REVIEW: Year 1: A. Number systems, integers, fractions, decimals: 2. Revisiting Integers and Their Properties

Lesson: Revisiting Integers and Their Properties

Introduction

Welcome back to the world of integers! Integers are like the whole numbers you know, but they also include their negative counterparts. In this lesson, we’ll revisit the key properties of integers – specifically, how we add, subtract, multiply, and divide them. Understanding these properties is like learning the basic rules of a game. Once you know them, you can play around with integers in all sorts of mathematical situations. Let’s get started!

Objectives

  • Review the fundamental properties of integers.
  • Understand how to perform addition, subtraction, multiplication, and division with integers.
  • Practice solving integer problems using online calculators.

Exploring Integer Properties

  1. Addition:
    • Adding integers can be thought of as moving along a number line.
    • Rule: Adding a positive number moves you to the right, while adding a negative number moves you to the left.
  2. Subtraction:
    • Subtraction is like addition’s mirror image. It can also be seen as adding the opposite.
    • Rule: Subtracting an integer is the same as adding its opposite.
  3. Multiplication:
    • When multiplying integers, the sign of the result depends on the signs of the numbers you’re multiplying.
    • Rule: Multiplying two integers with the same sign gives a positive product, while different signs give a negative product.
  4. Division:
    • Division with integers follows the same sign rules as multiplication.
    • Rule: Dividing integers with the same sign results in a positive quotient, while different signs result in a negative quotient.

Practical Application: Using Online Calculators

For practicing these operations, you can use the built-in calculator on your smartphone or a conventional calculator. These tools are perfect for quickly computing integer problems and testing your understanding of these concepts.

How to Use
  1. Simple Calculations: Use your calculator for basic operations with integers. For example, try calculating −5+3 or −8×−2.
  2. Combining Operations: Challenge yourself with combined operations. For instance, calculate (4−(−3))×2.
  3. Voice-Activated Assistance: You can also use voice-activated services like Siri, Google Assistant, or Alexa. Just say the operation out loud, like “What’s negative 7 plus 5?” and hear the answer.

Exercise

  • Integer Exploration: Create a set of integer problems involving different operations. Solve them using your calculator and check your understanding of integer properties.
  • Real-Life Scenarios: Think of real-life situations involving integers, like temperatures or bank transactions, and use them to create and solve practical problems.

Conclusion

Integers are a fundamental part of mathematics, and their properties form the basis of many mathematical operations. By revisiting and practicing these properties, you’re strengthening your mathematical foundation, preparing you for more complex concepts ahead. Keep practicing, and don’t hesitate to use your calculator to help master these skills!