CBSE Class 6 Mathematics Chapter 6: Integers NCERT Solutions

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NCERT Solutions PDF Class 6 PDF

CBSE Class 6 Mathematics Chapter 6 introduces students to the fascinating world of integers. This chapter helps you understand whole numbers and their opposites, like positive and negative numbers. You'll learn how to identify the opposite of different numbers and real-life situations, such as gains and losses, or going up and down. The solutions guide you in representing integers using plus (+) and minus (-) signs, which is essential for understanding concepts like altitude above or below sea level, or money deposited and withdrawn from a bank. You'll also get to visualize these integers on a number line, making it easier to grasp their order and relationships. Interpreting points on a vertical number line and comparing temperatures are also covered, building a solid foundation in number systems for your future math journey.

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Quick info

BoardCBSE
ClassClass 6
SubjectMathematics
Session2026
LanguageEnglish
TypeNCERT Solutions
ChapterChapter 6

Chapter summary

Chapter 6 of NCERT Class 6 Mathematics focuses on Integers. These solutions cover the fundamental concepts of integers, including their opposites and representation using positive and negative signs. Students will practice plotting integers on a number line and interpreting data presented on vertical number lines, such as temperature variations. The exercises are designed to solidify understanding of integer properties and their real-world applications.

Learning outcomes

  • Understand the concept of opposites for numbers and real-world situations.
  • Represent integers using appropriate positive and negative signs.
  • Visualize and plot integers on a number line.
  • Interpret and analyze data presented on a vertical number line.
  • Compare and order integers based on their values.

Topics covered

Paper topics

  • Integers
  • Opposites of numbers
  • Positive and negative integers
  • Representation of integers
  • Number line
  • Vertical number line
  • Integers and temperature
  • Comparing integers

Important topics

  • Understanding Integers
  • Opposites and Signs
  • Number Line Representation
  • Vertical Number Line Interpretation
  • Real-world application of Integers (Temperature)

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Questions and Solutions

Question 1

Write the opposite of the following statements:
  1. Increase in weight
  2. 30 km north
  3. 326 BC
  4. Loss of ₹700
  5. 100 m above sea level
Solution:

The opposite of a statement reverses its meaning. We need to find the opposite for each given situation:

  1. The opposite of 'Increase in weight' is Decrease in weight.
  2. The opposite of '30 km north' is 30 km south. North and South are opposite directions.
  3. The opposite of '326 BC' (Before Christ) is 326 AD (Anno Domini), which represents years after the reference point.
  4. The opposite of 'Loss of ₹700' is Profit of ₹700. Loss and profit are opposite financial outcomes.
  5. The opposite of '100 m above sea level' is 100 m below sea level. 'Above' and 'below' are opposite directions relative to a reference point like sea level.

Question 2

Represent the following numbers as integers with appropriate signs:
  1. An aeroplane is flying at a height two thousand meters above the ground.
  2. A submarine is moving at a depth eight thousand meters below the sea level.
  3. A deposit of rupees two hundred.
  4. Withdrawal of rupees seven hundred.
Solution:

We use positive (+) signs for quantities above a reference point or increases, and negative (-) signs for quantities below a reference point or decreases.

  1. An aeroplane flying above the ground indicates a positive height. So, it is represented as +2000 meters.
  2. A submarine moving below sea level indicates a negative depth. So, it is represented as -8000 meters.
  3. A deposit means money is added, which is a positive change. So, it is represented as +₹200.
  4. A withdrawal means money is taken out, which is a negative change. So, it is represented as -₹700.

Question 3

Represent the following numbers on a number line:
  1. +5
  2. -10
  3. +8
  4. -1
  5. -6
Solution:

To represent integers on a number line, we draw a line and mark points at equal distances. Zero is usually placed in the middle. Positive integers are marked to the right of zero, and negative integers are marked to the left of zero.

(a) For +5, we start at zero and move 5 units to the right.

Number line showing +5

(b) For -10, we start at zero and move 10 units to the left.

Number line showing -10

(c) For +8, we start at zero and move 8 units to the right.

Number line showing +8

(d) For -1, we start at zero and move 1 unit to the left.

Number line showing -1

(e) For -6, we start at zero and move 6 units to the left.

Number line showing -6

Question 4

The adjacent figure is a vertical number line, representing integers. Observe it and locate the following points:

(a) If point D is +8 then which point is -8?

(b) Is point G a negative integer or a positive integer?

(c) Write integers for points B and E.

(d) Which point marked on this number line has the least value?

(e) Arrange all the points in decreasing order of values.

Vertical number line with points labeled A through H
Solution:

The figure shows a vertical number line where points above zero are positive integers and points below zero are negative integers. The distance between consecutive points is 1 unit.

  1. If point D represents +8, then the point representing -8 would be at the same distance from zero but in the opposite direction (below zero). Observing the number line, point F is located at -8. So, point F is -8.
  2. Point G is located below zero on the number line. Therefore, point G represents a negative integer.
  3. Point B is located 4 units above zero, so it represents the integer +4. Point E is located 10 units below zero, so it represents the integer -10. Thus, B = +4 and E = -10.
  4. The least value on a number line is the point furthest to the left (on a horizontal line) or furthest down (on a vertical line). Point E is the lowest point on this vertical number line, representing -10. Therefore, point E has the least value.
  5. To arrange the points in decreasing order, we list them from the largest value to the smallest value. Based on the number line, the order is: D (+8), C (+7), B (+4), A (+3), O (0), H (-2), G (-5), F (-8), E (-10). So, the decreasing order is D, C, B, A, O, H, G, F, E.

Question 5

The following is the list of temperatures of five places in India, on a particular day of the year. Observe it and answer the following:
Place Temperature
Siachin 10°C below 0°C
Shimla 2°C below 0°C
Ahmedabad 30°C above 0°C
Delhi 20°C above 0°C
Srinagar 5°C below 0°C
Solution:

We can represent these temperatures using integers. Temperatures below 0°C are represented by negative integers, and temperatures above 0°C are represented by positive integers.

  • Siachin: 10°C below 0°C can be written as -10°C.
  • Shimla: 2°C below 0°C can be written as -2°C.
  • Ahmedabad: 30°C above 0°C can be written as +30°C or 30°C.
  • Delhi: 20°C above 0°C can be written as +20°C or 20°C.
  • Srinagar: 5°C below 0°C can be written as -5°C.

If we were asked to order these temperatures, for example, from coldest to warmest, we would arrange the negative numbers first (from smallest to largest) followed by the positive numbers (from smallest to largest): Siachin (-10°C), Srinagar (-5°C), Shimla (-2°C), Delhi (20°C), Ahmedabad (30°C).

Common mistakes

  • Confusing positive and negative signs when representing quantities.
  • Incorrectly plotting integers on the number line, especially negative numbers.
  • Misinterpreting the 'opposite' of a given number or situation.
  • Errors in determining the greatest or least value among a set of integers.

Revision tips

  • Draw number lines for each question to visualize the integers.
  • Practice writing the opposite for various real-world scenarios.
  • Pay close attention to the signs (+/-) when representing quantities.
  • Review the order of integers on the number line from least to greatest and vice versa.

Practice MCQs

Q1. What is the opposite of 'increase in weight'?

Q2. Which integer represents a deposit of ₹200?

Q3. On a number line, which number is to the right of -5?

Q4. If point D is +8 on a vertical number line, which point represents -8?

Q5. What is the temperature in Srinagar if it is 5°C below 0°C?

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 are used to represent quantities that can be positive, negative, or zero.

How do NCERT Solutions for Class 6 Maths Chapter 6 help?

These solutions provide step-by-step explanations for all exercises in Chapter 6 (Integers), helping students understand concepts like opposites, number lines, and signed numbers clearly for better learning and exam preparation.

What does 'opposite' mean for integers?

The opposite of an integer is the number that is the same distance from zero but on the other side. For example, the opposite of 5 is -5, and the opposite of -3 is 3. It's also used for real-world situations like 'increase' vs. 'decrease'.

How are integers represented on a number line?

Integers are represented on a number line with zero at the center. Positive integers are to the right of zero, and negative integers are to the left of zero, with equal spacing between consecutive integers.

Can you explain the representation of temperature using integers?

Temperatures above 0°C are represented by positive integers (e.g., 20°C above 0°C is +20°C). Temperatures below 0°C are represented by negative integers (e.g., 10°C below 0°C is -10°C).

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