NCERT Exemplar Solutions: Integers | Mathematics (Maths) Class 6 PDF Download

Ans: (b)
The numbers –1, –2, –3, –4, ……. are referred to as negative integers.

All negative integers are less than zero.

Ans: (a)

Ans: (c)
The number which comes immediately before a particular number is called its predecessor.
To find the predecessor of a number, subtract one from the given number.
So, predecessor of -1 = -1 -1 = -2

Ans: (a)
Integer that comes between -1 and 1 is 0.

Ans: (d)
We know that, whole numbers are starts from 0.
Then, number of whole numbers between -5 and 5 are 0, 1, 2, 3, and 4.

Ans: (b)
In case of negative integer, small number is greater.

Ans: (d)
In case of negative integer, big number is smaller.

Ans: (b)

Ans: (b)

Ans: (a)
Negative integers are always comes left to the 0, so negative integers are always less than 0.

Ans: (a)
Positive integers are always coming right to the 0, so positive integers always greater than 0.

Ans: (c)
The successor of a whole number is the number obtained by adding 1 to it.
To find the predecessor of a number, subtract one from the given number.
So, predecessor of – 50 = – 50 – 1 = – 51
Then, successor of – 51 = – 51 + 1 = 50

Ans: (b)

Ans: (a)
We know that, in case of negative integer, big number is smaller.

Ans: (b)
In the above question, the most temperature is risen in option B.
The difference between two temperatures = 8 – (-4)
= 8 + 4
= 12ºC

False.
We know that, natural numbers start from 1, so smallest natural number is 1.

False.
Zero is an integer even though it is neither positive nor negative.

False.
The sum of all integers between -5 and -1 = -4 -3 -2
= -9

False.
The successor of a whole number is the number obtained by adding 1 to it.
Successor of 1 = 1 + 1
= 2

True.
Every positive integer is always larger than every negative integer.
Positive integers are always coming right to the 0, so positive integers always greater than 0.

False.
In negative integer = -4 + (-6)
= – 4 – 6
= – 10
In negative integer the sum is less than both the integer.

True.
In negative integer = -6 + (-7)
= – 6 – 7
= – 13
In negative integer the sum is less than both the integer.

True.
Example: consider the two positive integer 11 and 21
Sum of two integers = 11 + 21
= 32
Therefore, sum of any two positive integers is greater than both the integers.

True.
Whole numbers start from 0, 1, 2, 3…. so it contains 0 and other positive integers.
Hence, all whole numbers are integers.

False.
Whole numbers start from 0, 1, 2, 3….
Whole numbers can not be negative integers, but integers are both positive and negative numbers.
Therefore, all integers are not whole numbers.

False.
In case of negative integer, the bigger number is smaller.
So, – 5 < -3

True.

Zero is always less than positive integer and greater than negative integer.

True.
Zero is always less than positive integer and greater than negative integer.

True.
Zero is neither positive nor negative.

True.
By observing the number line below, we can say that an integer on the right of a given integer is always larger than the integer.

False.
-2 is to the right of the number line.

False.
As we know that, 0 is greater than negative integers.
So, 0 is not smallest integer.

True.

From the above number line we can say that, 6 and –6 are at the same distance of 6 units from 0 on the number line.

True.
Example:
Consider an integer 5.
Its additive invers is -5
Difference between an integer and its additive inverse = 5 – (-5)
= 5 + 5
= 10

True.
Example:
Consider an integer 8.
Its additive invers is -8
Sum of an integer and its additive inverse = 8 + (-8)
= 8 – 8
= 0

False.
Sum of two negative integers is always negative.
Example:
Consider two negative integers – 8 and – 10.
Sum of two negative integers = – 8 + (-10)
= – 8 – 10
= – 18

False.
Example:
Consider 3 different integers 5, 10 and -15.
Sum of 3 integers = 5 + 10 + (-15)
= 5 + 10 – 15
= 15 – 15
= 0
Therefore, the sum of three different integers can be zero.

On the number line, –15 is to the left of zero.
Negative integers are always left to the number zero, thus they are less than 0.

On the number line, 10 is to the right of zero.
Positive integers are always right to the number zero, thus they are greater than zero.

-14
Additive inverse of an integer is obtained by changing the sign of the integer.
∴ Additive inverse of 14 is -14.

1

0

9 
The integers lying between -5 and 5 are -4, -3, -2, -1, 0, 1, 2, 3, 4 i.e., 9 in number.

-14 
(-11) + (-2) + (-1) = -11 – 2 -1 = -14

30

-170 
(-80) + 0 + (-90) = -80 + 0 – 90 = -170

-5454

(-11) + (-15) = -11 – 15 = -26
11 + 15 = 26 and -26 < 26

(-71) + (9) = -71 + 9 = -62
(-81) + (-9) = -81 – 9 = -90 and -62 > -90

0 < 1

-60 < 50

-10 > -11

-101 > -102

(-2) + (-5) + (-6) = -2 – 5 – 6 = -13 (-3) + (-4) + (-6) = -3 – 4 – 6—13 And-13 = -13

0 > -2

1 + 2 + 3 = 6
(-1) + (-2) + (-3) = -1 – 2 – 3 = -6
And 6 > -6

(i) ➝ (B), (ii) ➝ (E), (iii) ➝ (B), (iv) ➝ (A), (v) ➝ (B)
(i) The additive inverse of +2 is -2.
(ii) The greatest negative integer is -1.
(iii) The greatest negative even integer is -2.
(iv) The smallest integer 0 is greater than every negative integer.
(v) Predecessor and successor of -1 are -2 and 0 respectively.
∴ Sum = -2 + 0 = -2

(a) 30 + (-25) + (-10) = 30 + (-25 – 10)
= 30 + (-35) = 30 – 35 = -5
(b) (-20) + (-5) = -20 – 5 = -25
(c) 70 + (-20) + (-30) = 70 + (-20 – 30)
= 70 + (-50) = 70 – 50 = 20
(d) -50 + (-60) + 50 = (-50 – 60) + 50
= -110+ 50 = -60
(e) 1 + (-2) + (-3) + (-4) = 1 + (-2 – 3 – 4) = 1 + (-9)
= 1 – 9 = – 8
(f) 0 + (-5) + (-2) = 0 + (-5 -2) = 0 + (-7)
= 0 – 7 = -7
(g) 0 – (-6) – (+6) = 0 + 6 – 6 = 6 – 6 = 0
(h) 0 – 2 – (-2) = 0 – 2 + 2 = -2 + 2 = 0

(a) 200 m above sea level = + 200
(b) 100 m below sea level – – 100
(c) 10 m above sea level = + 10
(d) Sea level = 0

(a) Increase in size.
(b) Success.
(c) Loss of ₹ 10
(d) 1000 BC
(e) Fall in water level.
(f) 60 km north.
(g) 10 m below the danger mark of river Ganga.
(h) 20 m above the danger mark of the river Brahmaputra.
(i) Losing by a margin of 2000 votes.
(j) Withdrawing ₹ 100 from the Bank account.
(k) 20°C fall in temperature.

Temperature at 12 : 00 noon = + 5°C
∴ Temperature at 1 : 00 p.m. = 5°C + 3°C = 8°C
And temperature at 2 : 00 p.m. = 8°C – 1°C = 7°C

The digits can be written as
0 – 1 – 2 – 3 – 4 – 5 – 6 + 7 + 8 + 9 = 3

0 is the integer which is its own additive inverse.

1 + 2 + 3 + 6 + (-2) + (-3) = 7
∴ The six distinct integers are 1, 2, 3, 6, -2 and -3.

Let x be the required integer.
According to question,
x = 4 + (-x), where (-x) is the additive inverse of x.
⇒ x = 4 – x ⇒ x + x = 4 => 2x = 4 => x = 2
∴ The required integer is 2.

Let the required integer be x.
According to question,
x = (-x) – 2, where -x is the additive inverse of x.
⇒ x = -x – 2 ⇒ x + x = -2
⇒ 2x = -2 ⇒ x = —1

We can take any two negative integers, i.c., -2 and -4.
∴ Sum = -2 + (-4) = -2 – 4 = -6,
which is less than both -2 and -4.

Two distinct integers whose sum is equal to one of the integer, then one must be 0 in them.
Let us take 0 and 4.
∴ Sum =0 + 4 = 4.

Since, the integer lying on right is greater than the integer lying on left.
∴ In all of the given cases (a), (b) and (c), we can compare by using the number line by observing which one of the given integers lie on the right or left.

On observing the given expression, 1 + 2 – 3 + 4 + 5 – 6 – 7 + 8 – 9 = -5, we noticed that (-7) should be replaced by (+7) to get a result  of 9.
Thus, 1 + 2 – 3 + 4 + 5 – 6 + 7 + 8 – 9
= (1 + 2 + 4 + 5 + 7 + 8) – (3 + 6 + 9)
= 27 – 18 = 9

Ascending order of given integers is, -5, -3, -2, 0, 1, 4

Descending order of given integers is, 0, -1, -3, -4, -6

We have, 6 + 0 = 6,
6 – 0 = 6
∴ The required two integers are 6 and 0.

The required five integers which are less than -100 but greater than -150 are -101, -102, -103, -104 and -105.

There are many pairs of integers which are at the same distance from 2 i.e.,
(1, 3), (0, 4), (-1, 5) and (-2, 6)

Let the required integer be x.
According to question,
x + (-42) = 30
⇒ x – 42 = 30
⇒ x = 30 + 42 = 72

Let the required integer be x.
According to question,
x + (-90) = -80
⇒ x – 90 = – 80 ⇒ x = -80 + 90 = 10

(a) If we are at 8 on the number line, then to reach the integer -5, we must move towards the left on the number line.
(b) If we are at 8 on the number line, then to reach the integer 11, we must move towards the right on the number line.
(c) If we are at 8 on the number line, then to reach the integer 0, we must move towards the left on the number line.

(a) We want to know an integer 4 more than -5.
So, we start from -5 and proceed 4 steps to the right, then we obtain -1 as shown below.
Hence, 4 more than -5 is -1.
(b) We want to know an integer 3 less than 2.
So, we start from 2 and proceed 3 steps to the left, then we obtain -1 as shown below.
Hence, 3 less than 2 is -1.
(c) We want to know an integer 2 less than -2. So, we start from -2 and proceed 2 steps to the left, then we obtain -4 as shown below.
Hence, 2 less than -2 is -4.

We have,
49 – (-40) – (-3) + 69
= 49 + 40 + 3 + 69 = 161

We have, [(-2100) + (-2001)]
= [-2100 – 2001]
= -4101
Required difference = -4101 – (-5308) = -4101 + 5308 = 1207