Fractions For Dummies Cheat Sheet

Basic Fraction Operations:

\[ \frac{a}{b} \text{ op } \frac{c}{d} \]

Numerator 1 (a):

Denominator 1 (b):

Operation:

Numerator 2 (c):

Denominator 2 (d):

Result:

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1. Understanding Fractions

A fraction represents a part of a whole. The top number (numerator) represents how many parts you have, while the bottom number (denominator) represents how many equal parts the whole is divided into.

2. Basic Fraction Operations

The four basic operations with fractions:

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

3. How the Calculator Works

The calculator performs the selected operation (addition, subtraction, multiplication, or division) on the two input fractions using the standard mathematical formulas shown above.

4. Practical Examples

Example 1: $\frac{1}{2} + \frac{1}{4} = \frac{3}{4}$
Example 2: $\frac{3}{4} \times \frac{2}{5} = \frac{6}{20} = \frac{3}{10}$
Example 3: $\frac{2}{3} \div \frac{4}{5} = \frac{10}{12} = \frac{5}{6}$

5. Frequently Asked Questions (FAQ)

Q1: What if my denominator is zero?
A: The denominator can never be zero in a fraction as division by zero is undefined.

Q2: Should I simplify my results?
A: Yes, always simplify fractions to their lowest terms for the most accurate representation.

Q3: How do I add fractions with different denominators?
A: Find a common denominator (usually the product of the denominators) before adding.

Q4: Why do we invert and multiply when dividing fractions?
A: This is equivalent to multiplying by the reciprocal, which is the mathematical definition of division by a fraction.

Q5: Can I use this for mixed numbers?
A: First convert mixed numbers to improper fractions before using this calculator.