Chapter 8 — Fractions in Disguise

Chapter 8 of the Class 8 Maths NCERT textbook (Ganita Prakash), "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.

• Percentage as a shared scale — By treating a percentage as a fraction out of 100, the chapter gives a common scale for comparing proportions fairly — such as test scores out of different totals — and moves fluidly between fractions, decimals and percentages.
• Percentage change and commerce — Learners compute increases and decreases and apply them to profit, loss, discount and tax, seeing how everyday shopping and finance problems reduce to percentage-of-a-quantity calculations.
• Growth through compounding — The chapter reaches compound interest, where interest is added back to the principal each period, illustrating exponential growth and connecting percentages to population change and long-term finance.

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)