CBSE Class 6 Maths Notes Chapter 6 Integers PDF Download

CBSE Class 6 Maths Notes Chapter 6: Students are introduced to integers, a collection of numbers that includes positive, negative, and zero, in Chapter 6 of CBSE Class 6 Maths. The idea of the number line—which represents integers as positive numbers to the right of zero and negative numbers to the left—is explained in this chapter. It includes guidelines for handling signs and covers operations like adding and subtracting integers.

CBSE Class 6 Maths Notes Chapter 6 Overview

CBSE Class 6 Maths Notes Chapter 6 PDF

CBSE Class 6 Maths Notes Chapter 6 PDF

CBSE Class 6 Maths Notes Chapter 6 Integers Quick Revision Notes

Introduction

Whole Numbers

Whole numbers are a set of numbers that include all natural numbers (starting from 0) and do not include any fractions, decimals, or negative numbers. In simple terms, whole numbers are non-negative integers . The set of whole numbers is represented as {0, 1, 2, 3, 4, ...}, extending infinitely in the positive direction.

• Whole numbers include zero and all natural numbers, i.e., 0, 1, 2, 3, 4, and so on.

Negative Numbers

Introduction to Zero

The Number Zero

• The number zero means an absence of value.

The Number Line

Integers

• Collection of all positive and negative numbers including zero are called integers. ⇒ Numbers …, – 4, – 3, – 2, – 1, 0, 1, 2, 3, 4, … are integers.

• Draw a line and mark a point as 0 on it
• Points marked to the left (-1, -2, -3, -4, -5, -6) are called negative integers.
• Points marked to the right (1, 2, 3, 4, 5, 6) or (+1, +2, +3, +4, +5, +6) are called positive integers.

Absolute Value of an Integer

Ordering Integers

Addition of Integers

Positive integer + Negative integer

• Example: (+5) + (-2) Subtract: 5 – 2 = 3 Sign of bigger integer (5): + Answer: +3
• Example: (-5) + (2) Subtract: 5-2 = 3 Sign of the bigger integer (-5): – Answer: -3

Positive integer + Positive integer

• Example: (+5) + (+2) = +7
• Add the 2 integers and add the positive sign.

Negative integer + Negative integer

• Example: (-5) + (-2) = -7
• Add the two integers and add the negative sign.

Properties of Addition and Subtraction of Integers

Operations on Integers

• Addition
• Subtraction
• Multiplication
• Division.

Subtraction of Integers

• The subtraction of an integer from another integer is same as the addition of the integer and its additive inverse.
• Example: 56 – (–73) = 56 + 73 = 129 and 14 – (8) = 14 – 8 = 6

Properties of Addition and Subtraction of Integers

Closure under Addition

• a + b and a – b are integers, where a and b are any integers.

Commutativity Property

• a + b = b + a for all integers a and b.

Associativity of Addition

• (a + b) + c = a + (b + c) for all integers a, b and c.

Additive Identity

• Additive Identity is 0, because adding 0 to a number leaves it unchanged.
• a + 0 = 0 + a = a for every integer a.

Multiplication of Integers

• Product of a negative integer and a positive integer is always a negative integer. 10×−2=−20
• Product of two negative integers is a positive integer. −10×−2=20
• Product of even number of negative integers is positive. (−2)×(−5)=10
• Product of an odd number of negative integers is negative. (−2)×(−5)×(6)=−60

Properties of Multiplication of Integers

Closure under Multiplication

• Integer * Integer = Integer

Commutativity of Multiplication

• For any two integers a and b, a × b = b × a.

Associativity of Multiplication

• For any three integers a, b and c, (a × b) × c = a × (b × c).

Distributive Property of Integers

• Under addition and multiplication, integers show the distributive property.
• For any integers a, b and c, a × (b + c) = a × b + a × c.

Multiplication by Zero

• For any integer a, a × 0 = 0 × a = 0.

Multiplicative Identity

• 1 is the multiplicative identity for integers.
• a × 1 = 1 × a = a

Division of Integers

• (positive integer/negative integer)or(negative integer/positive integer) ⇒ The quotient obtained is a negative integer.
• (positive integer/positive integer)or(negative integer/negative integer) ⇒ The quotient obtained is a positive integer.

Properties of Division of Integers

• a/0 is not defined
• a/1=a

Benefits of CBSE Class 6 Maths Notes Chapter 6

Understanding Negative Numbers : Students are introduced to negative numbers, broadening their number sense beyond positive whole numbers.

Real-Life Applications : Integers are used in daily scenarios like tracking temperature changes, financial transactions (profit/loss), and elevations above or below sea level.

Improved Problem-Solving : Learning to add and subtract integers strengthens students’ logical thinking and problem-solving abilities.

Foundation for Advanced Math : This chapter prepares students for advanced topics like algebra, where positive and negative numbers play a key role.

Critical Thinking : Understanding rules related to integer operations enhances analytical skills, helping students tackle complex math problems in higher grades.