Fraction Calculator
A comprehensive tool to add, subtract, multiply, and divide fractions. Supports proper, improper, and mixed fractions, and shows detailed steps.
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Working with Fractions: A Comprehensive Guide
Fractions are a fundamental concept in mathematics, representing parts of a whole. While the rules for fraction arithmetic are straightforward, they can be tedious to perform by hand. This Fraction Calculator simplifies the process, allowing you to add, subtract, multiply, and divide fractions with ease.
How to Perform Fraction Operations
This calculator handles proper fractions, improper fractions, and mixed numbers. Here's a brief overview of the mathematical rules it applies:
1. Addition and Subtraction ( + , - )
To add or subtract fractions, they must have a common denominator.
- Find the Least Common Multiple (LCM) of the denominators. This becomes the new common denominator.
- Convert each fraction into an equivalent fraction with the new denominator.
- Add or subtract the numerators, keeping the denominator the same.
- Simplify the resulting fraction if possible.
Example: 1/3 + 1/2
- LCM of 3 and 2 is 6.
- 1/3 becomes 2/6. 1/2 becomes 3/6.
- 2/6 + 3/6 = 5/6.
2. Multiplication ( × )
Multiplying fractions is more direct:
- Multiply the numerators together.
- Multiply the denominators together.
- Simplify the result.
Example: 2/3 × 3/4 = (2×3)/(3×4) = 6/12, which simplifies to 1/2.
3. Division ( ÷ )
To divide by a fraction, you multiply by its reciprocal (the fraction flipped upside down).
- Invert the second fraction (the divisor) to get its reciprocal.
- Change the division sign to a multiplication sign.
- Multiply the first fraction by the reciprocal of the second.
- Simplify the result.
Example: 1/2 ÷ 1/4 = 1/2 × 4/1 = 4/2, which simplifies to 2.
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