Math & Education
Fraction Calculator
Add, subtract, multiply, and divide fractions. Get step-by-step solutions with simplified results.
Inputs
Fraction 1
Fraction 2
Results
Result Fraction
3/4
Improper Fraction
3/4
Decimal Value
0.75
Step-by-Step Solution
Calculating steps...
How It Works
The fraction calculator performs standard numerical rational arithmetic. First, it parses inputs (including mixed whole coefficients) into improper ratios ($a/b$ and $c/d$).\n\nFor addition and subtraction, it computes the Least Common Multiple (LCM) of the denominators to create an identical scale basis. Multiplications and divisions operate directly on cross-factors. It simplifies the results using Euclid's GCD reduction algorithm.
Formula Used
Simplified Fraction = (Numerator / GCD) / (Denominator / GCD)
To simplify a fraction, we calculate the Greatest Common Divisor (GCD) of the numerator and denominator using Euclid's algorithm. Dividing both terms by their GCD reduces the fraction to its lowest possible integer terms.
Worked Example
Here is a step-by-step example of how these values are calculated:
Fraction 1
1/2
Operator
+
Fraction 2
1/4
Result: Common denominator: 4. Equation: 2/4 + 1/4 = 3/4. Decimal: 0.75.
Frequently Asked Questions
What is an improper fraction?
An improper fraction is a rational fraction where the absolute value of the numerator is greater than or equal to the absolute value of the denominator (e.g., 7/4).
How does division of fractions work?
Dividing fractions is accomplished by multiplying the first fraction by the reciprocal (flipped version) of the second fraction: $(a/b) \div (c/d) = (a/b) \times (d/c) = (ad)/(bc)$.