Fraction Calculator
Add, subtract, multiply, and divide fractions with step-by-step solutions. Shows LCM for common denominators and simplifies using GCD.
Fractions
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Operation
34+13
Visual Representation
Step 1: Find LCM of Denominators
LCM(4, 3) = 12
Step 2: Convert to Common Denominator
34→912(×3)
13→412(×4)
Step 3: Add Numerators
912+412=1312
Result
13/12
Decimal Equivalent
1.0833
The Formula
Fraction arithmetic follows specific rules depending on the operation. For addition and subtraction, the fractions must share a common denominator — the least common multiple (LCM) of the denominators is used. For multiplication, multiply numerators and denominators directly. For division, multiply by the reciprocal (flip the second fraction). Always simplify the final result by dividing by the greatest common divisor (GCD).
Variable Definitions
Fractions
Two fractions with numerators and denominators. a and c are numerators, b and d are denominators (must be positive integers).
LCM & GCD
Least Common Multiple finds a common denominator for addition/subtraction. Greatest Common Divisor simplifies the result to lowest terms.
How to Use This Calculator
- 1
Select the operation: add, subtract, multiply, or divide.
- 2
Enter the numerator (top) and denominator (bottom) for both fractions. Denominators must be positive integers.
- 3
The step-by-step solution shows the LCM calculation for addition/subtraction and the reciprocal flip for division.
- 4
The result is always simplified to its lowest terms using the GCD.
- 5
The decimal equivalent is displayed alongside the fraction result for easy reference.
A fraction shows how many equal parts of a whole you have
Understanding the Concept
Fractions represent parts of a whole. The denominator shows how many equal parts the whole is divided into, and the numerator shows how many of those parts you have. Working with fractions is foundational to algebra, measurement, probability, and many real-world scenarios like cooking (cup measurements), construction (inch fractions), and finance (stock splits). The key insight: you can only directly add or subtract fractions with the same denominator — otherwise you must find a common denominator first. For multiplication, you simply multiply numerators and denominators directly, no common denominator needed. For division, you multiply by the reciprocal of the second fraction (flip it upside down). The step-by-step display helps build understanding of each operation by showing the intermediate steps. Fractions are everywhere: recipes use 1/2 cup and 1/4 teaspoon, carpenters work in 1/16-inch increments, music uses time signatures like 3/4 and 4/4, and odds are expressed as fractions like 5/1.
Frequently Asked Questions
Sources & References
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