Understanding Exercise 7.3: Comparing Quantities
In Chapter 7 of your maths syllabus, the focus is on comparing quantities, which involves understanding ratios, percentages, and how to express one quantity in relation to another. Let’s break down Exercise 7.3 in detail.
Key Concepts
- Ratios: A ratio compares two quantities, showing how much of one exists in relation to the other.
- Percentages: A percentage is a way of expressing a number as a fraction of 100. It helps in understanding how much one quantity is of another.
- Proportions: When two ratios are equal, they are said to be in proportion. This concept helps in solving problems involving comparisons.
Common Types of Questions
- Finding Percentages: You may be asked to find what percentage one quantity is of another, which involves division and multiplication by 100.
- Increasing/Decreasing Quantities: Questions may involve increasing or decreasing a quantity by a certain percentage. Remember to calculate the new quantity by adding or subtracting the percentage of the original amount.
- Real-life Applications: Many questions may relate to real-life scenarios, such as discounts in shopping or comparing heights of individuals.
Example Problem Breakdown
- Problem Statement: If a book costs Rs. 200 and is available at a 10% discount, what is the selling price?
- Solution Steps:
- Calculate the discount: 10% of 200 = (10/100) * 200 = Rs. 20.
- Determine the selling price: Selling Price = Original Price - Discount = 200 - 20 = Rs. 180.
Practice Makes Perfect
- Work through each question carefully.
- Use the concepts of ratios and percentages to guide you.
- Ensure you understand each step before moving on to the next question.
By mastering these concepts, you’ll excel in comparing quantities. Happy studying!