7. Comparing Quantities

7. Comparing Quantities

  • 7

    Comparing Quantities

    This section introduces the concepts of comparing quantities using ratios, percentages, and practical applications in everyday situations.

  • 7.1

    Recalling Ratios And Percentages

    This section focuses on understanding ratios and percentages through comparisons of quantities.

  • 7.2

    Finding Discounts

    This section discusses discounts as reductions on the marked price of items, explaining how to calculate both the discount amount and the discount percentage.

  • 7.2.1

    Estimation In Percentages

    This section focuses on estimating percentages, specifically how to calculate approximate values based on rounding and application of percentage concepts.

  • 7.3

    Sales Tax/value Added Tax/goods And Services Tax

    This section introduces sales tax, value added tax (VAT), and goods and services tax (GST) as important financial concepts related to taxation on goods and services in an economy.

  • 7.4

    Compound Interest

    This section introduces compound interest, explaining how it differs from simple interest and providing methods for its calculation.

  • 7.5

    Deducing A Formula For Compound Interest

    This section outlines a method for deducing a formula to calculate compound interest.

  • 7.6

    Applications Of Compound Interest Formula

    This section discusses the practical applications of the compound interest formula in various real-world scenarios.

    • Key Summary

    This chapter explores the concepts of comparing quantities, including ratios, percentages, discounts, sales tax, and the basics of compound interest. It provides practical examples and exercises to help understand how to calculate these quantities in various scenarios, from everyday applications to financial calculations. Additionally, it emphasizes the importance of understanding percent changes in different contexts, such as population growth and depreciation.

    Key Takeaways

    • Ratios express the relative size of two quantities.
    • Percentages provide a way to compare proportions within a whole.
    • Discounts and taxes directly impact the final price of goods and services.
    • Compound interest grows on the previously accrued interest, leading to exponential growth over time.

    Key Concepts

    • Ratio: A comparison between two quantities showing how many times one value contains or is contained within the other.
    • Percentage: A fraction expressed as a part of 100, used to compare quantities relative to a total.
    • Discount: A reduction of the marked price of a product, often expressed as a percentage.
    • Sales Tax: A tax imposed on sales of goods and services, typically added to the final bill amount.
    • Compound Interest: Interest calculated on the initial principal, which also includes all accumulated interest from previous periods.