How To Do Math With Fractions

Fraction Operations:

\[ \frac{a}{b} \pm \frac{c}{d} = \frac{ad \pm bc}{bd} \] \[ \frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd} \] \[ \frac{a}{b} \div \frac{c}{d} = \frac{ad}{bc} \]

Operation:

First Fraction:

Second Fraction:

Result:

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1. What Are Fraction Operations?

Fraction operations include addition, subtraction, multiplication, and division of fractions. These operations follow specific rules to maintain mathematical accuracy while working with parts of whole numbers.

2. How Fraction Math Works

The fundamental rules for fraction operations are:

\[ \text{Addition: } \frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd} \] \[ \text{Subtraction: } \frac{a}{b} - \frac{c}{d} = \frac{ad - bc}{bd} \] \[ \text{Multiplication: } \frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd} \] \[ \text{Division: } \frac{a}{b} \div \frac{c}{d} = \frac{ad}{bc} \]

Key Concepts:

Common denominator needed for addition/subtraction
Numerators multiply directly in multiplication
Division is multiplication by the reciprocal
Always simplify the final result

3. Step-by-Step Examples

Addition Example: 1/4 + 1/3
1. Find common denominator: 4×3 = 12
2. Convert: (1×3)/12 + (1×4)/12 = 3/12 + 4/12
3. Add numerators: 7/12
4. Simplify: 7/12 (already simplified)

Multiplication Example: 2/5 × 3/7
1. Multiply numerators: 2×3 = 6
2. Multiply denominators: 5×7 = 35
3. Result: 6/35
4. Simplify: 6/35 (already simplified)

4. Using the Calculator

Instructions: Select operation, enter numerators and denominators for both fractions. The calculator will show the complete calculation with simplified result.

5. Frequently Asked Questions (FAQ)

Q1: What if I get a negative denominator?
A: Move the negative sign to the numerator or make both numerator and denominator positive.

Q2: How to handle whole numbers in fractions?
A: Treat whole numbers as fractions with denominator 1 (e.g., 3 = 3/1).

Q3: What about mixed numbers?
A: Convert to improper fractions first (e.g., 1½ = 3/2).

Q4: Why simplify fractions?
A: Simplified form is standard and easier to work with in further calculations.

Q5: What if denominator becomes zero?
A: Division by zero is undefined - calculator will not compute invalid fractions.