NCERT Exemplar Class 6 Maths Chapter 3 Integers are part of NCERT Exemplar Class 6 Maths. Here we have given NCERT Exemplar Class 6 Maths Solutions Chapter 3 Integers.
NCERT Exemplar Class 6 Maths Solutions Chapter 3 Integers
Directions: In questions 1 to 17, only one of the four options is correct. Write the correct one.
Question 1.
Every integer less than 0 has the sign
(A) +
(B) –
(C) ×
(D) +
Solution:
(B): Every integer which is less than 0 has negative sign.
Question 2.
The integer ‘5 units to the right of 0 on the number line’ is
(A) +5
(B) -5
(C) +4
(D) -4
Solution:
(A): The integer which is 5 units to the right of 0 on the number line is + 5.
Question 3.
The predecessor of the integer -1 is
(A) 0
(B) 2
(C) – 2
(D) 1
Solution:
(C) : The predecessor of the integer – 1 is – 2.
Question 4.
Number of integers lying between -1 and 1 is
(A) 1
(B) 2
(C) 3
(D) 0
Solution:
(A) : Only 1 integer lies between -1 and 1 i.e., 0.
Question 5.
Number of whole numbers lying between -5 and 5 is
(A) 10
(B) 3
(C) 4
(D) 5
Solution:
(D) : There are 5 whole numbers lying between -5 and 5 i.e., 0, 1, 2, 3 and 4.
Question 6.
The greatest integer lying between -10 and -15 is
(A) -10
(B) -11
(C) -15
(D) -14
Solution:
(B) : -11 is the greatest integer lying between -10 and -15.
Question 7.
The least integer lying between -10 and -15 is
(A) -10
(B) -11
(C) -15
(D) -14
Solution:
(D) : -14 is the least integer lying between -10 and -15.
Question 8.
On the number line, the integer 5 is located
(A) to the left of 0
(B) to the right of 0
(C) to the left of 1
(D) to the left of -2
Solution:
(B):
The above number line shows that the integer 5 is located to the right of 0.
Question 9.
In which of the following pairs of integers, the first integer is not on the left of the other integer on the number line?
(A) (-1, 10)
(B) (-3, -5)
(C) (-5, -3)
(D) (-6,0)
Solution :
On observing all the options by using a number line, we get that there is only one pair (-3, -5) in which the first integer is not on the left of the other integer.
Question 10.
The integer with negative sign (-) is always less than
(A) 0
(B) -3
(C) -1
(D) -2
Solution:
(A) : All the negative integers are less than 0.
Question 11.
An integer with positive sign (+) is always greater than
(A) 0
(B) 1
(C) 2
(D) 3
Solution:
(A): All the positive integers are greater than 0.
Question 12.
The successor of the predecessor of -50 is
(A) -48
(B) -49
(C) -50
(D) -51
Solution:
(C) : The predecessor of -50 is -51 and the successor of -51 is -50.
Question 13.
The additive inverse of a negative integer
(A) is always negative
(B) is always positive
(C) is the same integer
(D) zero
Solution:
(B) : The additive inverse of a negative integer is always positive.
Question 14.
Amulya and Amar visited two places A and B respectively in Kashmir and recorded the minimum temperatures on a particular day as -4°C at A and -1 °C at B. Which of the following statement is true?
(A) A is cooler than B
(B) B is cooler than A
(C) There is a difference of 2°C in the temperature
(D) The temperature at A is 4°C higher than that at B.
Solution:
(A) : -4°C < -1° C
[ ∵ -4 lies on the left of -1 on the number line]
Thus, A is cooler than B.
Question 15.
When a negative integer is subtracted from another negative integer, the sign of the result
(A) is always negative
(B) is always positive
(C) is never negative
(D) depends on the numerical value of the integers
Solution:
(D) : When a negative integer is subtracted from another negative integer, the sign of the result depends on the numerical value of the integers.
Question 16.
The statement “When an integer is added to itself, the sum is greater than the integer” is
(A) always true
(B) never true
(C) true only when the integer is positive
(D) true for non-negative integers
Solution:
(C): When an integer is added to itself, the sum is greater than the integer only when the integer is positive.
Question 17.
Which of the following shows the maximum rise in temperature?
(A) 0°C to 10°C
(B) -4°C to 8°C
(C) -15°C to -8°C
(D) -7°C to 0°C
Solution:
(B): (A) Rise in temperature = (10 – 0)°C = 10°C
(B) Rise in temperature = (8 – (-4))°C = (8 + 4)°C = 12°C
(C) Rise in temperature = (-8 – (-15))°C = (-8 + 15)°C = 7°C
(D) Rise in temperature = (0 – (-7))°C = (0 + 7)°C = 7° C
Thus, option (B) has maximum rise in temperature.
Directions: In questions 18 to 39, state whether the given statements are true (T) or false (F).
Question 18.
The smallest natural number is zero.
Solution:
False
Since, 1 is the smallest natural number.
Question 19.
Zero is not an integer as it is neither positive nor negative.
Solution:
False
0 is neither positive nor negative, but it is an integer.
Question 20.
The sum of all the integers between -5 and -1 is -6.
Solution:
False
-4, -3 and -2 lie between -5 and -1 and their sum is (-4) + (-3) + (-2) = -4 – 3 – 2 = -9
Question 21.
The successor of the integer 1 is 0.
Solution:
False
∵ 0 is the predecessor of 1.
Question 22.
Every positive integer is larger than every negative integer.
Solution:
True
Since positive integers lies on the right side of 0 and negative integers lies on the left side of 0 and the integers lying on the right are always greater.
Question 23.
The sum of any two negative integers is always greater than both the integers.
Solution:
False
Since, the sum of any two negative integers is always smaller than both the integers.
Question 24.
The sum of any two negative integers is always smaller than both the integers.
Solution:
True
Question 25.
The sum of any two positive integers is greater than both the integers.
Solution:
True
Question 26.
All whole numbers are integers.
Solution:
True
Integers are the collection of 0, positive integers and negative integers.
Whole numbers are the collection of 0 and positive integers.
∴ All whole numbers are integers.
Question 27.
All integers are whole numbers.
Solution:
False
Integers are the collection of 0, positive integers and negative integers.
Whole numbers are the collection of 0 and positive integers.
∴ All integers are not whole numbers.
Question 28.
Since 5 > 3, therefore -5 > -3.
Solution:
False
Since, 5 lies on the right of 3 on the number line
∴ 5 > 3
And -3 lies on the right of -5 on the number line,
∴ -3 > -5.
Question 29.
Zero is less than every positive integer.
Solution:
True
Since, zero lies on the left side of every positive integer on the number line. Therefore, zero is less than every positive integer.
Question 30.
Zero is larger than every negative integer.
Solution:
True
Since, zero lies on the right side of every negative integer on the number line. Therefore, zero is larger than every negative integer.
Question 31.
Zero is neither positive nor negative.
Solution:
True
Question 32.
On the number line, an integer on the right of a given integer is always larger than the integer.
Solution:
True
Question 33.
-2 is to the left of -5 on the number line.
Solution:
False
Since, -2 lies on the right of -5 on the number line.
Question 34.
The smallest integer is 0.
Solution:
False
Since, zero is greater than all the negative integers.
∴ 0 is not the smallest integer.
Question 35.
6 and -6 are at the same distance from 0 on the number line.
Solution:
True
The integer 6 is 6 units to the right of 0 and the integer -6 is 6 units to the left of 0.
Thus, 6 and -6 are at the same distance from 0 on the number line.
Question 36.
The difference between an integer and its additive inverse is always even.
Solution:
True
Let a be any integer and -a is its additive inverse.
∴ Difference = a – (-a) = a + a = 2a, which is an even number.
Question 37.
The sum of an integer and its additive inverse is always zero.
Solution:
True
Let a be any integer and -a is its additive inverse.
∴ Sum = a + (-a) = a – a = 0.
Question 38.
The sum of two negative integers is a positive integer.
Solution:
False
Since, the sum of two negative integers is always negative.
Question 39.
The sum of three different integers can never be zero.
Solution:
False
Let -3, 1, 2 are three different integers.
∴ Sum = (-3) + 1+ 2 = -3 + 3 = 0
Directions: In questions 40 to 49, fill in the blanks to make the statements true.
Question 40.
On the number line, -15 is to the ____ of zero.
Solution:
Left
Question 41.
On the number line, 10 is to the ____ of zero.
Solution:
Right
Question 42.
The additive inverse of 14 is .
Solution:
-14: Additive inverse of an integer is obtained by changing the sign of the integer.
∴ Additive inverse of 14 is -14.
Question 43.
The additive inverse of -1 is ____ .
Solution:
1
Question 44.
The additive inverse of 0 is
Solution:
0
Question 45.
The number of integers lying between -5 and 5 is ____ .
Solution:
9 : The integers lying between -5 and 5 are -4, -3, -2, -1, 0, 1, 2, 3, 4 i.e., 9 in number.
Question 46.
(-11) + (-2) + (-1) = ____ .
Solution:
-14 : (-11) + (-2) + (-1) = -11 – 2 -1 = -14
Question 47.
____ + (-11) + 111 = 130
Solution:
30
Question 48.
(-80) + 0 + (-90) =
Solution:
-170 : (-80) + 0 + (-90) = -80 + 0 – 90 = -170
Question 49.
_____ -3456 = -8910
Solution:
-5454
Directions: In questions 50 to 58, fill in the blanks using <, = or >.
Question 50.
(-11)+ (-15) ____ 11 + 15
Solution:
< : (-11) + (-15) = -11 – 15 = -26
11 + 15 = 26 and -26 < 26
Question 51.
(-71) + (+9) ____ (-81) + (-9)
Solution:
> : (-71) + (9) = -71 + 9 = -62
(-81) + (-9) = -81 – 9 = -90 and -62 > -90
Question 52.
0 ____ 1
Solution:
< : 0 < 1
Question 53.
-60 ___ 50
Solution:
< : : -60 < 50
Question 54.
-10 ___ -11
Solution:
> : -10 > -11
Question 55.
-101 ___ -102
Solution:
> : -101 > -102
Question 56.
(-2) + (-5) + (-6) ___ (-3) + (-4) + (-6)
Solution:
= : (-2) + (-5) + (-6) = -2 – 5 – 6 = -13 (-3) + (-4) + (-6) = -3 – 4 – 6—13 And-13 = -13
Question 57.
0 ___ -2
Solution:
> : 0 > -2
Question 58.
1 + 2 + 3 ____ (-1) + (-2) + (-3)
Solution:
> : 1 + 2 + 3 = 6
(-1) + (-2) + (-3) = -1 – 2 – 3 = -6
And 6 > -6
Question 59.
Match the items of Column I with that of Column II:
| Column I | Column II | |
| (i) | The additive inverse of +2 | (A) 0 |
| (ii) | The greatest negative integer | (B) -2 |
| (iii) | The greatest negative even integer | (C) 2 |
| (iv) | The smallest integer greater than every negative integer | (D) 1 |
| (v) | Sum of predecessor and successor of-1 | (E) -1 |
Solution:
(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
Question 60.
Compute each of the following :
(a) 30+ (-25)+ (-10)
(b) (-20) +(-5)
(c) 70 + (-20) + (-30)
(d) -50+ (-60)+ 50
(e) 1 + (-2) + (-3) + (-4)
(f) 0 + (-5) + (-2)
(g) 0 – (-6) – (+6)
(h) 0 – 2 – (-2)
Solution:
(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
Question 61.
If we denote the height of a place above sea level by a positive integer and depth below the sea level by a negative integer, write the following using integers with the appropriate signs:
(a) 200 m above sea level
(b) 100 m below sea level
(c) 10 m above sea level
(d) sea level
Solution:
(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
Question 62.
Write the opposite of each of the following:
(a) Decrease in size
(b) Failure
(c) Profit of ₹ 10
(d) 1000 AD
(e) Rise in water level
(f) 60 km south
(g) 10m above the danger mark of river Ganga
(h) 20 m below the danger mark of the river Brahmaputra
(i) Winning by a margin of 2000 votes
(j) Depositing ₹ 100 in the Bank account
(k) 20°C rise in temperature.
Solution:
(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.
Question 63.
Temperature of a place at 12:00 noon was +5°C. Temperature increased by 3°C in first hour and decreased by 1°C in the second hour. What was the temperature at 2:00 pm ?
Solution:
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
Question 64.
Write the digits 0, 1, 2, 3, …., 9 in this order and insert ‘+’ or ‘-‘ between them to get the result 3.
Solution:
The digits can be written as
0 – 1 – 2 – 3 – 4 – 5 – 6 + 7 + 8 + 9 = 3
Question 65.
Write the integer which is its own additive inverse.
Solution:
0 is the integer which is its own additive inverse.
Question 66.
Write six distinct integers whose sum is 7.
Solution:
1 + 2 + 3 + 6 + (-2) + (-3) = 7
∴ The six distinct integers are 1, 2, 3, 6, -2 and -3.
Question 67.
Write the integer which is 4 more than its additive inverse.
Solution:
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.
Question 68.
Write the integer which is 2 less than its additive inverse.
Solution:
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
Question 69.
Write two integers whose sum is less than both the integers.
Solution:
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.
Question 70.
Write two distinct integers whose sum is equal to one of the integers.
Solution:
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.
Question 71.
Using number line, how do you compare
(a) two negative integers?
(b) two positive integers?
(c) one positive and one negative integer?
Solution:
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.
Question 72.
Observe the following:
1 + 2 – 3 + 4 + 5 – 6 – 7 + 8 – 9 = -5 Change one ‘-‘ sign as ‘+’ sign to get the sum 9.
Solution:
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
Question 73.
Arrange the following integers in the ascending order:
-2, 1, 0, -3, 4, -5
Solution:
Ascending order of given integers is, -5, -3, -2, 0, 1, 4
Question 74.
Arrange the following integers in the descending order:
-3, 0, -1, -4, -6
Solution:
Descending order of given integers is, 0, -1, -3, -4, -6
Question 75.
Write two integers whose sum is 6 and difference is also 6.
Solution:
We have, 6 + 0 = 6,
6 – 0 = 6
∴ The required two integers are 6 and 0.
Question 76.
Write five integers which are less than -100 but greater than -150.
Solution:
The required five integers which are less than -100 but greater than -150 are -101, -102, -103, -104 and -105.
Question 77.
Write four pairs of integers which are at the same distance from 2 on the number line.
Solution:
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)
Question 78.
The sum of two integers is 30. If one of the integers is -42, then find the other.
Solution:
Let the required integer be x.
According to question,
x + (-42) = 30
⇒ x – 42 = 30
⇒ x = 30 + 42 = 72
Question 79.
Sum of two integers is -80. If one of the integers is -90, then find the other.
Solution:
Let the required integer be x.
According to question,
x + (-90) = -80
⇒ x – 90 = – 80 ⇒ x = -80 + 90 = 10
Question 80.
If we are at 8 on the number line, in which direction should we move to reach the integer
(a) -5
(b) 11
(c) 0?
Solution:
(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.
Question 81.
Using the number line, write the integer which is
(a) 4 more than-5
(b) 3 less than 2
(c) 2 less than -2
Solution:
(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.
Question 82.
Find the value of 49 – (-40) – (-3) + 69
Solution:
We have,
49 – (-40) – (-3) + 69
= 49 + 40 + 3 + 69 = 161
Question 83.
Subtract -5308 from the sum [(-2100)+ (-2001)]
Solution:
We have, [(-2100) + (-2001)]
= [-2100 – 2001]
= -4101
Required difference = -4101 – (-5308) = -4101 + 5308 = 1207
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