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: Integers introduces students to the world of whole numbers and their negative counterparts. This chapter focuses on understanding integers, how to represent them on a number line, and comparing their values. You'll learn to identify integers in real-life situations like temperature changes, sea level, and bank balances, using positive and negative signs correctly. The exercises will guide you through plotting these numbers on a number line, understanding points on a vertical number line, and comparing different temperatures. Mastering integers is a key step in building a solid foundation for more advanced mathematical concepts. These solutions are a great way to prepare for exams and revise the chapter's key ideas.

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Quick info

BoardCBSE
ClassClass 6
SubjectMathematics
Session2026
LanguageEnglish
TypeNCERT Solutions
ChapterChapter 6: Integers

Chapter summary

Chapter 6 of the NCERT Class 6 Mathematics textbook focuses on Integers. This chapter's solutions cover the definition of integers, their representation on a number line, and the concept of opposites. It includes exercises on identifying integers from real-world contexts like temperature and altitude, plotting integers on a number line, and comparing integer values. The solutions aim to provide a clear understanding of positive and negative numbers and their properties.

Learning outcomes

  • Understand the concept of opposite numbers.
  • Represent integers on a number line.
  • Identify and write integers with appropriate signs based on given situations.
  • Compare integers and determine their values on a vertical number line.
  • Apply the concept of integers to real-world scenarios like temperature.

Topics covered

Paper topics

  • Opposites of integers
  • Integers with signs
  • Number line representation
  • Positive and negative integers
  • Comparing integers
  • Vertical number line
  • Temperature representation

Important topics

  • Representation of integers on a number line
  • Understanding positive and negative signs
  • Comparing integers
  • Real-world applications of integers (temperature, altitude)

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Questions and Solutions

Question 1

Write the opposite of the following:
  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 or quantity reverses its meaning or direction.
  1. The opposite of an 'Increase in weight' is a 'Decrease in weight'.
  2. The opposite of '30 km north' is '30 km south'.
  3. The opposite of '326 BC' (Before Christ) is '326 AD' (Anno Domini), which signifies years after the birth of Christ.
  4. The opposite of a 'Loss of ₹700' is a 'Profit of ₹700'.
  5. The opposite of '100 m above sea level' is '100 m below 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 gains, and negative signs (-) for quantities below a reference point or losses.
  1. The aeroplane is flying above the ground, so its height is represented as a positive integer: +2000 meters.
  2. The submarine is moving below sea level, so its depth is represented as a negative integer: -8000 meters.
  3. A deposit means adding money, which is a gain. So, it is represented as a positive integer: +₹200.
  4. A withdrawal means taking money out, which is a loss. So, it is represented as a negative integer: -₹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 intervals. Zero is the center. Positive integers are marked to the right of zero, and negative integers are marked to the left of zero.

a) To represent +5, start at 0 and move 5 units to the right.

b) To represent -10, start at 0 and move 10 units to the left.

c) To represent +8, start at 0 and move 8 units to the right.

d) To represent -1, start at 0 and move 1 unit to the left.

e) To represent -6, start at 0 and move 6 units to the left.

(Note: The actual drawing of the number line with points marked would be done on paper.)

Question 4

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

(Assume the figure shows points labeled A, B, C, D, E, F, G, H, O with D at +8 and E at -10, and other points in sequence.)

  1. If point D is +8 then which point is -8?
  2. Is point G a negative integer or a positive integer?
  3. Write integers for points B and E.
  4. Which point marked on this number line has the least value?
  5. Arrange all the points in decreasing order of values.
Solution: Observing the vertical number line, we see that points above zero are positive integers and points below zero are negative integers. The value increases as we move upwards and decreases as we move downwards.
  1. If point D represents +8, then moving downwards symmetrically, point F represents -8.
  2. Point G is below the zero mark (O), so it represents a negative integer.
  3. Point B is above zero and is 4 units away from zero, so B = (+) 4. Point E is below zero and is 10 units away from zero, so E = (-) 10.
  4. The least value is the lowest point on the number line. Point E is the lowest point, representing -10. Therefore, E has the least value.
  5. Arranging the points in decreasing order means arranging them from the largest value to the smallest value (from top to bottom on the number line). Based on the typical representation where D is +8 and E is -10, the order would be: D (+8), C (+6), B (+4), A (+2), O (0), H (-2), G (-4), F (-6), 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:
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 represent temperatures below 0°C using negative integers and temperatures above 0°C using positive integers.
  • Siachin: 10°C below 0°C is represented as -10°C.
  • Shimla: 2°C below 0°C is represented as -2°C.
  • Ahmedabad: 30°C above 0°C is represented as +30°C.
  • Delhi: 20°C above 0°C is represented as +20°C.
  • Srinagar: 5°C below 0°C is represented as -5°C.

Common mistakes

  • Confusing the direction on the number line (e.g., placing negative numbers to the right of zero).
  • Incorrectly assigning signs (+ or -) to real-world situations.
  • Difficulty in determining the least or greatest value among a set of integers.
  • Misinterpreting the scale on a vertical number line.

Revision tips

  • Practice drawing number lines accurately for each question.
  • Pay close attention to the 'above'/'below' and 'profit'/'loss' cues to assign correct signs.
  • Visualize the number line when comparing integers to determine the smallest or largest value.
  • Relate the abstract integer concepts to the real-world examples provided in the chapter.

Practice MCQs

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

Q2. Which integer represents a deposit of rupees two hundred?

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

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

Q5. What does '10°C below 0°C' represent as an integer?

Frequently asked questions

What are integers in Class 6 Maths?

Integers are whole numbers, both positive and negative, including zero. They are used to represent quantities that can be positive, negative, or zero, such as temperature, altitude, or financial transactions.

How do I represent integers on a number line?

On a number line, zero is the center. Positive integers are to the right of zero, and negative integers are to the left of zero. Equal spacing is maintained between consecutive integers.

What is the opposite of a number?

The opposite of a number 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.

How can I use these NCERT solutions for revision?

These solutions provide rewritten, detailed explanations for each question. You can use them to understand the concepts thoroughly, check your answers, and learn different methods to solve problems related to integers.

What does 'below 0°C' mean in terms of integers?

'Below 0°C' indicates a negative temperature. For example, 5°C below 0°C is represented as -5°C.

Important links

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