NCERT Solutions for Class 6 Maths Chapter 6 Integers

 

NCERT solutions for class 6 maths chapter 6 Integers- You have studied about whole numbers and natural numbers in the second chapter of this class. Now we are going to study integers in this chapter. Before discussing the integers you must have cleared concepts regarding natural numbers and whole numbers. CBSE NCERT solutions for class 6 maths chapter 6 Integers is covering the solutions of each question of the integer. Natural numbers are the collection of 1, 2, 3, 4, 5,..... If you include number 0 (zero) to this collection you get a new collection of numbers known as whole numbers. So, the whole number is the collection of 0, 1, 2, 3, 4,... You have studied these numbers in the second chapter. If you put the negative numbers and the whole numbers together, the new collection of numbers will look like –1, – 2, – 3,–4,  –5,...... 0, 1, 2, 3, 4, 5,..., and this collection of numbers is known as Integers. Integers are the collection of numbers between negative infinity to positive infinity ( – 3, – 2, – 1, 0, 1, 2, 3). Numbers 1, 2, 3,.... called positive numbers are the positive integers and – 1, – 2, – 3, ... called negative integers. Solutions of NCERT for class 6 maths chapter 6 Integers are there to assist you while solving the unsolved problems. This chapter contains a total of 19 questions in 3 exercises. NCERT solutions for class 6 maths chapter 6 Integers is covering every question in detail. If you need NCERT Solutions for other classes and subjects then you click on the given link.

NCERT solutions for class 6 maths chapter 6 Integers Excercise: 6.1

Q1 Write opposites of the following :

(a) Increase in weight

(b) 30 \; km north

(c) 80 \; m east

(d) Loss of Rs \; 700

(e) 100\; m above sea level

Answer:

The opposites are-

(a) Decrease in weight

(b) 30 km south

(c) 326 AD

(d) profit of Rs 700

(e) 100 m below sea level

Q2 Represent the following numbers as integers with appropriate signs.

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

(b) A submarine is moving at a depth, eight hundred metre below the sea level.

(c) A deposit of rupees two hundred.

(d) Withdrawal of rupees seven hundred.

Answer:

 (a) An airplane is flying at a height two thousand meters above the ground. So it can be written as-
   +2000m

 (b) A submarine is moving at a depth, eight hundred meters below the sea level. In integers, it can be written as-
  - 800m

(c) A deposit of rupees two hundred. In integer form, it can be written as-

 + Rs 200

 (d) Withdrawal of rupees seven hundred. It can be written as-

  - Rs 700

Q3 Represent the following numbers on a number line :

(a) + 5

(b) – 10

(c) + 8

(d) – 1

(e) – 6

Answer:

Draw a straight line and place a mark on it at a distance of the 1cm unit.


(a) Here A indicates the position of +5

(b) Here B indicates the position of -10

(c) Here C represents the position of +8

(d) Here D represents the -1

(e) Here E represents the -6

 

 

Q4 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 value

Answer:


(a) If D is a +8 then F represents -8 (by counting on the vertical number line)

(b) G is a negative integer because it is below than point zero (0)

(c) Integers for point B and E are +4 and -10 respectively.

(d) E has the least value of -10

(e) Decreasing order of all the points are-
D>C>B>A>0>H>G>F

 

Q5 Following is the list of temperatures of five places in India on a particular day of the year.

Place                           Temperature

Siachin                       10^{\circ}C below 0^{\circ}C            .................

Shimla                       2^{\circ}C below 0^{\circ}C                 .................

Ahmedabad              30^{\circ}C above 0^{\circ}C              .................

Delhi                         20^{\circ}C above 0^{\circ}C                .................

Srinagar                     5^{\circ}C below 0^{\circ}C               .................

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

(b) Following is the number line representing the temperature in degree Celsius. Plot the name of the city against its temperature.

                
(c) Which is the coolest place?

(d) Write the names of the places where temperatures are above 10^{\circ}C.

Answer:

(a) 

Place

Temperature

Integer form

Siachin

10^{\circ}C below 0^{\circ}C 

 -10 ^0C

Shimla

2^{\circ}C below 0^{\circ}C  

-2 ^0C

Ahmedabad

30^{\circ}C above 0^{\circ}C 

+30 ^0C

Delhi

20^{\circ}C above 0^{\circ}C

+20 ^0C

Srinagar

  5^{\circ}C below 0^{\circ}C   

-5 ^0C

(b) 

(c) The coolest pace is Siachin with -10 ^0C

(d) The places where the temperature is above 10 ^0C are-
     (i) Delhi 20 ^0C
     (ii) Ahmedabad 30 ^0C

 

Q6 In each of the following pairs, which number is to the right of the other on the number line?

(a)  2,9

(b) -3,-8

(c)  0,-1

(d) -11,1

(e)  -6,6

(f) 1,-100

Answer:

In a number line, if an integer is greater than another integer, then it is placed on the right side of the number line. So, by this information, we can quickly identify which number is on the right side, in the given following pairs.
(a) 9 is right to the 2 (9 > 2)

(b) -3 is right to the - 8 (-3 > -8

(c) 0 is right to the -1   (0 > -1)

(d) 10 is right to the -11 (10 > -11)

(e) 6 is right to the -6 (6 > -6)

(f) 1 is right to the -100 (1 > -100)

 

 

Q7 Write all the integers between the given pairs (write them in the increasing order.)

(a) 0 \; and\; -7

(b) -4 \; and\; 4

(c) -8 \; and\; -15

(d) -30 \; and\; -23

Answer:

(a) The integers between 0 \; and\; -7 are;
       -6,-5,-4,-3,-3,-1

(b) Integers between -4 \; and\; 4 are;
      -3,-2,-1,0,1,2,3,

(c) Integers between -8 \; and\; -15 are;

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

(d) Integers between -30 \; and\; -23 are;

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

 

 

Q8 (a) Write four negative integers greater than -20.

(b) Write four integers less than -10.

Answer:

(a)  four negative integers greater than -20. are;

-19,-18,16,-9 (all negative integers wg=ho comes before -20)

(b) four integers less than -10.are;
     -19,-18,16,-11 (integers which comes after the -10)

Q9 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.

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

(c) A smallest negative integer is -1.

(d) -26 is greater than -25

Answer:

(a) True, (-8 is greater than -10so it comes on the right side)

(b) False. -100 is to the left side of -50 on a number line

(c) False,
Correction-There is no smallest negative integer

(d) False,
Correction;-26 is smaller than -25

 

Q10 Draw a number line and answer the following :

(a) Which number will we reach if we move  4 numbers to the right of -2.

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

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

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

Answer:

(a)  if we move  4 numbers to the right of -2. we get 2.

(b)  if we move 5 numbers to the left of 1 we get -4

(c)  If we are at -8 on the number line, we should move 5 number to the -8 left side on the number line.

(d)  If we are at -6 on the number line, then we should move 5 number right to the -6 on the number line.

NCERT solutions for class 6 maths chapter 6 Integers Excercise: 6.2

Q1 Using the number line write the integer which is :

(a) 3 more than 5

(b) 5 more than -5

(c) 6 less than 2

(d) 3 less than -2

Answer:

(a) 3 more than 5
The answer is 5 + 3  = 8

(b) 5 more than -5
The answer is 5 + (-5) = 0

(c) 6 less than 2
the answer is 2 - 6 = -4

(d) 3 less than -2
The answer is 3 + (-2) = 1

 

Q2 Use number line and add the following integers :

(a)  9+(-6)

(b) 5+(-11)

(c) (-1)+(-7)

(d) (-5)+10

(e) (-1)+(-2)+(-3)

(f)  (-2)+8+(-4)

Answer:

Addition by using the number line method-   
(a)  9+(-6) 
Initially, move 0 to 9 and then 6 number left to the 9 on the numberline.

(b) 5+(-11) 
Initially, move 0 to 5 and then 11 number left to the 5 on the number line.

(c) (-1)+(-7) 
Initially, move 0 to -1 and then 7 number left to the -1