NCERT Solutions for Class 8th Maths Chapter 1 Fractions in Disguise
Updated on 2026-09-19
About this chapter
x% means x out of every 100 , so x% = x/100. A fraction becomes a percentage by multiplying it by 100; a percentage becomes a fraction by writing it over 100. y% of a quantity z is (y/100) × z. Because 100 fits our base-ten system, every percentage also has a neat decimal form — 43% = 43/100 = 0.43 — so the same job can be done by fraction, decimal or proportion. A percentage always answers “a part of which whole?” 35% of 95 g is smaller than 25% of 120 g, so two percentages can only be compared directly when their bases are the same. Percentage increase or decrease is measured against the original amount: (change ÷ original) × 100. An increase of r turns a quantity into (1 + r) times itself, and a decrease turns it into (1 – r) times itself. Profit and loss are percentages of the cost pri
- Fractions as Percentages
- Percentage of Some Quantity
- The FDP Trio: Fractions, Decimals, and Percentages
- Percentages Greater than 100
- Using Percentages
- Profit and Loss
- Profit, Loss and Discount
- Taxes
- Profit, Loss, Discount and Percentage Change
- Growth and Compounding
Quick revision
| Idea | What it means | Rule | Worked example |
|---|---|---|---|
| Per cent | A fraction whose denominator is 100 | x% = x/100 | 25% = 25/100 = 1/4 |
| Fraction → per cent | A fraction is of one unit; a percentage is per 100 | (a/b) × 100 % | 3/4 → 75% |
| Per cent of a quantity | Take that many hundredths of it | y% of z = (y/100) × z | 35% of 95 g = 33.25 g |
| Ratio → per cent | Make it a fraction of the whole first | (part/whole) × 100 | millet : water = 2 : 7 → 2/9 → 22.22% |
| Percentage increase | Change measured against the original | (increase/original) × 100 | ₹30 → ₹42 is a 40% rise |
| Percentage decrease | Same rule, with the fall | (decrease/original) × 100 | 160 → 100 is a 37.5% fall |
| Profit % / Loss % | Measured on the cost price | (profit/CP) × 100 | CP ₹300, SP ₹430 → 43.33% profit |
| Discount | Measured on the marked price | SP = MP × (1 – d) | 35% off ₹1800 → ₹1170 |
| Percentage above 100 | More than the whole | 120% of z = 1.2z | ₹6000 sales on a ₹5000 target = 120% |
| Growth, no compounding | The principal never changes | p(1 + rt) | ₹6000 at 10% for 3 yr → ₹7800 |
| Growth with compounding | Interest joins the principal each term | p(1 + r)t | ₹6000 at 10% for 3 yr → ₹7986 |
| Successive percentages | They multiply, they never add | (1 + a)(1 + b) | 30% off then 20% off = 44% off, not 50% |
Exercises
- In-text Questions — Fractions as Percentages Page 2
- In-text Questions — Fractions as Percentages Page 3
- Figure it Out — Fractions as Percentages Page 3–4
- In-text Questions — Fractions as Percentages Page 4
- In-text Questions — Percentage of Some Quantity Page 7
- In-text Questions — The FDP Trio: Fractions, Decimals, and Percentages Page 8
- In-text Questions — Percentages Greater than 100 Page 11
- In-text Questions — Percentages Greater than 100 Page 12
- Figure it Out — Percentage of Some Quantity Page 12–14
- In-text Questions — Using Percentages Page 15
- In-text Questions — Profit and Loss Page 17
- In-text Questions — Profit, Loss and Discount Page 18
- In-text Questions — Taxes Page 19
- Figure it Out — Profit, Loss, Discount and Percentage Change Page 19–20
- Figure it Out — Growth and Compounding Page 22–24
- In-text Questions — Growth and Compounding Page 24
- In-text Questions — Tricky Percentages: Would You Rather? Page 25
- In-text Questions — Tricky Percentages Page 26
- In-text Questions — A Mishap Page 27
- Figure it Out — Using Percentages Page 28–30