Math & ArithmeticVerified: 2026-10-05
Fraction Calculator
Add, subtract, multiply, and divide fractions with step-by-step solutions, simplification to lowest terms, mixed number conversions, and decimal values.
Direct Answer:To add or subtract fractions, find a common denominator, adjust the numerators, and reduce using the greatest common divisor (e.g., 1/2 + 1/3 = 5/6). To multiply, multiply numerators and denominators directly (e.g., 1/2 × 1/3 = 1/6). To divide, multiply by the reciprocal (e.g., 1/2 ÷ 1/3 = 3/2 = 1 1/2).
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Adjust Parameters
First Fraction
Must not be 0
Second Fraction
Must not be 0
Reduced Result Fraction
5/6
Decimal Equivalent: 0.833333
Decimal Value
0.833333
Original Operation
1/2 + 1/3
Step-by-Step Solution
- Step 1: Find Least Common Multiple (LCM) of denominators 2 and 3 = 6.
- Step 2: Adjust numerators: (1 × 3) + (1 × 2) = 3 + 2 = 5.
- Step 3: Combine over common denominator: 5 / 6.
- Step 4: Fraction is already in its simplest irreducible form: 5 / 6.
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How Fraction Calculator is Calculated
Transparent mathematical formulas and assumptions used across our financial engines.
Mathematical Formula
\frac{n_1}{d_1} \pm \frac{n_2}{d_2} = \frac{n_1 d_2 \pm n_2 d_1}{d_1 d_2} \quad | \quad \frac{n_1}{d_1} \times \frac{n_2}{d_2} = \frac{n_1 n_2}{d_1 d_2} \quad | \quad \frac{n_1}{d_1} \div \frac{n_2}{d_2} = \frac{n_1 d_2}{d_1 n_2}
Variables & Legend
n₁, n₂
Numerators
d₁, d₂
Denominators
Step-by-Step Calculation
- Addition/Subtraction:
(n1*d2 ± n2*d1) / (d1*d2)Finds common denominator and adds/subtracts adjusted numerators.
- Multiplication:
(n1*n2) / (d1*d2)Multiplies numerators together and denominators together.
- Division:
(n1*d2) / (d1*n2)Multiplies the first fraction by the reciprocal of the second.
- Simplification:
n / gcd(n, d) and d / gcd(n, d)Reduces to lowest terms using the Greatest Common Divisor.
Conventions & Assumptions
- Denominators can never be zero.
- Improper fractions (numerator > denominator) are converted to mixed numbers.
Frequently Asked Questions
Find the Least Common Denominator (LCD) of the two fractions. Multiply the numerator and denominator of each fraction so both have the LCD as their bottom number. Add the new numerators together while keeping the denominator unchanged, then simplify by dividing by the GCD.