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Mathematics Class 8 - Comparing Quantities Notes

Comprehensive study notes for Class 8 - Comparing Quantities olympiad preparation

Comparing Quantities

Welcome to the chapter on Comparing Quantities for Class 8. In this chapter, you will learn how to compare different quantities using ratios, percentages, profit and loss, discount, and simple interest. By the end of this chapter, you will be able to solve real-life problems involving comparison of quantities!

Introduction

Comparing quantities helps us understand how much one value is in relation to another. We use ratios, percentages, profit and loss, discount, and interest to compare quantities in daily life.

Ratios

A ratio compares two quantities of the same kind by division.

  • Example: The ratio of 2 to 5 is written as 2:5.
  • Ratios can be simplified like fractions.

Percentages

Percentage means "out of 100". It is used to express a number as a part of 100.

  • Example: 25% means 25 out of 100.
  • To find a percentage, divide the part by the whole and multiply by 100.

Profit and Loss

Profit is the gain made in a transaction, and loss is the money lost.

  • Profit = Selling Price - Cost Price
  • Loss = Cost Price - Selling Price
  • Profit or Loss Percentage = (Profit or Loss / Cost Price) × 100

Discount

Discount is the reduction in price given on goods.

  • Discount = Marked Price - Selling Price
  • Discount Percentage = (Discount / Marked Price) × 100

Simple Interest

Simple interest is the extra money paid for borrowing money for a certain time.

  • Simple Interest (SI) = (Principal × Rate × Time) / 100
  • Principal: The money borrowed
  • Rate: Interest rate per year
  • Time: Number of years

Fun Activity: Shopping Math!

Make a list of items with their prices. Calculate the total cost, apply a discount, and find out how much you save!

Summary

  • Ratios, percentages, profit and loss, discount, and simple interest help us compare quantities.
  • These concepts are used in shopping, banking, and daily life.

Practice Questions

  1. Express 3 out of 8 as a percentage.
  2. Find the ratio of 15 to 45 in simplest form.
  3. A shopkeeper buys a toy for ₹120 and sells it for ₹150. Find the profit and profit percentage.
  4. The marked price of a shirt is ₹500. It is sold for ₹400. Find the discount and discount percentage.
  5. Find the simple interest on ₹2000 at 5% per annum for 2 years.

Challenge Yourself

  • Create your own word problem using percentage and solve it.
  • Find the ratio of boys to girls in your class.

Did You Know?

  • Percentages are used in exams, shopping, and sports!
  • Banks use simple interest to calculate money you earn or pay.

Glossary

  • Ratio: Comparison of two numbers by division.
  • Percentage: Number out of 100.
  • Profit: Money gained in a transaction.
  • Loss: Money lost in a transaction.
  • Discount: Reduction in price.
  • Simple Interest: Extra money paid for borrowing money.

Answers to Practice Questions

  1. 37.5%
  2. 1:3
  3. Profit = ₹30; Profit % = 25%
  4. Discount = ₹100; Discount % = 20%
  5. SI = ₹200

Practice comparing quantities to become confident in solving real-life math problems!

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