Summary
The topic of Ratio and Proportions involves understanding how quantities relate to each other and how they can be simplified or used in practical applications like map scales and direct or inverse relationships.
- Ratio — a comparison of two quantities by division. Example: The ratio of Charlene's and Danielle's money is 2:3.
- Simplest Form of a Ratio — reducing a ratio to its smallest whole number form. Example: The ratio 12:30 simplifies to 2:5.
- Map Scale — a ratio that represents the relationship between a distance on a map and the actual distance. Example: A map scale of 1 cm : 4 km means 1 cm on the map equals 4 km in reality.
- Direct Proportion — a relationship where one quantity increases as another increases. Example: If y is directly proportional to x, then y = kx.
- Inverse Proportion — a relationship where one quantity increases as another decreases. Example: If r is inversely proportional to s, then r = k/s.
Exam Tips
Key Definitions to Remember
- Ratio: A comparison of two quantities by division.
- Simplest Form: The smallest whole number ratio equivalent to the original ratio.
- Map Scale: A ratio representing the relationship between a map distance and actual distance.
- Direct Proportion: When one quantity increases, another increases at a constant rate.
- Inverse Proportion: When one quantity increases, another decreases at a constant rate.
Common Confusions
- Confusing direct proportion with inverse proportion.
- Forgetting to convert units when using map scales.
Typical Exam Questions
- What is the simplest form of the ratio 18:45? Answer: 2:5
- If a map scale is 1 cm : 5 km, what is the actual distance if the map distance is 3 cm? Answer: 15 km
- If y is directly proportional to x and y = 10 when x = 2, what is y when x = 5? Answer: 25
What Examiners Usually Test
- Ability to simplify ratios to their simplest form.
- Understanding and application of map scales.
- Solving problems involving direct and inverse proportions.