Math Tool✨ New Release
Fraction Calculator
Add, subtract, multiply, and divide fractions easily. Supports mixed numbers, improper fractions, proper fractions, and simplifies results to the lowest terms.
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Interactive Fraction Calculator Workspace
First Fraction
Whole
Numerator
Denominator
Operator
Second Fraction
Whole
Numerator
Denominator
Calculated Fraction Solution
Simplified Fraction7/12
Mixed Number7/12
Decimal Equivalent0.583333
Detailed Mathematical Proof
- Convert operands to improper fractions: 1/3 and 1/4.
- Find the Least Common Denominator (LCD) of 3 and 4, which is 12.
- Adjust both fractions: (1 × 4) / 12 = 4/12, and (1 × 3) / 12 = 3/12.
- Add the adjusted numerators over the common denominator: (4 + 3) / 12 = 7/12.
Mathematical Formula & Variables
Equation Model
(a/b) ± (c/d) = (ad ± bc) / bd | (a/b) × (c/d) = ac / bd | (a/b) ÷ (c/d) = ad / bcOperations depend on the operator. For addition/subtraction, a common denominator is required. For multiplication, multiply numerators and denominators. For division, multiply by the reciprocal.
Variable Definitions
| Symbol | Description |
|---|---|
| a, c | Numerators of the first and second fractions |
| b, d | Denominators of the first and second fractions (cannot be zero) |
How to Use the Fraction Calculator
- Select whether you are calculating proper/improper fractions or mixed numbers.
- Enter the numerators and denominators (and whole numbers if using mixed fractions) for both fraction operands.
- Choose the operation you wish to perform: Addition (+), Subtraction (-), Multiplication (×), or Division (÷).
- Review the results, which display the simplified proper/improper fraction, the mixed number equivalent, the step-by-step common denominator working, and the decimal value.
Practical Example Calculation
Scenario Context: Adding the proper fractions 2/3 and 1/4.
Step 1: Find the Least Common Denominator (LCD) of 3 and 4, which is 12.
Step 2: Convert 2/3: Multiply numerator and denominator by 4: (2×4)/(3×4) = 8/12.
Step 3: Convert 1/4: Multiply numerator and denominator by 3: (1×3)/(4×3) = 3/12.
Step 4: Add the new numerators over the common denominator: (8 + 3) / 12 = 11/12.
Step 5: Check if simplification is possible. 11/12 is already in simplest terms.
The sum of 2/3 and 1/4 is 11/12 (or 0.9167 as a decimal).
Frequently Asked Questions
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