Class 8 Mathematics – Direct and Inverse Proportions

1. Introduction

• Proportion shows how two quantities are related to each other.

• Helps in solving real-life problems in speed, distance, work, cost, and time.

Key Concept:

• Direct and inverse proportions describe how one quantity changes when another changes.

2. Direct Proportion

• Two quantities are in direct proportion if one increases, the other increases, and one decreases, the other decreases.

• Key Idea: Both quantities change in the same way.

Examples in Daily Life:

• More workers → More work done in same time.

• More money invested → More profit earned.

• More fuel in a car → Longer distance traveled.

Conceptual Tip:

• If you double one quantity, the other also doubles in direct proportion.

3. Inverse Proportion

• Two quantities are in inverse proportion if one increases, the other decreases, and one decreases, the other increases.

• Key Idea: Quantities change in opposite ways.

Examples in Daily Life:

• More workers → Less time required to complete a job.

• More pipes filling a tank → Less time to fill the tank.

• Faster speed of a vehicle → Less time to cover a distance.

Conceptual Tip:

• If you double one quantity, the other reduces by half in inverse proportion.

4. Key Differences

5. Applications

• Daily Life: Cooking recipes, distributing work, planning travel.

• Business: Cost and quantity, profit and investment.

• Science: Speed, time, force, density, and other physical quantities.

• Engineering: Designing systems where resources and outputs are linked.

6. Key Points to Remember

• Direct proportion → same direction change

• Inverse proportion → opposite direction change

• Can be applied in real-life problems involving work, speed, time, cost, and quantity.

• Understanding proportion helps in simplifying problems without complex calculations.