CBSE Class 7 Maths Notes Chapter 1 Integers

Below, you'll find detailed notes for Chapter 1 of CBSE Class 7 Mathematics, focusing on Integers. The notes cover topics such as the definition of integers, their representation on a number line, and various arithmetic operations including addition, subtraction, multiplication, and division. For detailed notes on CBSE Class 7 Maths Chapter 1 - Integers, please refer to the provided resource.

CBSE Class 7 Maths Notes Chapter 1 Integers PDF

CBSE Class 7 Maths Notes Chapter 1 Integers

In Chapter 1 of CBSE Class 7 Maths, you'll learn about Integers. These notes explain the basic ideas in an easy-to-understand way, helping you grasp the concepts better. Integers are whole numbers, including positive numbers, negative numbers, and zero. Understanding how to work with integers is important for your math skills. The notes cover things like what integers are, how they're shown on a number line, and how to add, subtract, multiply, and divide them. You'll also see how integers are used in everyday life. These notes make learning about integers easier and help you do better in math.

What is an Integer?

Introduction to Numbers

Numbers are used to count and measure things. There are different types of numbers.

Natural Numbers: These are the numbers we use for counting things. They start from 1 and go on infinitely: 1, 2, 3, 4, and so on.

Whole Numbers: Whole numbers are like natural numbers, but they also include zero. So, they start from zero and go on infinitely: 0, 1, 2, 3, 4, and so forth.

CBSE Syllabus Class 7
CBSE Class 7 English Syllabus	CBSE Class 7 Math Syllabus
CBSE Class 7 Social Science Syllabus	CBSE Class 7 Science Syllabus

Properties of Addition and Subtraction of Integers

• Closure under Addition and Subtraction: For any integers a and b, a+b and a−b are also integers.
• Commutativity Property for Addition: For any integers a and b, a+b = b+a.
• Associativity Property for Addition: For any integers a, b, and c, (a+b)+c = a+(b+c).

Additive Identity & Additive Inverse

• Additive Identity: Adding 0 to any integer leaves it unchanged. For example, 2+0 = 0+2 = 2.
• Additive Inverse: The additive inverse of an integer a is denoted by -a, where a + (-a) = 0. For example, the additive inverse of 2 is -2.

Properties of Multiplication of Integers

• Closure under Multiplication: For any integers a and b, a×b is also an integer.
• Commutative Property of Multiplication: For any integers a and b, a×b = b×a.
• Multiplication by Zero: Multiplying any integer by 0 gives 0.
• Multiplicative Identity: Multiplying any integer by 1 leaves it unchanged.

Division of Integers

• When a positive integer is divided by a positive integer, the quotient obtained is positive.
• When a negative integer is divided by a negative integer, the quotient obtained is positive.
• When a positive integer is divided by a negative integer or vice versa, the quotient obtained is negative.

The Number Line: Integers can be represented on a number line where adding positive integers moves to the right and adding negative integers moves to the left.

Addition and Subtraction of Integers

• Adding two positive integers results in a positive integer.
• Adding two negative integers results in a negative integer.
• When adding a positive and a negative integer, take their difference and place the sign of the bigger integer.
• For subtraction, add the additive inverse of the integer being subtracted.

Introduction to Zero: Integers include whole numbers and their negatives, denoted by Z or I, where I = {..., -4, -3, -2, -1, 0, 1, 2, 3, 4,…}.

Properties of Division of Integers

• Division by 0 is not defined.
• Dividing any integer by 1 results in the integer itself.

Note: Integers are not closed under division.

Multiplication of Integers

• The product of two positive integers is positive.
• The product of two negative integers is positive.
• The product of a positive and a negative integer is negative.

Identity Property of Integers

The identity property of integers refers to the property that states that when an integer is combined with a specific value, the result remains unchanged. There are two types of identity properties:

Additive Identity: This property states that when any integer is added to zero, the result is the original integer. In other words, the sum of any integer and zero is equal to the original integer. Symbolically, for any integer a, $a+0=a$ . Here, zero acts as the additive identity element.

Multiplicative Identity: This property states that when any integer is multiplied by one, the result is the original integer. In other words, the product of any integer and one is equal to the original integer. Symbolically, for any integer a, a × 1 $=a$ . Here, one acts as the multiplicative identity element.

Integer Examples

Q1. Solve the following:

1. 5 + 3 = ?
2. 5 + (-3) = ?
3. (-5) + (-3) = ?
4. (-5) x (-3) = ?

Solution:

1. 5 + 3 = 8
2. 5 + (-3) = 5 – 3 = 2
3. (-5) + (-3) = -5 – 3 = -8
4. (-5) x (-3) = 15

Q2. Calculate the following product of integers:

1. (+5) × (+10)
2. (12) × (5)
3. (- 5) × (7)
4. 5 × (-4)

Solution:

1. (+5) × (+10) = +50
2. (12) × (5) = 60
3. (- 5) × (7) = -35
4. 5 × (-4) = -20

Q3. Solve the following division of integers:

1. (-9) ÷ (-3)
2. (-18) ÷ (3)
3. (4000) ÷ (- 100)

Solution:

1. (-9) ÷ (-3) = 3
2. (-18) ÷ (3) = -6
3. (4000) ÷ (- 100) = -40