NCERT Solutions for Class 6 Maths Chapter 6 - Integers

Refer to page 1 - 10 for Exercise 6.1 in the PDF

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 –

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(b) \[-10\]    

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

(Image Will Be Updated Soon)

(c) \[+8\]  

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

(Image Will Be Updated Soon)

(d) \[-1\]  

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

(Image Will Be Updated Soon)

(e) \[-6\]

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

(Image Will Be Updated Soon)

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 $-10$.

(Image Will Be Updated Soon)

(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.

(Image Will Be Updated Soon)

Plot the name of the city against its temperature.

Ans:

(Image Will Be Updated Soon)

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 \[2\].

(Image Will Be Updated Soon)

(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 \[-4\].

(Image Will Be Updated Soon)

(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:

(Image Will Be Updated Soon)

(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:

(Image Will Be Updated Soon)

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

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

(Image Will Be Updated Soon)

2. Use number line and add the following integers:

(a) $9+(-6)$                    

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

(Image Will Be Updated Soon)

(b) $5+(-11)$

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

(Image Will Be Updated Soon)

(c) $(-1)+(-7)$                

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

(Image Will Be Updated Soon)

(d) $(-5)+10$

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

(Image Will Be Updated Soon)

(e) $(-1)+(-2)+(-3)$      

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

(Image Will Be Updated Soon)

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

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

(Image Will Be Updated Soon)

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 Solutions for Class 6 Maths Chapter 6 - Integers

NCERT solutions for Class 6 Maths Chapter 6 are an essential study material for students who are preparing for their exam. This solution explains the concept in a more straightforward manner, and aid students to grasp a topic quickly. Hence, understanding the basics as well as advanced concepts becomes easy. These solutions are available online for free, and once can easily access them via various websites.

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.

Why NCERT Solution For Class 6 Maths Chapter 6 Integers is a Must-Read?

Using the NCERT solutions for Class 6 Maths Chapter 6 students can grasp any concept quickly. Here are some other advantages of following it –

• The language used in these solutions is lucid and helps students to comprehend any topic better.

• The simple yet detailed explanation helps individuals to get a better idea about every topic.

• The use of bullet points, graphs, charts, etc. makes the learning experience engaging.

• Moreover, the use of real-life examples helps individuals to relate to a topic better and understand it comfortably.

• Since NCERT solutions of Class 6th Math integers follow the CBSE guidelines; it helps students to prepare better for their exam.
  
  

A Final Word

NCERT solutions for Class 6 Maths Chapter 6 offers further assistance to the students to improve their preparations. Also, these books are easily accessible via online learning platforms like Vedantu. Being one of India’s top e-learning platforms, Vedantu offers study material, online classes, and special sessions to aid students further.

Chapter wise NCERT Solutions for Class 6 Maths

• Chapter 1 - Knowing Our Numbers

• Chapter 2 - Whole Numbers

• Chapter 3 - Playing with Numbers

• Chapter 4 - Basic Geometrical Ideas

• Chapter 5 - Understanding Elementary Shapes

• Chapter 6 - Integers

• Chapter 7 - Fractions

• Chapter 8 - Decimals

• Chapter 9 - Data Handling

• Chapter 10 - Mensuration

• Chapter 11 - Algebra

• Chapter 12 - Ratio and Proportion

• Chapter 13 - Symmetry

• Chapter 14 - Practical Geometry

Along with this, students can also view additional study materials provided by Vedantu, for Class 6 Maths Chapter 1 Knowing Our Numbers

• NCERT Books Class 6

• CBSE Class 6 Maths Syllabus

NCERT Solution Class 6 Maths of Chapter 6 All Exercises