Fraction Calculator
Formula and Calculation Method
Fraction Arithmetic Rules:
Addition: (a/b) + (c/d) = (ad + bc) ÷ bdSubtraction: (a/b) - (c/d) = (ad - bc) ÷ bdMultiplication: (a/b) × (c/d) = (a × c) ÷ (b × d)Division: (a/b) ÷ (c/d) = (a/b) × (d/c) = (a × d) ÷ (b × c)
Worked Example and Step-by-Step Calculation
- Fraction 1: 2/3
- Operation: Addition (+)
- Fraction 2: 3/4
1. Find Least Common Denominator (LCD) of 3 and 4 = 12
2. Convert Fraction 1: (2 × 4) ÷ (3 × 4) = 8/12
3. Convert Fraction 2: (3 × 3) ÷ (4 × 3) = 9/12
4. Add numerators: (8 + 9) ÷ 12 = 17/12
5. Convert to Mixed Number: 17 ÷ 12 = 1 with remainder 5 = 1 5/12
6. Decimal Equivalent = 1.4167
How to Use the Fraction Calculator
- Enter the numerator and denominator for the first fraction (or use mixed number inputs).
- Select the arithmetic operation: + (Add), − (Subtract), × (Multiply), or ÷ (Divide).
- Enter the second fraction.
- Review the step-by-step reduction, improper fraction, simplified mixed number, and decimal equivalent.
Common Mistakes, Limitations & Practical Guidance
- A fraction denominator cannot be zero (division by zero is mathematically undefined).
- Extremely large denominators with large prime factors are reduced using Euclidean Greatest Common Divisor (GCD) algorithms.
Frequently Asked Questions About Fraction Calculator
How do you add fractions with unlike denominators?
Find the Least Common Denominator (LCD), convert each fraction into an equivalent fraction with that common denominator, add the numerators, and simplify to lowest terms.
How do you find the Least Common Denominator (LCD)?
The Least Common Denominator is the smallest positive number that is a common multiple of the denominators. For example, for denominators 4 and 6, the multiples of 4 are (4, 8, 12, 16...) and 6 are (6, 12, 18...), making 12 the LCD.
How do you divide two fractions?
To divide fractions, multiply the first fraction by the reciprocal (the inverted fraction) of the second: (a/b) ÷ (c/d) = (a/b) × (d/c) = (ad) / (bc).
What is the difference between a proper fraction and an improper fraction?
A proper fraction has a numerator smaller than its denominator (e.g. 3/4), representing a value less than 1. An improper fraction has a numerator greater than or equal to its denominator (e.g. 7/4), representing a value greater than or equal to 1.
How do you simplify a fraction to lowest terms?
Divide both the numerator and the denominator by their Greatest Common Divisor (GCD). For example, for 8/12, the GCD is 4. Dividing both by 4 yields 2/3.
How does this tool connect to the Percentage Calculator?
Every fraction represents a division that converts into a decimal and percentage. To convert fractions into percentage increase/decrease or parts of a whole, visit our Percentage Calculator.