CBSE Class 6 Maths Revision Notes Chapter 2

CBSE Class 6 Mathematics Chapter 2 Revision Notes – Whole Numbers

Class 6 Mathematics Chapter 2 Notes deal with the important concepts of whole numbers. These notes are curated for students to understand the whole number, where they are placed on the number line, their properties, and their importance. The FAQs section at the end has been added to give a glimpse of the types of questions asked in the exams. With these notes, students can cover all the important points without much ado.

Revision Notes For CBSE Class 6 Mathematics Chapter 2

Whole Numbers

• Whole numbers are a part of the number system that includes numbers from zero to infinite.
• All these numbers exist in the number line. Hence, all the whole numbers are real numbers.
• Whole numbers include all the natural numbers (one to infinite), and zero. Therefore, all the natural numbers are whole numbers, but all the whole numbers are not natural numbers.
• Integers are a set of numbers consisting of all the whole numbers and the negatives of the natural numbers. Hence, all whole numbers are integers, whereas all integers are not whole numbers.
• As the term is named “whole numbers”, it is easy to remember that these numbers do not include any fractions.
• Whole numbers can never be negative. These numbers are placed on the right side of zero in the number line.
• Examples of whole numbers are 0, 1, 2, 3, 4, 5, ….
• If 1 is added to a number then the sum is the successor number.
• If 1 is subtracted from a number, the result is the predecessor number.

The Number Line

• The number line is a straight line on which numbers are placed at equal distances.
• This distance is called the unit distance.
• The number line starts with zero.
• The number line is extended to infinite.
• As the number line moves towards the right, the number becomes greater.
• Mathematical operations on the number line are given below:
• Addition: When two numbers are given, first locate the smaller number on the number line. Then move in a rightward direction. Cross the distance equal to the greater number. For example, if 4 and 5 are given numbers, first locate 4 on the number line. Then move five places to the right, it will give nine. So, the sum of 4 and 5 is 9.
• Subtraction: This method is similar to the addition method. But, first, locate the greater number here. Then move in a leftward direction. Cross the distance equal to the smaller number. Suppose, 5 is to be subtracted from 9. Locate the number 9 first. Then move five places to the left. It will give four. Therefore, the result is 4.
• Multiplication: When two numbers are to be multiplied on a number line, always start with zero. Then take the first number, say x. Skip x places to the right y times, that is the second number. For example, if 3 and 9 are the given numbers, skip three places from zero to the right side nine times. It will stop at the place where 27 is. Therefore, the product of 3 and 9 is 27. If someone skips nine places three times, the result will be the same, according to the commutative property of whole numbers.
• Division: To perform division first locate the greater number and move towards zero. Subtract the smaller number for a number of times till zero is reached. The total number of times the smaller number is subtracted is the quotient. For example, 15 is to be divided by 3. Start with the place of 15. Then move towards zero. Subtract 3 every time. It will take five times to reach zero. Therefore, the answer will be 5, i.e., 15 ÷ 3 = 5.
• In the case of divisional operations, if it is impossible to reach zero despite following the above-mentioned method, then the greater number would not be divisible by the smaller one. Consider, 17 and 3. Start with 17 and skip three places every time. After reaching the position of 2, only two places are left to reach zero. Therefore, 17 would not be divisible by 3.

Properties of the Whole Number

• Closure Property: This property is based on addition and multiplication. If two whole numbers are added or multiplied, the sum and the product also must be whole numbers.
• Consider numbers 2 and 3.
• 2 + 3 = 5
• 2 * 3 = 6
• Here, both 5 and 6 are whole numbers.
• Commutative Property: The sum and the product of two whole numbers do not depend on the placement order of the numbers.
• For example, the sum of 5 + 6 will be the same as the sum of 6 + 5, that is, 11.
• Similarly, the product of 5 * 6 is 30 which is the same as the product of 6 * 5.
• Additive Identity: The sum of any whole number and zero will always be the whole number. The value remains unchanged if a whole number is added to zero.
• For example, 8 + 0 = 8.
• Hence, zero is considered the additive identity of the whole numbers.
• Multiplicative Identity: If a whole number is multiplied by one, the value does not change.
• For example, 13 * 1 = 13. The value remains unchanged.
• Associative Property: When more than two whole numbers are added or multiplied they can be grouped in any combination and the result will be the same.
• Suppose 3, 5, and 7 are the given numbers.
• The sum of {3 + (5 + 7)} will be the same as the sum of {(3 + 5) + 7} or {5 + (3 + 7)}, that is, 15.
• Similarly, 3 * (5 * 7) = (3 * 5) * 7 = 5 * (3 * 7) = 105.
• Distributive Property: This property is applied when the sum or subtraction of two whole numbers is multiplied by another whole number.
• For example, 5 * (5 + 4) = (5 * 5) + (5 * 4) = 45.
• 20 * (17 – 2) = (20 * 17) – (20 * 2) = 300.
• Multiplication By Zero: The product of a whole number and zero is always zero.
• Example: 7 * 0 = 0.
• Division By Zero: Division of a whole number by zero is undefined.

Importance of Whole Numbers

All natural numbers are whole numbers which are used for counting. Without natural numbers counting would have been impossible. But, the drawback is these numbers do not include zero which is crucial to make natural numbers. For example, ten is a natural number. It consists of one at the tens place and zero at the ones place. But, zero itself is not a natural number. So, the natural numbers that are used in mathematics as well as in daily life would not have existed without the whole number zero. Besides, zero makes the calculation easy in the number line.

Why Choose Extramarks for Notes on Whole Numbers?

At Extramarks, the Class 6 Mathematics Chapter 2 Notes are curated carefully by experts to impart in-depth knowledge on the whole numbers. Numbers are the basis of Mathematics. There are different kinds of numbers, such as real numbers, imaginary numbers, integers, positive numbers, negative numbers, whole numbers, fractions, etc. Therefore, this chapter is important to grasp these crucial concepts and answer questions in the exam.

If the concepts are clear then students can solve any question in the exam. Students can refer to these notes before the exam to recall all the important points covered in the chapter.

1. What are whole numbers?

Whole numbers are positive natural integers including zero. In the number line, whole numbers start from zero and end at infinity.

2. Can whole numbers be negative?

Whole numbers can never be negative as they start with zero and move in the direction of the right hand on the number line.

3. Identify the whole numbers: -2, -0.1, 5, 2/3, 6, 0.

Whole numbers are positive integers starting from zero. Therefore, the whole numbers among the given numbers are 0, 5, and 6.

4. All natural numbers are whole numbers, but not all whole numbers are natural numbers. Justify the statement.

Natural numbers are a part of the number system used for counting. We start counting from one. Hence, natural numbers begin with one and end with infinite. The smallest natural number is one. But, whole numbers start with zero, which is not a natural number. In fact, it is the smallest whole number. Therefore, all the natural numbers are whole numbers, but all the whole numbers are not natural numbers.

5. Are all the whole numbers real numbers?

Real numbers include rational numbers, integers, whole numbers, and natural numbers. So, whole numbers are a part or subset of real numbers. Therefore, all the whole numbers are real numbers.