Class 7 Maths Chapter 1 | Integers Full Chapter Explanation and Exercise 1.1 to 1.4

Introduction

This tutorial provides a comprehensive overview of Class 7 Maths Chapter 1: Integers. It covers the fundamentals of integers, their properties, and exercises (1.1 to 1.4) to reinforce understanding. Whether you're preparing for exams or simply want to grasp the concept of integers better, this guide will help you navigate through the chapter step by step.

Step 1: Understanding Integers

• Definition: Integers are whole numbers that can be positive, negative, or zero.
• Natural Numbers: These are the set of positive integers (1, 2, 3, ...).
• Integers include: Natural numbers, their negative counterparts, and zero (e.g., -3, -2, -1, 0, 1, 2, 3, ...).

Step 2: Visualizing Integers on a Number Line

• Number Line: A straight line where each point corresponds to a real number.
• Placement:
  • Zero is at the center.
  • Positive integers are to the right of zero.
  • Negative integers are to the left.
• Tip: Use the number line to visually understand addition and subtraction of integers.

Step 3: Learning Absolute Value

• Definition: The absolute value of an integer is its distance from zero on the number line, regardless of direction.
• Example:
  • |5| = 5
  • |-5| = 5
• Practical Application: Useful in real-world scenarios such as measuring temperature changes.

Step 4: Multiplying Integers with Different Signs

• Rules:
  • Positive × Positive = Positive
  • Negative × Negative = Positive
  • Positive × Negative = Negative
  • Negative × Positive = Negative
• Example:
  • 3 × (-2) = -6
  • (-3) × (-2) = 6

Step 5: Adding and Subtracting Integers on the Number Line

• Adding Integers:
  • Move to the right for positive integers.
  • Move to the left for negative integers.
• Subtracting Integers:
  • Convert subtraction into addition by adding the opposite integer.
  • Example: To solve 5 - 3, move 5 units right, then 3 units left.

Step 6: Properties of Addition and Subtraction of Integers

• Commutative Property: a + b = b + a
• Associative Property: (a + b) + c = a + (b + c)
• Identity Element: a + 0 = a
• Inverse Element: a + (-a) = 0

Step 7: Properties of Multiplication of Integers

• Commutative Property: a × b = b × a
• Associative Property: (a × b) × c = a × (b × c)
• Distributive Property: a × (b + c) = (a × b) + (a × c)
• Identity Element: a × 1 = a
• Inverse Element: a × (1/a) = 1 (for non-zero integers)

Step 8: Solving Exercises 1.1 to 1.4

Exercise 1.1

• Solve questions 1 to 9 focusing on addition and subtraction.

Exercise 1.2

• Complete questions 1 to 4 emphasizing properties of integers.

Exercise 1.3

• Tackle questions 1 to 9, applying multiplication rules.

Exercise 1.4

• Work through questions 1 to 7, combining all concepts learned.

Conclusion

In this tutorial, we explored the concept of integers, their properties, and practical applications. We also provided step-by-step guidance on how to visualize, add, subtract, and multiply integers, along with exercises for practice. To deepen your understanding, consider reviewing each exercise and applying these concepts in real-world scenarios. Happy studying!