NCERT Exemplar Class 6 Maths Integers Solution: NCERT Exemplar Solution Class 6 Maths Chapter 3 Integers Full Explanation. NCERT Exemplar Class 6 Maths – Chapter 3 Integers. NCERT Exemplar Class 6 Maths Integers Solution by Expert.
NCERT Exemplar Class 6 Maths Integers Solution
Question 1:
Every integer less than 0 has the sign
(A) +
(B) –
(C) ×
(D) ÷
Solution: The correct answer is (B).
Every integer less than 0 has the sign (-) Negative.
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: The correct answer is (A).
The integer ‘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: The correct answer is (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: The correct answer is (A).
integers lying between –1 and 1
Question 5:
Number of whole numbers lying between –5 and 5 is
(A) 10
(B) 3
(C) 4
(D) 5
Solution: The correct answer is (D).
Whole number starts from zero so, 5 whole number lying between -5 and 5.
Question 6:
The greatest integer lying between –10 and –15 is
(A) –10
(B) –11
(C) –15
(D) –14
Solution: The correct answer is (B).
The greatest integer lying between –10 and –15 is -11.
Question 7:
The least integer lying between –10 and –15 is
(A) –10
(B) –11
(C) –15
(D) –14
Solution: The correct answer is (D).
The least integer lying between –10 and –15 is -14.
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: The correct answer is (B).
To the right of 0, on the number line 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: The correct answer is (B).
(–3, –5) is the pair of integers whose first integer is not on the left of the other integer on the number line.
Question 10:
The integer with negative sign (–) is always less than
(A) 0
(B) –3
(C) –1
(D) –2
Solution: The correct answer is (A).
The integer with negative sign (–) is always less than 0.
Question 11:
An integer with positive sign (+) is always greater than
(A) 0
(B) 1
(C) 2
(D) 3
Solution: The correct answer is (A).
An integer with positive sign (+) is always greater than 0.
Question 12:
The successor of the predecessor of –50 is
(A) –48
(B) –49
(C) –50
(D) –51
Solution: The correct answer is (C).
The successor of the predecessor of –50 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: The correct answer is (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: The correct answer is (A).
On the number line
if negative sign increase, then temperature decrease.
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: The correct answer is (D).
Depend on the numerical value of the integers, when a negative integer is subtracted from another negative integers 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: The correct answer is (C).
When an integer is added to itself the sum is greater than the integers true 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: The correct answer is (B).
–4°C to 8°C is shows the maximum rise in temperature.
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, The smallest natural number is 1.
Question 19:
Zero is not an integer as it is neither positive nor negative.
Solution: False, zero is an integer as it is neither positive nor negative.
Question 20:
The sum of all the integers between –5 and –1 is –6.
Solution: False, The sum of all the integers between –5 and –1 is –9.
( – 4 ) + ( – 3 ) + ( – 2 ) = -9
Question 21:
The successor of the integer 1 is 0.
Solution: False, the successor of the 1 is 2.
Question 22:
Every positive integer is larger than every negative integer.
Solution: The statement is true.
Question 23:
The sum of any two negative integers is always greater than both
the integers.
Solution: False, 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: The statement is true.
Question 25:
The sum of any two positive integers is greater than both the integers.
Solution: The statement is true.
Question 26:
All whole numbers are integers.
Solution: The statement is true.
Question 27:
All integers are whole numbers.
Solution: False, all integer is not a whole number.
Question 28:
Since 5 > 3, therefore –5 > –3
Solution: False, since 5 > 3, Therefore – 5 > – 3.
Question 29:
Zero is less than every positive integer.
Solution: The statement is true.
Question 30:
Zero is larger than every negative integer.
Solution: The statement is true.
Question 31:
Zero is neither positive nor negative.
Solution: The statement is true.
Question 32:
On the number line, an integer on the right of a given integer is always larger than the integer.
Solution: The statement is true.
Question 33:
–2 is to the left of –5 on the number line.
Solution: False, – 2 is to the right of -5 on the number line.
Question 34:
The smallest integer is 0.
Solution: False, the smallest is not zero.
Question 35:
6 and –6 are at the same distance from 0 on the number line.
Solution: The statement is true.
Question 36:
The difference between an integer and its additive inverse is always even.
Solution: The statement is true.
Question 37:
The sum of an integer and its additive inverse is always zero.
Solution: The statement is true.
Question 38:
The sum of two negative integers is a positive integer.
Solution: False, the sum of two negative integer is negative integer Like as (-5) + (-4) = – 9
Question 39:
The sum of three different integers can never be zero.
Solution: False, the sum of three different integers may be zero.
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: On the number line, –15 is to the Left of zero.
Question 41:
On the number line, 10 is to the ______ of zero.
Solution: On the number line, 10 is to the Right of zero.
Question 42:
The additive inverse of 14 is ______.
Solution: The additive inverse of 14 is -14.
Question 43:
The additive inverse of –1 is ______.
Solution: The additive inverse of –1 is 1.
Question 44:
The additive inverse of 0 is ______.
Solution: The additive inverse of 0 is 0.
Question 45:
The number of integers lying between –5 and 5 is ______.
Solution: The number of integers lying between –5 and 5 is 9.
Question 46:
(–11) + (–2) + (–1) = _____.
Solution: (–11) + (–2) + (–1) = -14.
Question 47:
_____ + (–11) + 111 = 130
Solution: 30 + (–11) + 111 = 130
Question 48:
(–80) + 0 + (–90) = ______
Solution: (–80) + 0 + (–90) = -170
Question 49:
______ –3456 = –8910
Solution: – 5454 –3456 = –8910
In questions 50 to 58, fill in the blanks using <, = or > :
Question 50:
(–11) + (–15) _____ 11 + 15
Solution: (–11) + (–15) < 11 + 15
Question 51:
(–71) + (+9) _____ (–81) + (–9)
Solution: (–71) + (+9) > (–81) + (–9)
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) = (–3) + (–4) + (–6)
Question 57:
0 _______ –2
Solution: 0 > –2
Question 58:
1 + 2 + 3 _______ (–1) + (–2) + (–3)
Solution: 1 + 2 + 3 > (–1) + (–2) + (–3)
Question 59:
Match the items of Column I with that of Column II:
Column I |
Column II |
(i) The additive inverse of +2
(ii) The greatest negative integer (iii) The greatest negative even integer (iv) The smallest integer greater than every negative integer (v) Sum of predecessor and successor of –1 |
(A) 0
(B) –2 (C) 2 (D) 1 (E) –1 |
Solution:
(i) The additive inverse of +2 is = (B) -2
(ii) The greatest negative integer = (B) -2
(iii) The greatest negative even integer = (B) -2
(iv) The smallest integer greater than every negative integer = (a) 0.
(v) Sum of predecessor and successor of –1 = (B) -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 = -5
(b) (–20) + (–5) = -25
(c) 70 + (–20) + (–30) = 20
(d) –50 + (–60) + 50 = -60
(e) 1 + (–2) + (– 3) + (– 4) = 1 – 2 – 3 – 4 = 8
(f) 0 + (– 5) + (– 2) = 0 – 5 -2 = -7
(g) 0 – (–6) – (+6) = 0 + 6 – 6 = 0
(h) 0 – 2 – (–2) = 0 – 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 indicate that +200
(b) 100 m below sea level indicate that -100
(c) 10 m above sea level indicate that +10
(d) sea level is 0 (Zero)
Question 62:
Write the opposite of each of the following:
(a) Decrease in size
(b) Failure
(c) Profit of Rs.10
(d) 1000 A.D.
(e) Rise in water level
(f) 60 km south
(g) 10 m 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 Rs.100 in the Bank account
(k) 20°C rise in temperature.
Solution:
(a) Decrease in size in opposite to the increase in size.
(b) Failure in opposite to the success.
(c) Profile of Rs. 10 is opposite to the loss of Rs. 10.
(d) 1000 A. D. is opposite to the 1000 B. C.
(e) Rise in water level is opposite to the fall in water level.
(f) 60KM south is opposite to the 60KM North.
(g) 10m above the danger mark of river ganga is opposite to the 10m below the danger mark of river ganga.
(h) 20 m below the danger mark of the river Brahmaputra is opposite to the 20m above the danger mark of river Brahmaputra.
(i) Winning by a margin of 2000 votes is opposite the losing by a margin 2000 votes.
(j) Depositing Rs. 100 in the bank account is opposite to the withdrawing Rs. 100 in the bank account.
(k) 20°C rise in temperature is opposite to the 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 of a place at 12:00 noon was +5°C and increased in temperature in the first Hours is +3°C i.e., 8°C and decrease in temperature for second hours is 1°C i.e., 7°C.4
Question 64:
Write the digits 0, 1, 2, 3, …, 9 in this order and insert ‘+’ or ‘–’ between them to get the result 3.
Solution: 0,-1,-2,-3,-4,-5,-6,+7,+8,+9 by adding this number like as +9 – 6 = 3 + 7 – 4 =3 we get 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) we find sum as 7 like as +1, +6 = + 7, + 3 + 6 – 2 = 7.
Question 67:
Write the integer which is 4 more than its additive inverse.
Solution: 2 is the integer which is 4 more than its additive inverse and the additive inverse +2.
Question 68:
Write the integer which is 2 less than its additive inverse.
Solution: -1 is the integers which is 2 less than its additive inverse and additive inverse is 1.
Question 69:
Write two integers whose sum is less than both the integers.
Solution: -5 and -3 are the two integers whose sum is less than both the inverse.
Question 70:
Write two distinct integers whose sum is equal to one of the integers.
Solution: 0, 4 these two-district integer whose sum is equal to one of the integers.
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:
(a) Assume two negative integer is -1 and -2.
–1 is greater than -2.
(b) Two positive integer is +1 and +2
+2 is greater than +1.
(c) +1 is position integer and -1 is negative integer +1 is greater than -1.
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:
Question 73:
Arrange the following integers in the ascending order :
–2, 1, 0, –3, +4, –5
Solution: -5, -3, -2 0, 1, 4 these number are arranging descending order.
Question 74:
Arrange the following integers in the descending order :
–3, 0, –1, –4, –3, –6
Solution: 0., -1, -3, -3, -4, -6 these number are arranging descending order.
Question 75:
Write two integers whose sum is 6 and difference is also 6.
Solution: 0, 6 these two integers whose sum is 6 and difference is also 6.
Question 76:
Write five integers which are less than –100 but greater than –150.
Solution: -101, -110, -120, -125, -130 are the integer which are less than -100 but greater than -150.
Question 77:
Write four pairs of integers which are at the same distance from 2 on the number line.
Solution: (-2, 6), (1, 3), (0, 4), (-1, 5) are the four pairs of integers which are at the same distance from 2 on the number line.
Question 78:
The sum of two integers is 30. If one of the integers is –42, then find the other.
Solution:
The sum of the two integer is 30 and one is -42 then the other is x – 42=30
x =72.
Then the other is 72 ( we assume X for calculation)
Question 79:
Sum of two integers is –80. If one of the integers is –90, then find the other.
Solution: Sum of two integers is -80 and one integers is -90 .
X – 90 = -80
X = 10 then the other is 10
(We assume x for easy calculation)
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) -5 is to the left of 8.
(b) 11 is to the right of 8.
(c) 0 is to the left of 8.
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) 4 more than -5
-5 + 4 = -1
(b) 8 less than 2
2 – 3 = -1
(c) 2 less than -2
-2 – 2 = -4
Question 82:
Find the value of 49 – (–40) – (–3) + 69
Solution:
= 49 – (-40) – (-3) + 69
= 49 + 40 + 3 + 69
= 161
Question 83:
Subtract –5308 from the sum [(–2100) + (–2001)]
Solution:
= [(-2100) + (-2001)] – (-5308)
= -4101 + 5308
= 1207
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