Mastering Ratios, Proportions, and Percent Applications

📋 Course Outline

1. Ratios and Proportions
2. Decimal and Percent Conversion
3. Percent Equations
4. Percent Proportions
5. Application of Percent
6. Sales Tax Calculations
7. Simple Interest Formula
8. Square Root and Pythagoras
9. Polygon Perimeter and Circumference
10. Polygon and Circle Area

📖 1. Ratios and Proportions

🔑 Key Concepts & Definitions

• Ratio: A comparison of two quantities expressed as a quotient, typically written as a : b or a/b. It indicates how many times one value contains or is contained within the other.

• Ratio notation: The way ratios are written, often using a colon (a : b) or fraction (a/b), to compare quantities directly.

• Proportion: An equation stating that two ratios are equivalent, written as a : b = c : d or a/b = c/d. It signifies that the relationship between the first pair is the same as the second pair.

• Equivalent ratios: Ratios that express the same relationship, meaning a : b = c : d if and only if a × d = b × c (cross-multiplication).

• Cross-multiplication method: A technique to solve proportions by multiplying across the equal sign, transforming the proportion a/b = c/d into a × d = b × c.

• Unit rate: The ratio of two quantities where the second quantity is 1, often used to compare per-unit quantities, e.g., miles per hour or price per item.

📝 Essential Points