Overview
This lecture introduces the concept of ratio, explains how to represent and interpret ratios, discusses their importance in daily life, and introduces special types of ratios used in mathematics and other contexts.
What is a Ratio?
- A ratio is a comparison between two quantities, expressed as the quotient of one divided by the other.
- Ratios are written as a/b, a:b, or as a decimal (a ÷ b).
- The order in a ratio matters: the first term is the antecedent and the second is the consequent.
- The consequent (b) must not be zero.
Representing and Interpreting Ratios
- A ratio shows how many times one quantity contains another (e.g., 3 green dots to 4 orange dots means a ratio of 3:4).
- The same ratio can be represented in different equivalent forms (e.g., 3:4 is equivalent to 6:8).
- Ratios can be simplified by dividing both terms by their greatest common factor.
Real-life Examples of Ratios
- Recipes: For every 1 liter of juice concentrate, use 2 liters of water (ratio 1:2).
- Classroom example: 15 girls and 25 boys have a ratio of girls to boys as 15:25, which simplifies to 3:5.
- Chocolate milk: 200 ml milk to 2 spoons of powder is a 200:2 or 100:1 ratio.
- Exam scores: If the ratio of correct answers to total questions is 2:5, then for 20 questions, the student got 8 right.
Special Types of Ratios
- Average speed: Ratio of distance traveled to time taken (e.g., 80 km in 1 hour = 80 km/h).
- Demographic density: Ratio of number of inhabitants to area (inhabitants per square kilometer).
- Scale: Ratio of drawing/model length to real object length (e.g., 5 cm model = 200 cm real means ratio 5:200).
Key Terms & Definitions
- Ratio — comparison of two quantities, usually as a fraction or with a colon.
- Antecedent — the first term in a ratio (the quantity being compared).
- Consequent — the second term in a ratio (the quantity compared against).
- Equivalent ratios — different ratios that express the same relationship.
- Average speed — distance divided by time taken (ratio).
- Demographic density — inhabitants divided by area.
- Scale — model or drawing length divided by actual length.
Action Items / Next Steps
- Research the population and area of your city to calculate its demographic density.
- Watch the next class to learn about proportion.
- Review division and percentage if unclear on these concepts.