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Class 8

Mathematics

Fractions in Disguise

Learning Objectives

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Learning Objectives

Understand how to calculate percentages of given values.
Apply mental math strategies to estimate percentages.
Recognize the relationship between fractions, decimals, and percentages.
Calculate total amounts and interest using appropriate formulas.
Compare different percentages to determine better options in practical scenarios.
Analyze and interpret data presented in percentage form.

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Revision Notes & Summary

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Notes on Percentages and Interest

Understanding Percentages

Percentages are a way to express a number as a fraction of 100.
Example: To find 50% of a value, multiply by 0.5.
- Calculation: 50% of 24 = 0.5 × 24 = 12

Calculating Percentages

To find various percentages, use the following conversions:
- 10% = 0.1
- 25% = 0.25
- 50% = 0.5
- 75% = 0.75
- 100% = 1.0

Example Calculations

Finding Percentages:
- 10% of 200 = 20
- 25% of 400 = 100
- 75% of 80 = 60

Interest Calculations

Simple Interest

Formula: Total Interest = Principal × Rate × Time
- Example: For a principal of ₹6000 at 10% for 3 years:
  - Total Interest = 6000 × 0.1 × 3 = ₹1800

Compound Interest

Formula: Total Amount = Principal × (1 + Rate)^Time
- Example: For a principal of ₹6000 at 10% compounded annually for 3 years:
  - Total Amount = 6000 × (1 + 0.1)^3 = ₹6000 × 1.331 = ₹7986

Visualizing Percentages

Diagrams can help visualize the relationship between percentages and values.
Example: A number line showing percentages from 0% to 100% with corresponding fractions.

Common Applications of Percentages

Grades: Converting scores to percentages for comparison.
- Example: Eesha scored 42 out of 50 in English, which is 84%. In Science, she scored 70 out of 80, which is 87.5%.
Population Estimates: Calculating populations based on percentages.
- Example: If 90% of the world's population lives in the Northern Hemisphere, estimate based on current population figures.

Activities for Practice

Estimation Games: Estimate percentages of chosen numbers in pairs.
Real-life Applications: Calculate discounts, interest on savings, and other financial scenarios.

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Practice Test – MCQs, True/False

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Fractions in Disguise

Learning Objectives

Learning Objectives

Practice, Analyze & Improve 🚀

Revision Notes & Summary

Notes on Percentages and Interest

Understanding Percentages

Calculating Percentages

Example Calculations

Interest Calculations

Simple Interest

Compound Interest

Visualizing Percentages

Common Applications of Percentages

Activities for Practice

Do you belong in the Top 10%?

Practice Test – MCQs, True/False