Kidz Olympiad🎉

Mathematics Class 7 - Comparing Quantities Notes

Comprehensive study notes for Class 7 - Comparing Quantities olympiad preparation

Comparing Quantities

Welcome to the chapter on Comparing Quantities for Class 7. In this chapter, you will learn how to compare different quantities using ratios, percentages, and proportions. By the end of this chapter, you will be able to solve problems involving discounts, profit and loss, and simple interest!

Introduction

Comparing quantities helps us understand how much one thing is compared to another. We use ratios, percentages, and proportions to compare quantities in daily life, shopping, banking, and more.

Ratios

A ratio compares two quantities of the same kind. It shows how many times one quantity is compared to another.

  • Example: If there are 2 apples and 3 oranges, the ratio of apples to oranges is 2:3.
  • Ratios can be simplified like fractions.

Proportion

Proportion means two ratios are equal. It helps us solve problems where quantities increase or decrease together.

  • Example: 2:3 :: 4:6 (2 is to 3 as 4 is to 6)

Percentages

Percentage means "out of 100". It is used to compare quantities easily.

  • Example: 25% means 25 out of 100.
  • To find a percentage of a number: (percentage × number) ÷ 100

Applications of Comparing Quantities

  • Discount: Reduction in price. Example: If a shirt costs ₹500 and there is a 10% discount, the discount is ₹50.
  • Profit and Loss: Used in buying and selling. Profit = Selling Price - Cost Price. Loss = Cost Price - Selling Price.
  • Simple Interest: Money earned or paid for borrowing. Formula: SI = (Principal × Rate × Time) ÷ 100

Fun Activity: Shopping Math!

Make a list of items and their prices. Calculate the total cost, discounts, and final price using percentages!

Summary

  • Ratios, proportions, and percentages help us compare quantities.
  • We use these concepts in shopping, banking, and daily life.
  • Practice solving problems to understand comparing quantities better.

Practice Questions

  1. Find the ratio of 8 pens to 12 pencils.
  2. Is 3:4 and 6:8 in proportion?
  3. What is 20% of 150?
  4. A book costs ₹200. If there is a 15% discount, what is the discount amount?
  5. Find the simple interest on ₹1000 at 5% per year for 2 years.

Challenge Yourself

  • Make your own word problem using percentages and solve it.
  • Find the profit if a toy is bought for ₹120 and sold for ₹150.

Did You Know?

  • Percentages are used in exams, shopping, and sports scores!
  • Banks use simple interest to calculate money earned or paid.

Glossary

  • Ratio: Comparison of two quantities.
  • Proportion: When two ratios are equal.
  • Percentage: A number out of 100.
  • Discount: Reduction in price.
  • Profit: Money gained in selling.
  • Loss: Money lost in selling.
  • Simple Interest: Money earned or paid for borrowing.

Answers to Practice Questions

  1. 2:3
  2. Yes, because 3/4 = 6/8
  3. 30
  4. ₹30
  5. ₹100

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

Quick Navigation