Integers: The World of Positive and Negative Numbers

Integers form the backbone of many mathematical concepts. Chapter 1 of the NCERT Grade 7 Maths textbook introduces you to these fascinating numbers, bringing clarity to their nature and the operations involving them.

Introduction to Integers

• Integers are a set of whole numbers including zero, positive numbers, and their negative counterparts.

• It can be represented on a number line, where numbers to the right are positive and those to the left are negative.

Understanding Positive and Negative Integers

Positive Integers

• Located to the right of zero on the number line.

• Used to represent quantities that increase.

Negative Integers

• Located to the left of zero on the number line.

• Represent quantities that decrease or are below a reference level.

Addition of Integers

1. Same Sign: Add the absolute values and keep the common sign.
   • Example: -3 + (-5) = -8
2. Different Signs: Subtract the smaller absolute value from the larger and take the sign of the number with the larger absolute value.
   • Example: 7 + (-3) = 4

Subtraction of Integers

Subtracting an integer is the same as adding its opposite.

• Example: 5 - 3 is the same as 5 + (-3) = 2

Multiplication and Division of Integers

1. Same Sign: Result is positive.
   • Example: (-3) × (-2) = 6
2. Different Signs: Result is negative.
   • Example: -6 ÷ 2 = -3

Properties of Integers

Closure Property

• Integers are closed under addition, subtraction, multiplication, and division (except division by zero).

Commutative Property

• The order doesn’t affect the result in addition and multiplication.
  • Example: 3 + (-4) = (-4) + 3

Associative Property

• Grouping doesn’t change the result in addition and multiplication.
  • Example: [2 + (-3)] + 4 = 2 + [(-3) + 4]

Distributive Property

• Multiplication distributes over addition and subtraction for integers.
  • Example: 2 × [3 + (-5)] = (2 × 3) + (2 × (-5))

Additive Identity

• Zero is the additive identity for integers. Any integer added to zero results in the integer itself.

Additive Inverse

• The additive inverse of an integer is its opposite. The sum of an integer and its additive inverse is zero.

Real-life Applications of Integers

1. Bank Transactions: Deposits (positive) and withdrawals (negative).

2. Temperature: Above freezing point (positive) and below freezing point (negative).

3. Elevation: Above sea level (positive) and below sea level (negative).

Practising with Integers

Consistent practice is key to mastering integers. Solve exercises, tackle word problems, and visualize scenarios where integers are used. This chapter sets a solid foundation for more complex mathematical ideas you’ll encounter in future studies.

Conclusion: Embracing the World of Integers

Chapter 1 of the NCERT Grade 7 Maths textbook simplifies the complex world of integers, making it approachable and understandable. As you delve deeper into mathematics, you’ll find integers to be indispensable tools in your arithmetic arsenal.

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