Rasio (Perbandingan) [Part 3] - Laju Perubahan Satuan

Introduction

This tutorial will guide you through the concept of rate of change in units, differentiating it from basic ratios. Understanding these concepts is essential for solving everyday problems involving comparisons and measurements.

Step 1: Understanding Ratios

• Definition of Ratio: A ratio is a way to compare two quantities, indicating how many times one value contains or is contained within the other.
• Example: If there are 2 apples and 3 oranges, the ratio of apples to oranges is 2:3.
• Key Takeaway: Ratios provide a simple comparison but do not imply any change over time or units.

Step 2: Exploring Rate of Change

• Definition of Rate of Change: This refers to how much one quantity changes in relation to another quantity over a specific period or unit.
• Difference from Basic Ratio: While a ratio is static, the rate of change focuses on the dynamic relationship between quantities, such as speed or growth rate.
• Practical Example: If a car travels 100 kilometers in 2 hours, the rate of change (speed) is 50 kilometers per hour.

Step 3: Applying Ratios and Rates of Change in Real Life

• Identifying Situations: Look for scenarios where you can compare quantities or track changes over time.

Examples in Daily Life

• Cooking: Adjusting a recipe based on the ratio of ingredients.
• Finance: Tracking the rate of interest on savings.
• Health: Monitoring weight loss over weeks as a rate of change.

Step 4: Practice Problems

1. Example Problem 1: If a plant grows 10 cm in 5 days, what is the rate of growth per day?

   • Calculation: 10 cm / 5 days = 2 cm/day.

2. Example Problem 2: A car uses 8 liters of fuel to travel 100 kilometers. What is the fuel consumption per kilometer?

   • Calculation: 8 liters / 100 km = 0.08 liters/km.

3. Your Turn: Create your problems using the concepts of ratio and rate of change. Try to relate them to your daily activities.

Conclusion

Understanding ratios and rates of change helps in making informed comparisons and decisions in various aspects of life. Practice the concepts with real-world examples to enhance your comprehension. As you become more comfortable, try tackling more complex scenarios to solidify your understanding. Keep studying and applying these concepts, and you'll develop a strong foundation for mathematical reasoning.