
13751000
Move the decimal 3 place(s): write as 1375/1000.
118
Reduce to simplest terms by dividing by the GCD.
138
Optionally show the mixed-number form.

Decimal → Fraction - Final result

118
= 138

Fraction to Decimal Calculator

Steps to convert Fraction to Decimal

27
Start with the fraction in simplest form.
2 ÷ 7
Divide numerator by denominator to convert to decimal.

Fraction → Decimal - Final result

0.285714285714

Big Number Fraction Calculator

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

Steps to calculate Big-Number Fractions

1234748892928829 + 3343442113223232343338877277388288288288
Start with normalized big-integer fractions (denominators positive).
1234 × 8877277388288288288748892928829 × 8877277388288288288 + 334344211322323234333 × 7488929288298877277388288288288 × 748892928829
Cross-multiply to a common denominator, then add numerators.
2503880156651513102054242060334496648130263342672078999418254752
Reduce using BigInt GCD for an exact simplified fraction.

Big-Number Fractions - Final result

2503880156651513102054242060334496648130263342672078999418254752

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 our Fraction Calculator does

Fractions are the language of exact quantities. Our 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, our calculator 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.