Chapter 8: Fractions in Disguise

1. Percentage as a Fraction

Percent means “per hundred”. Therefore 35%=35/100=7/20. A percentage, fraction and decimal can describe the same quantity.

2. Percentage of a Quantity

To find 15% of 240, calculate 15/100×240=36. The percentage is a multiplicative fraction of the original quantity.

3. Percentage Increase and Decrease

Percentage change uses the original value as the reference: percentage increase=(increase/original)×100. The same principle applies to decrease.

4. Profit, Loss and Discount

Profit compares selling price with cost price; loss occurs when selling price is lower. Discount is the reduction from marked price. The reference quantity must be identified before calculating a percentage.

5. Simple Interest

Simple interest is calculated on the original principal: SI=P×R×T/100. If P=₹5000, R=8% per year and T=2 years, SI=₹800.

6. Compound Interest

Compound interest adds interest to the amount, so the next period’s interest is calculated on the increased amount. For ₹1000 at 10% annually, the first year gives ₹1100; the second year gives ₹1210.

7. Financial Reasoning

Percentages can hide important differences in reference amounts. A 20% discount and a 20% increase are not automatically inverse operations. Always calculate from the stated base value.

🧠 MCQs

1. 25% equals: A) 1/2 B) 1/4 C) 1/5 D) 1/8
2. 10% of ₹450 is: A) ₹4.5 B) ₹45 C) ₹90 D) ₹400
3. Profit percentage is normally calculated on: A) cost price B) selling price C) discount D) marked price only
4. Simple interest is calculated on: A) original principal B) changing amount every year C) profit only D) discount

Answers: 1-B, 2-B, 3-A, 4-A.

📌 Case Study

A bag marked ₹2000 is sold at 15% discount. Calculate the discount and selling price. Then explain why the 15% is taken from ₹2000.

🔥 HOTS

1. Explain why a 10% increase followed by a 10% decrease does not return exactly to the original amount.
2. Compare simple and compound interest for the same principal, rate and two-year period.
3. Create a shopping problem involving two successive percentage changes.

✍️ Practice

1. Convert 0.375 to a percentage.
2. Find 18% of ₹750.
3. A price rises from ₹800 to ₹920. Find the percentage increase.
4. Calculate simple interest on ₹6000 at 5% for 3 years.

🏆 Mastery Checklist

• ☐ I can move between fractions, decimals and percentages.
• ☐ I can calculate percentage changes.
• ☐ I can solve profit, loss and discount problems.
• ☐ I can distinguish simple and compound interest.

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