Chapter 8 — Fractions in Disguise

Chapter 8 of Class 8 maths, "Fractions in Disguise", introduces percentages as fractions with denominator 100, and teaches how to convert between fractions, decimals, and percentages, then apply percentages to real-world scenarios like profit-loss, discounts, and compound interest.

This chapter explores percentages—a way of expressing fractions out of 100. It covers converting fractions to percentages and vice versa, calculating percentages of quantities, comparing proportions using percentages, finding percentage increases and decreases, profit and loss in commerce, discount and tax calculations, and exponential growth through compound interest. Students learn mental computation strategies and multiple solution methods, with practical examples from shopping, finance, and population changes.

1. 01Percentages are fractions with denominator 100: x% means x out of every 100
2. 02Conversions: express any fraction as a percentage by multiplying by 100, or convert a percentage to a fraction by writing it over 100
3. 03Finding a percentage of a quantity: y% of n = (y/100) × n, also equals the fraction multiplied by the number
4. 04Percentage change: (change/original) × 100 for increases or decreases; compounding means interest is added back to principal each period
5. 05Profit and loss: profit % = (profit/cost price) × 100; loss % = (loss/cost price) × 100; discount reduces marked price
6. 06Simple interest formula: amount = p(1 + rt) without compounding; amount = p(1 + r)^t with compounding
7. 07Comparison using percentages: convert different quantities to percentages to compare fairly (e.g., test scores out of different totals)