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Proportional Reasoning-2

Learning Objectives

Understand and apply the concept of proportional reasoning.
Identify and differentiate between direct and inverse proportions.
Construct and interpret pie charts based on given data.
Solve problems involving ratios with more than two terms.
Calculate time and speed relationships using proportional reasoning.
Analyze data presented in tables and convert them into visual representations.

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Revision Notes & Summary

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Chapter Notes

Proportional Reasoning

Direct Proportion

If two quantities are in direct proportion, they can be represented as:
- Formula: $a : b = c : d$ implies $d = \frac{bc}{a}$
Example: If 5 workers can move 4500 bricks in a day, how many workers are needed to move 18000 bricks?
- Solution: $4500 : 18000 = 5 : X$ leads to $X = 20$

Inverse Proportion

Inverse proportions occur when one quantity increases as the other decreases.
Example: The number of taps filling a water tank and the time taken to fill it.

Ratios

Ratios with More than 2 Terms

Example: Viswanath's spice mix ratio is 8:4:2:1 for coriander seeds, red chillies, toor dal, and fenugreek seeds.
If Puneet has only 2 red chillies, he should use 4 spoons of coriander seeds, 2 red chillies, 1 spoon of toor dal, and 0.5 spoon of fenugreek seeds to maintain the ratio.

Pie Charts

Construction of Pie Charts

Step 1: Draw a circle and mark the radius.
Step 2: Measure angles proportional to the data.
- Example: For grades A (12), B (10), C (8), D (6), E (4), the angles are:
  - Grade A: 108°
  - Grade B: 90°
  - Grade C: 72°
  - Grade D: 54°
  - Grade E: 36°
Step 3: Label each segment accordingly.

Grade Distribution

Table of Grades:
Grade Students
A 12
B 10
C 8
D 6
E 4

Grade	Students
A	12
B	10
C	8
D	6
E	4

Important Diagrams

Triangle Angles: Sum of angles in a triangle is always 180°.
- Example: Angles A (20°), B (60°), C (100°).
Pie Chart Example: Divided into segments for grades A, B, C, D, E with respective angles.

Common Mistakes

Misunderstanding the difference between direct and inverse proportions.
Incorrectly calculating angles for pie charts based on ratios.

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Practice Test – MCQs, True/False

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