CBSE Class 7 Maths Exemplar Chapter 1: Integers NCERT Solutions

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NCERT Solutions PDF Class 7 PDF

This chapter provides NCERT Solutions for Class 7 Maths Exemplar, focusing on Integers. Students will learn to arrange integers in ascending and descending order, identify the middle integer, and interpret number lines to compare integers. The solutions cover problems involving patterns in sequences of integers, including arithmetic progressions with positive and negative differences. Key concepts like additive inverses and properties of integer addition are also addressed. These detailed, step-by-step solutions are designed to help students understand the fundamental concepts of integers and prepare effectively for their exams by clarifying common problem-solving approaches.

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BoardCBSE
ClassClass 7
SubjectMaths Exemplar
Session2026
LanguageEnglish
TypeNCERT Solutions
ChapterChapter 1

Chapter summary

Chapter 1, Integers, for CBSE Class 7 Maths Exemplar, covers the properties and applications of integers. The NCERT Solutions focus on ordering integers, interpreting number lines, identifying patterns in integer sequences, and understanding basic integer addition properties and additive inverses. The exercises are designed to build a strong foundation in working with positive and negative whole numbers.

Learning outcomes

  • Understand the concept of arranging integers in ascending and descending order.
  • Identify the middle integer in an ordered set.
  • Interpret number lines to compare integers and determine their values.
  • Solve problems involving patterns in integer sequences.
  • Apply the concept of additive inverse for integers.
  • Recognize properties of integer addition, particularly with positive and negative integers.

Topics covered

Paper topics

  • Integers
  • Ordering of Integers
  • Ascending Order
  • Descending Order
  • Number Line
  • Comparing Integers
  • Integer Patterns
  • Arithmetic Progression
  • Additive Inverse
  • Properties of Integer Addition

Important topics

  • Ordering Integers
  • Number Line Interpretation
  • Identifying Patterns
  • Properties of Integer Addition

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Questions and Solutions

Question 1

When the integers <math>10, 0, 5, -5, -7</math> are arranged in descending or ascending order, then find out which of the following integers always remains in the middle of the arrangement.

(a) 0

(b) 5

(c) -7

(d) -5

Solution: The correct option is (a) 0.

To find the integer that remains in the middle, we first arrange the given integers in both descending and ascending orders.

Descending Order: Arranging the integers from largest to smallest, we get: 10, 5, 0, -5, -7.

Ascending Order: Arranging the integers from smallest to largest, we get: -7, -5, 0, 5, 10.

In both arrangements, the integer that is positioned exactly in the middle is 0.

Question 2

By observing the number line (Fig. 1.2), state which of the following statements is not true.

(a) B is greater than –10

(b) A is greater than 0

(c) B is greater than A

(d) B is smaller than 0

(Note: Fig. 1.2 shows a number line with point A to the right of 0 and point B to the left of 0, with -10 marked to the left of B.)

Solution: The statement that is not true is (c) B is greater than A.

Observing the number line:

  • Point B is located to the left of zero, indicating it represents a negative integer.
  • Point A is located to the right of zero, indicating it represents a positive integer.

On a number line, any number to the right of another number is greater than it. Since A is to the right of B (and also to the right of 0, while B is to the left of 0), A must be greater than B. Therefore, the statement 'B is greater than A' is false.

Question 3

By observing the above number line (Fig. 1.2), state which of the following statements is true.

(a) B is 2

(b) A is -4

(c) B is -13

(d) B is -4

(Note: Fig. 1.2 shows a number line with point A to the right of 0 and point B to the left of 0, with -10 marked to the left of B. The spacing suggests B is between -10 and 0.)

Solution: The true statement is (d) B is -4.

We need to determine the value of point B based on the number line.

The number line shows that each division represents one unit. Point B is located to the left of zero. Counting the units from zero to the left, we find that B is 4 units away from zero in the negative direction.

Therefore, the value of B is -4.

Let's check the other options:

  • (a) B is 2: This is incorrect as B is to the left of zero.
  • (b) A is -4: This is incorrect as A is to the right of zero.
  • (c) B is -13: This is incorrect as B is only 4 units from zero.

Question 4

Next three consecutive numbers in the pattern 11, 8, 5, 2, --, --, are:

(a) <math>0, -3, -6</math>

(b) <math>-1, -5, -8</math>

(c) <math>-2, -5, -8</math>

(d) <math>-1, -4, -7</math>

Solution: The correct option is (d) -1, -4, -7.

First, we identify the pattern in the given sequence: 11, 8, 5, 2.

Let's find the difference between consecutive terms:

  • 8 - 11 = -3
  • 5 - 8 = -3
  • 2 - 5 = -3

The pattern is that each subsequent number is obtained by subtracting 3 from the previous number.

Now, we continue this pattern to find the next three numbers after 2:

  • The next number is 2 - 3 = -1.
  • The number after that is -1 - 3 = -4.
  • The third number is -4 - 3 = -7.

So, the next three consecutive numbers in the pattern are -1, -4, and -7.

Question 5

The next number in the pattern <math>-62, -37, -12</math> _____ is:

(a) 25

(b) 13

(c) 0

(d) -13

Solution: The correct option is (b) 13.

We need to find the pattern in the given sequence of integers: -62, -37, -12.

Let's calculate the difference between consecutive terms:

  • -37 - (-62) = -37 + 62 = 25
  • -12 - (-37) = -12 + 37 = 25

The pattern is that each number is obtained by adding 25 to the previous number.

To find the next number in the pattern, we add 25 to the last given number, -12:

-12 + 25 = 13

Therefore, the next number in the pattern is 13.

Question 6

Which of the following statements is not true?

(a) When two positive integers are added, we always get a positive integer.

(b) When two negative integers are added we always get a negative integer.

(c) When a positive integer and a negative integer is added we always get a negative integer.

(d) Additive inverse of an integer 2 is (-2) and additive inverse of (-2) is 2.

Solution: The statement that is not true is (c).

Let's analyze each statement:

  • (a) When two positive integers are added, we always get a positive integer. This statement is true. For example, 5 + 3 = 8, and 8 is positive.
  • (b) When two negative integers are added we always get a negative integer. This statement is true. For example, -5 + (-3) = -8, and -8 is negative.
  • (c) When a positive integer and a negative integer is added we always get a negative integer. This statement is not always true. The result depends on the magnitudes of the two integers. For example:
    • 5 + (-3) = 2 (positive result)
    • -5 + 3 = -2 (negative result)
    • 5 + (-5) = 0 (zero result)
    So, the sum can be positive, negative, or zero.
  • (d) Additive inverse of an integer 2 is (-2) and additive inverse of (-2) is 2. This statement is true. The additive inverse of an integer is the number that when added to it gives zero. 2 + (-2) = 0, and -2 + 2 = 0.

Therefore, statement (c) is the one that is not always true.

Question 7

On the following number line value 'Zero' is shown by the point

(Note: The question is incomplete as it does not provide options or a number line image.)

Solution: This question is incomplete as presented in the source. It refers to a number line and options that are not provided. To answer this question, one would need to see the number line and the labeled points (options) to identify which point represents zero.

Common mistakes

  • Incorrectly ordering positive and negative integers.
  • Misinterpreting the position of numbers on a number line.
  • Errors in identifying the common difference in integer patterns.
  • Confusing the sign of the result when adding positive and negative integers.

Revision tips

  • Practice arranging various sets of integers to solidify ordering skills.
  • Draw number lines to visualize integer comparisons and additions.
  • Identify the pattern rule (common difference) before solving sequence problems.
  • Review the definition and application of additive inverse for integers.

Practice MCQs

Q1. When the integers 10, 0, 5, -5, -7 are arranged in descending order, which integer remains in the middle?

Q2. On a number line, if point A is to the right of 0 and point B is to the left of 0, which statement is always true?

Q3. If each division on a number line represents 1 unit, and point B is 4 units to the left of zero, what is the value of B?

Q4. What are the next three consecutive numbers in the pattern 11, 8, 5, 2,...?

Q5. What is the next number in the pattern -62, -37, -12,...?

Q6. Which statement about integer addition is NOT always true?

Frequently asked questions

What is the main focus of Chapter 1: Integers for CBSE Class 7 Maths Exemplar?

This chapter focuses on understanding and manipulating integers, including ordering them, representing them on a number line, identifying patterns in integer sequences, and understanding basic properties of integer addition.

How do these NCERT Solutions help in understanding number lines?

The solutions use number lines to visually represent integers, helping students understand concepts like comparing integers (which is greater/smaller) and determining the value of points on the line.

What kind of patterns are covered in the Integer chapter solutions?

The solutions cover patterns where consecutive integers differ by a constant value (an arithmetic progression), involving both increasing and decreasing sequences with positive and negative numbers.

Are the properties of integer addition explained?

Yes, the solutions address properties like the sum of two positive integers, two negative integers, and a positive and a negative integer, highlighting which statements are always true and which are not.

What is an additive inverse, and how is it explained in these solutions?

An additive inverse of an integer is the number that, when added to the original integer, results in zero. The solutions confirm that the additive inverse of an integer 'a' is '-a', and vice versa.

How can I use these solutions for exam revision?

These solutions provide clear, step-by-step explanations for each problem, helping you revise concepts, understand problem-solving techniques, and identify common mistakes to avoid during your exam.

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