CBSE Class 6 Maths Chapter 3 Integers NCERT Solutions

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NCERT Solutions PDF Class 6 PDF

This resource provides comprehensive NCERT Solutions for Class 6 Mathematics, Chapter 3: Integers. It covers fundamental concepts related to integers, including their representation on the number line, identifying positive and negative integers, and understanding the concepts of predecessor and successor. The solutions offer step-by-step explanations for various problems, helping students grasp the properties and operations of integers. This guide is designed to aid students in understanding the chapter thoroughly and preparing effectively for their examinations by clarifying common doubts and reinforcing key mathematical principles.

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Quick info

BoardCBSE
ClassClass 6
SubjectMaths Exemplar
Session2026
LanguageEnglish
TypeNCERT Solutions
ChapterChapter 3

Chapter summary

Chapter 3 of the Class 6 NCERT Maths textbook focuses on Integers. This solution set breaks down the exercises, explaining concepts like the sign of integers less than zero, locating integers on the number line, and finding predecessors and successors. It clarifies the distinction between whole numbers and integers and helps identify the greatest and least integers within given ranges. The solutions are designed for clarity and accuracy, supporting students in mastering the foundational aspects of integers.

Learning outcomes

  • Understand the concept of integers and their representation on a number line.
  • Identify positive and negative integers based on their position relative to zero.
  • Determine the predecessor and successor of a given integer.
  • Distinguish between whole numbers and integers.
  • Find the greatest and least integers within a specified range.

Topics covered

Paper topics

  • Introduction to Integers
  • Positive and Negative Integers
  • Integers on a Number Line
  • Predecessor of an Integer
  • Successor of an Integer
  • Whole Numbers vs. Integers
  • Identifying Integers Between Two Numbers
  • Greatest Integer
  • Least Integer

Important topics

  • Representation of Integers on a Number Line
  • Understanding Positive and Negative Integers
  • Finding Predecessors and Successors
  • Identifying Integers in a Range
  • Distinction between Whole Numbers and Integers

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Questions and Solutions

Question 1

1. Every integer less than 0 has the sign

(A) + (B) - (C) \times (D) \div

Solution:

Integers less than 0 are known as negative integers. By definition, all negative integers are represented with a minus (-) sign preceding them. For example, -1, -2, -3 are all integers less than 0 and carry the '-' sign.

Therefore, the correct option is (B).

Question 2

2. The integer '5 units to the right of 0 on the number line' is

(A) +5 \qquad (B) -5

(C) +4 \qquad (D) -4

Solution:

On a number line, movement to the right of 0 represents positive integers, and movement to the left represents negative integers. Each unit represents a step of 1.

Starting from 0, moving 5 units to the right means adding 5 to 0. This position corresponds to the integer +5.

Therefore, the correct option is (A).

Question 3

3. The predecessor of the integer −1 is

(A) 0

(\mathbf{C}) -2

(B) 2

(D) 1

Solution:

The predecessor of any integer is the integer that comes immediately before it on the number line. This is found by subtracting 1 from the given integer.

For the integer -1, the predecessor is calculated as:

-1 - 1 = -2

Thus, -2 is the predecessor of -1.

Therefore, the correct option is (C).

Question 4

4. Number of integers lying between –1 and 1 is

(A) 1

(B) 2

(C) 3

(D) 0

Solution:

We need to find the integers that are strictly greater than -1 and strictly less than 1. On the number line, the integer that fits this condition is 0.

The integers between -1 and 1 are: 0.

There is only one integer (0) lying between -1 and 1.

Therefore, the correct option is (A).

Question 5

5. Number of whole numbers lying between –5 and 5 is

(A) 10

(B) 3

(C) 4

(D) 5

Solution:

Whole numbers are non-negative integers (0, 1, 2, 3, ...). We need to find the whole numbers that are strictly greater than -5 and strictly less than 5.

The whole numbers satisfying this condition are 0, 1, 2, 3, and 4.

Counting these numbers, we find there are 5 whole numbers lying between -5 and 5.

Therefore, the correct option is (D).

Question 6

6. The greatest integer lying between –10 and –15 is

(A) -10

(B) –11

(C) -15

(D) -14

Solution:

We are looking for the greatest integer that is strictly greater than -15 and strictly less than -10.

The integers lying between -10 and -15 are -11, -12, -13, and -14.

Comparing these integers, -11 is the largest (closest to zero) among them.

Therefore, the correct option is (B).

Question 7

7. The least integer lying between -10 and -15 is

(A) -10

(B) -11

(C) -15

(D) -14

Solution:

We need to find the least integer that is strictly greater than -15 and strictly less than -10.

The integers lying between -10 and -15 are -11, -12, -13, and -14.

Comparing these integers, -14 is the smallest (furthest from zero in the negative direction) among them.

Therefore, the correct option is (D).

Question 8

8. On the number line, the integer 5 is located

(A) to the left of 0

(B) to the right of 0

(C) to the left of 1

(D) to the left of -2

Solution:

The number line is a representation where numbers increase from left to right. Zero (0) is the center point. Positive integers are located to the right of 0, and negative integers are located to the left of 0.

Since 5 is a positive integer, it is located to the right of 0 on the number line.

Therefore, the correct option is (B).

Common mistakes

  • Confusing the predecessor and successor of negative integers.
  • Incorrectly identifying the greatest or least integer in a negative range.
  • Misinterpreting the number of integers or whole numbers between two given numbers.
  • Confusing whole numbers with integers, especially around zero.

Revision tips

  • Draw a number line for each question involving positions or ranges of integers.
  • Practice identifying predecessors and successors for both positive and negative integers.
  • Pay close attention to the wording 'between' when counting integers or whole numbers.
  • Review the definitions of integers and whole numbers to avoid confusion.

Practice MCQs

Q1. Which sign is associated with every integer less than 0?

Q2. What integer is located 5 units to the right of 0 on the number line?

Q3. What is the predecessor of the integer -1?

Q4. How many integers lie strictly between -1 and 1?

Q5. How many whole numbers lie strictly between -5 and 5?

Q6. What is the greatest integer lying strictly between -10 and -15?

Q7. What is the least integer lying strictly between -10 and -15?

Q8. On a number line, the integer 5 is located:

Frequently asked questions

What are integers in Class 6 Maths?

Integers are a set of numbers that include all whole numbers (0, 1, 2, 3,...) and their negative counterparts (-1, -2, -3,...). They represent both positive and negative quantities.

How do I find the predecessor of an integer?

The predecessor of any integer is found by subtracting 1 from it. For example, the predecessor of -5 is -5 - 1 = -6.

What is the difference between whole numbers and integers?

Whole numbers include 0 and all positive counting numbers (0, 1, 2,...). Integers include whole numbers and all negative numbers (-..., -3, -2, -1, 0, 1, 2, 3,...).

How can I use these NCERT solutions for revision?

These solutions provide step-by-step explanations for each question. You can use them to review concepts, check your answers, and understand the methods used to solve problems related to integers.

What does it mean for an integer to be 'between' two other integers?

When an integer is 'between' two other integers, it means it is greater than the smaller integer and less than the larger integer. For example, integers between -3 and 3 are -2, -1, 0, 1, and 2.

Are there any specific rules for the greatest or least integer in a range?

Yes, for negative integers, the number closer to zero is the greatest (e.g., -11 is greater than -14). For positive integers, the number further from zero is the greatest. The least integer is the one furthest from zero in the negative direction.

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