NCERT Solutions Class 6 Maths Chapter 6 Integers

Exercise 6.1: Introduction to Integers

• Understanding Integers: Identify and write positive and negative numbers in various contexts.

• Number Line Representation: Plotting and marking integers on a number line.

Exercise 6.2: Addition of Integers

• Addition on a Number Line: Visual representation of adding integers on a number line.

• Rules of Addition: Adding positive and negative integers with examples and practice problems.

Exercise 6.3: Subtraction of Integers

• Subtraction on a Number Line: Visual representation of subtracting integers on a number line.

• Rules of Subtraction: Subtracting positive and negative integers with examples and practice problems.

Access NCERT Solutions for Class 6 Maths Chapter 6 – Integers

1. Write opposite of the following:

(a) Increase in weight   

Ans: Decrease in weight will be the opposite.

(b) \[30\] km north

Ans: $30$ km south will be the opposite.

(c) $326$ BC

Ans: $326$ AD will be the opposite.

(d) Loss of Rs \[700\] 

Ans: Gain of Rs $700$ will be the opposite.

(e) \[100\] m above sea level

Ans: $100$ m below sea level will be the opposite.

2. Represent the following numbers as integers with appropriate signs.

(a) An aeroplane is flying at a height two thousand meters above the ground.

Ans: $+2000$ m will be its representation.

(b) A submarine is moving at a depth eight thousand meters below the sea level.

Ans: $-8000$ m will be its representation.

(c) A deposit of rupees two hundred.

Ans: $+200$ Rs will be its representation.

(d) Withdrawal of rupees seven hundred.

Ans: $-700$ Rs will be its representation.

3. Represent the following numbers on number line:

(a) \[+5\] 

Ans: The number $+5$ on the number line will be –

(b) \[-10\]    

Ans: The number $-10$ on the number line will be –

(c) \[+8\]  

Ans: The number $+8$ on the number line will be –

(d) \[-1\]  

Ans: The number $-1$ on the number line will be –

(e) \[-6\]

Ans: The number $-6$ on the number line will be –

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

Vertical Number Line

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

Ans: If point $D$ is $+8$ then point $F$ will be $-8$.

Vertical Number Line from +8 to -8

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

Ans: $G$ is a negative integer as it represents $-6$ on the number line.

Integer G Pointing on the Number Line

(c) Write integers for points \[B\] and \[E\].

Ans: Point $B$ represents $4$ and point $E$ represents $-10$.

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

Ans: $E$ has the least value as it represents $-10$.

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

Ans: As the highest point is \[D\] and all other points lie below it. Hence,

\[D>C>B>A>O>H>G>F>E\].

5. Following is the list of temperatures of five places in India, on a particular day of the year.

(a) Write the temperature of these places in the form of integers in the blank column.

Ans: The temperature of these places in the form of integers will be –

Siachen \[=-10{}^\circ C\]

Shimla \[=-2{}^\circ C\]

Ahmedabad \[=+30{}^\circ C\]

Delhi \[=+20{}^\circ C\]

Srinagar \[=-5{}^\circ C\]

(b) Following is the number line representing the temperature in degree Celsius.

Plot the name of the city against its temperature.

Ans:

As, Siachen \[=-10{}^\circ C\]

Shimla \[=-2{}^\circ C\]

Ahmedabad \[=+30{}^\circ C\]

Delhi \[=+20{}^\circ C\]

Srinagar \[=-5{}^\circ C\]

(c) Which is the coolest place?

Ans: Since, the coolest place will have a very low temperature. Hence, Siachen is the coolest place.

(d) Write the names of the place where temperature is above ${{10}^{\text{O}}}\text{C}$.

Ans: The places where temperature is above \[10{}^\circ C\] are Delhi and Ahmedabad.

6. In each of the following pairs, which number is to the right of the other on the number line?

(a) $2,9$ 

Ans: As, we know that \[9\] is greater than \[2\]. Hence, \[9\] will be right to \[2\].

(b) $-3,-8$  

Ans: As, we know that \[-3\] is greater than \[-8\]. Hence, \[-3\] will be right to \[-8\].

(c) $0,-1$

Ans: As, we know that \[0\] is greater than \[-1\]. Hence, \[0\] will be right to \[-1\].

(d) $-11,10$ 

Ans: As, we know that \[10\] is greater than \[-11\]. Hence, \[10\] will be right to \[-11\].

(e) $-6,6$

Ans: As, we know that \[6\] is greater than \[-6\]. Hence, \[6\] will be right to \[-6\].

(f) $1,-100$

Ans: As, we know that \[1\] is greater than \[-100\]. Hence, \[1\] will be right to \[-100\].

7. Write all the integers between the given pairs (write them in the increasing order):

(a) $0$ and $-7$        

Ans: The integers between the given pairs in the increasing order will be –

$-6,-5,-4,-3,-2,-1$.

(b) $-4$ and $4$

Ans: The integers between the given pairs in the increasing order will be –

$-3,-2,-1,0,1,2,3$.

(c) $-8$ and $-15$ 

Ans: The integers between the given pairs in the increasing order will be –

$-14,-13,-12,-11,-10,-9$.

(d) $-30$ and $-23$

Ans: The integers between the given pairs in the increasing order will be –

$-29,-28,-27,-26,-25,-24$.

8. (a) Write four negative integers greater than $-20$.

Ans: The four negative integers greater than $-20$ are –

$-19,-18,-17,-16$.

(b) Write four negative integers less than $-10$.

Ans: The four negative integers less than $-10$ are –

$-11,-12,-13,-14$.

9. For the following statements write True (T) or False (F). If the statement is false, correct the statement:

(a) $-8$ is to the right of $-10$ on a number line.

Ans: True. As, we know that \[-8\] is greater than \[-10\]. Hence, \[-8\] will be right to \[-10\].

(b) $-100$ is the right of $-50$ on a number line.

Ans: False. As, we know that \[-50\] is greater than \[-100\]. Hence, \[-50\] will be right to \[-100\].

(c) Smallest negative integer is $-1$.

Ans: False, \[-1\] is a greater integer.

(d) $-26$ is larger than $-25$.

Ans: False. As, we know that \[-25\] is greater than \[-26\]. Hence, \[-25\] will be right to \[-26\].

10. Draw a number line and answer the following:

(a) Draw a number line, will we reach it if we move $4$ numbers to the right of $-2$.

Ans: When we move \[4\] numbers right of  \[-2\], we will reach at \[2\].

(b) Which number will we reach if we move $5$ numbers to the left of $1$.

Ans: When we move \[5\] numbers left of  \[1\], we will reach at \[-4\].

(c) If we are at $-8$ on the number line, in which direction should we move to reach $-13$?

Ans: We will move to the left side of \[-8\].

(d) If we are at $-6$ on the number line, in which direction should we move to reach $-1$? 

Ans: We will move to the right side of \[-6\] to reach \[-1\].

Refer to page 10 - 15 for Exercise 6.2 in the PDF

1. Using the number line write the integer which is:

(a) $3$ more than $5$               

Ans: The number which is \[3\] more than \[5\] is:

(b) $5$ more than $-5$

Ans: The number which is \[5\] more than \[-5\] is:

(Image Will Be Updated Soon)

(c) $6$ less than $2$                   

Ans: The number which is \[6\] less than \[2\] is:

(d) $3$ less than $-2$

Ans: The number which is \[3\] less than \[-2\] is:

2. Use number line and add the following integers:

(a) $9+(-6)$                    

Ans: The number obtained after addition is \[3\].

(b) $5+(-11)$

Ans: The number obtained after addition is \[-6\].

(c) $(-1)+(-7)$                

Ans: The number obtained after addition is \[-8\].

(d) $(-5)+10$

Ans: The number obtained after addition is \[5\].

(e) $(-1)+(-2)+(-3)$      

Ans: The number obtained after addition is \[-6\].

(f) $(-2)+8+(-4)$

Ans: The number obtained after addition is \[2\].

3. Add without using number line:

(a) $11+(-7)$                    

Ans: After addition we have:

$11-7=4$.

(b) $(-13)+(+18)$

Ans: After addition we have:

$-13+18=5$.

(c) $(-10)+(+19)$             

Ans: After addition we have:

$-10+19=9$.

(d) $(-250)+(+150)$

Ans: After addition we have:

$-250+150=-100$.

(e) $(-380)+(-270)$         

Ans: After addition we have:

$-380-270=-650$.

(f) $(-217)+(-100)$

Ans: After addition we have:

$-217-100=-317$.

4. Find the sum of:

(a) $137$ and $-354$              

Ans: After addition we have:

$137-354=-217$.

(b) $-52$ and $52$

Ans: After addition we have:

$-52+52=0$.

(c) $-213,39$ and $192$         

Ans: After addition we have:

$-213+39+192=18$.

(d) $-50,-200$ and $300$

Ans: After addition we have:

$-50-200+300=-250+300$

$\Rightarrow -250+300=50$.

5. Find the value of:

(a) $(-7)+(-9)+4+16$

Ans: After addition we have:

$-7-9+4+16=4$.

(b) $37+(-2)+(-65)+(-8)$

Ans: After addition we have:

$37-2-65-8=-38$.

Refer to page 15 - 18 for Exercise 6.3 in the PDF

1. Subtract the following –

(a) $35-(20)$          

Ans: After subtraction we have:

$35-20=15$.

(b) $72-(90)$

Ans: After subtraction we have:

$72-90=-18$.

(c) $(-15)-(-18)$   

Ans: After subtraction we have:

$-15+18=3$.

(d) $(-20)-(13)$

Ans: After subtraction we have:

$-20-13=-33$.

(e) $23-(-12)$         

Ans: After subtraction we have:

$23+12=35$.

(f) $(-32)-(-40)$

Ans: After subtraction we have:

$-32+40=8$.

2. Fill in the blanks with $>$, $<$ or $=$ sign:

(a) $(-3)+(-6)\_\_\_\_\_\_\_\_(-3)-(-6)$

Ans: After simplifying the expression, we have:

$-3-6=-9$ and

$-3+6=3$

Hence, $3>-9$.

(b) $(-21)-(-10)\_\_\_\_\_\_\_\_(-31)+(-11)$

Ans: After simplifying the expression, we have:

$-21+10=-11$ and

$-31-11=-42$

Hence, $-11>-42$.

(c) $45-(-11)\_\_\_\_\_\_\_\_57+(-4)$

Ans: After simplifying the expression, we have:

$45+11=56$ and

$57-4=53$

Hence, $56>53$.

(d) $(-25)-(-42)\_\_\_\_\_\_\_\_(-42)-(-25)$

Ans: After simplifying the expression, we have:

$-25+42=17$ and

$-42+25=-17$

Hence, $17>-17$.

3. Fill in the blanks:

(a) $(-8)+\_\_\_\_\_\_\_\_=0$

Ans: We have $-8+8=0$.

(b) $13+\_\_\_\_\_\_\_\_=0$

Ans: We have $13-13=0$.

(c) $12+(-12)=\_\_\_\_\_\_\_\_$

Ans: We have $12-12=0$.

(d) $(-4)+\_\_\_\_\_\_\_\_=-12$

Ans: We have $-4-8=-12$.

(e) $\_\_\_\_\_\_\_\_-15=-10$

Ans: We have $5-15=-10$.

4. Find:

(a) $(-7)-8-(-25)$

Ans: After simplifying, we have:

$-7-8+25=-15+25$

$\Rightarrow -15+25=10$.

(b) $(-13)+32-8-1$

Ans: After simplifying, we have:

$-13+32-8-1=-22+32$

$\Rightarrow -22+32=10$.

(c) $(-7)+(-8)+(-90)$

Ans: After simplifying, we have:

$-7-8-90=-15-90$

$\Rightarrow -15-90=-105$.

(d) $50-(-40)-(-2)$

Ans: After simplifying, we have:

$50+40+2=90+2$

$\Rightarrow 90+2=92$.

NCERT Class 6 Maths Solutions Topic-Wise Discussion

Class 6 Maths Chapter 6 has a total of four sections and following is a topic-wise discussion on each of them.

1. Introduction

The chapter of Integers Class 6 NCERT begins with an introduction that includes some examples. It talks about a girl named Sunita who needs 10 bananas for her picnic, but her mother has only 8 of them. Hence, she borrows two from her neighbour. This example further discusses how Sunita needs to return 2 bananas to her neighbour. Few other examples like this present in this chapter introduce the concept of integers to students.

This introduction then further discusses various signs attached to numbers and what they signify.

2. Integers

The second section of this chapter then moves into the discussion of Integers class 6. Students already know about the natural number; in this chapter, they move on to the concept of negative integers.

Use of various figures helps students further to grasp the concept of different numbers like the whole number, natural number, negative number, and integers easily. After that, they learn how to represent different integers with the assistance of a single line.

Ordering of integers follows next, where students learn how to arrange these integers according to their value. With the help of NCERT solutions, students can quickly learn these relatively complex concepts and get a better understanding of it.

3. Addition of Integers

Students must know the concept of how to add Integer Class 6, as it is an essential concept for their exam as well as their daily life. In this chapter, they get to learn it via an interesting example. There is a boy named Mohan, and his house has steps to access both the terrace and godown. Here the steps to the terrace are considered as positive integers and the ones towards the godown are negative integers, and the ground level is zero. In this way, they can learn how to count integers by moving up and down the stairs.

Along with that, there are other examples with dice, tiles and buttons to further simplify this concept. Also, students learn how to add Integers for Class 6 by using a straight line.

4. Subtraction of Integers With the Help of a Number Line

Following the addition, students learn how to subtract Class 6 Maths Integers using a single line. There are different methods to this process, which are further explained under this section.

Class 6 Maths Chapter 6: Exercises Breakdown

Conclusion

Integers for Class 6 is an essential part of the Maths curriculum. It introduces students to the concept of integers, including positive and negative numbers, and the operations that can be performed with them. Understanding integers is crucial as they form the foundation for more complex mathematical concepts encountered in higher classes. In previous years' exams, questions from class 6 math chapter 6  have been regularly asked, underlining its importance. Typically, 3-5 questions are asked annually, covering a range of topics from basic understanding and representation of integers to performing addition and subtraction using integers.

Other Study Material for CBSE Class 6 Maths Chapter 6

Chapter-Specific NCERT Solutions for Class 6 Maths

Given below are the chapter-wise NCERT Solutions for Class 6 Maths. Go through these chapter-wise solutions to be thoroughly familiar with the concepts.