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Math Calculators / Fraction Calculator

Fraction Calculator

Add, subtract, multiply, and divide proper, improper, and mixed fractions with step-by-step reduction.

Rational Arithmetic Solver
+
=
1 5/12
Exact Result
1 5/12
Simplified Fraction17/12
Decimal Equivalent1.416667
Percentage Value141.67%
Step-by-Step Reduction:
Fraction 1: 3/4, Fraction 2: 2/3
Common denominator (LCM) = 12
Convert fractions: (9/12) + (8/12)
Sum numerators: 9 + 8 = 17/12

About the Fraction Calculator

The CalcNest Fraction Calculator provides clear rational arithmetic for addition, subtraction, multiplication, and division of fractions. With instant step-by-step reductions, mixed number formatting, and decimal equivalents, solving homework and measurement math is effortless.

Mathematical Formula

Addition: a/b + c/d = (ad + bc) / bd Subtraction: a/b - c/d = (ad - bc) / bd Multiplication: a/b × c/d = ac / bd Division: a/b ÷ c/d = ad / bc

Exact rational fraction arithmetic with Greatest Common Divisor (GCD) simplification, mixed fraction conversion, and decimal translation.

Variables & Components

a/b First Fraction: Numerator (a) divided by non-zero Denominator (b).
c/d Second Fraction: Numerator (c) divided by non-zero Denominator (d).
GCD Greatest Common Divisor: Largest positive integer dividing both numerator and denominator to simplify to lowest terms.
LCM Least Common Multiple: Smallest common denominator used when adding or subtracting fractions.

Worked Example: Adding 3/4 + 2/3 Step-by-Step

Suppose you want to add two fractions with different denominators: 3/4 and 2/3.

Step-by-Step Calculation

  1. Find the Least Common Multiple (LCM) of denominators 4 and 3: LCM(4, 3) = 12
  2. Convert fractions to common denominator: 3/4 = 9/12 and 2/3 = 8/12
  3. Add the numerators: 9/12 + 8/12 = (9 + 8)/12 = 17/12
  4. Convert improper fraction 17/12 into mixed number: 17 ÷ 12 = 1 with remainder 5 → 1 5/12
  5. Decimal value: 17 ÷ 12 = 1.416667 (141.67%)
Final Result: Sum: 17/12 | Mixed Number: 1 5/12 | Decimal: 1.4167

How to Use This Calculator

1

Select your desired arithmetic operation (+, −, ×, ÷).

2

Enter the Numerators and Denominators for both fractions.

3

Instantly view the simplified fraction, mixed number, decimal value, and step-by-step reduction steps.

Frequently Asked Questions

A proper fraction has a numerator smaller than its denominator (e.g. 3/4, value < 1). An improper fraction has a numerator greater than or equal to its denominator (e.g. 7/4, value ≥ 1), which can be expressed as a mixed number (1 3/4).

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