Ncert -Class 7- maths -worksheet -Integers
Single Correct Choice Question
1.A boy walks 60m due North and then 75m due South. The position of the boy with respect to his starting point is
(a) 15m due North.
(b) 15m due South.
(c) 135m due North.
(d) 135 due south.
Ans: (b)
Explanation: Let 60m due North be represented by +60, then – 75m represents 75m due South.
On adding, +60 – 75 = -15 (negative)
The position of the man with respect to his starting point= 15m due South
2 The sum of two integers is 7 and their difference is also 7. The value of two integers is
(a) 2 and 5.
(b) 3 and 4.
(c) 5 and 2.
(d) 7 and 0.
Ans: (d)
Explanation:
Let x and y be two integers. Then according to the given question,
x + y = 7 and x – y = 7
On solving, we get
x = 7 and y = 0
3: The difference between a temperature of 70 C above zero and a temperature of 30 C below zero is
(a) 100 C.
(b) 70 C.
(c) 40 C.
(d) 30 C.
Ans: (a)
Explanation:
Difference between a temperature of 70 C above zero and a temperature of 30 C below zero = 70 C – (-30 C) = 100 C
4 The sum of two integers is 136. If one of the integers is 45, then the other integer is
(a) 90.
(b) 91.
(c) 92.
(d) 93.
Ans: (b)
Explanation:
Let the other integer = x , Given x + 45 = 136, Or x = 136 – 45 = 91
5. The sum of two integers is -25. If one of the integers is 25, then the other integer is
(a) 50.
(b) 0.
(c) -25.
(d) -50.
Ans: (d)
Explanation:
Let the other integer = x
Given x + 25 = -25
Or x = -25 – 25 = -50
6. If we add –22 to the difference of –7 and – 17, then we get
(a) -46.
(b) -32.
(c) -12.
(d) -10.
Ans: (c)
Explanation:
(-22) + [(-7) – (-17)] = -22 + (10) = -12
7: The simplified value of the given expression [14 – 3{3 –(7 – 4)} +3(5 + 3 – 2)] is
(a) 12.
(b) 15.
(c) 32.
(d) 34.
Ans: (c)
Explanation:
14 – 3{3 – (7 – 4)} + 3(5 + 3 – 2)
= 14 – 3(3 – 3) + 3(6)
= 14 – 0 + 18 = 32
8: The simplified value of the given expression 12[25 – {5 x 8(11 – 2 x 5)}] is
(a) 140.
(b) 100.
(c) -150.
(d) –180.
Ans: (d)
Explanation:
12[25 – {5 x 8(11 – 2 x 5)}]
= 12[25 – (5 x 8)] = 12[25 – 40] = -180
9 Additive inverse of 15 will be
(a) 1/15.
(b) 15.
(c) -15.
(d) 1/(-15).
Ans: (c)
Explanation:
Additive inverse of a number means the opposite of a number.
Therefore, additive inverse of 15 is –15.
10. Multiplicative inverse of 9 will be
(a) -9.
(b) -3.
(c) 1/9.
(d) 9.
Ans: (c)
Explanation:
Multiplicative inverse of x is 1/x.
11. The product of two integers is –72. If one of them is 12, then the other integer will be
(a) -6.
(b) -2.
(c) 6.
(d) 26.
Ans: (a)
Explanation:
Let the other integer = a
According to the question,
a x 12 = -72
or a = -72/12 = -6
12. The product of two integers is 120. If one of them is -8, then the other integer will be
(a) -20.
(b) -15.
(c) -12.
(d) -10.
Ans: (b)
Explanation:
Let the other integer = a
According to the question,
a x (-8) = 120
or a = 120/(-8) = -15
13. If we add ‘x’ to –25 we get 15, then the value of x is
(a) -35.
(b) -10.
(c) 10.
(d) 40.
Ans: (d)
Explanation:
According to the question,
x + (-25) = 15
or x = 15 + 25 = 40
14: A car traveled North of Delhi by 90km and then to the South by 120km. The position of the car with respect to its starting point is
(a) 30km due North.
(b) 30km due South.
(c) 210km due North.
(d) 210km due south.
Ans: (b)
Explanation:
Let 90km due North be represented by +90, then – 120km represents 120km due South. On adding, +90 – 120 = -30 (negative)
The position of the car with respect to its starting point = 30km due South
15. The opposite of a number 0 is
(a) -0.
(b) -1.
(c) 0.
(d) 1.
Ans: (c)
Descriptive Type Questions
Question : 1
Mohan deposits ₹ 2,000 in his bank account and then withdraws ₹ 1,642 from it the following day. Now, if the withdrawal of the amount from the account is represented by a negative integer, then how will you represent the total amount deposited? Also, Find the balance in Mohan’s account after the withdrawal.
Solution
Withdrawal of these amounts from the account is represented by a negative integer.
Then, the deposit of the amount to the account is represented by a positive integer.
From the above question,
The total amount that is deposited in the bank account by the Mohan = ₹ 2000
The total amount that is withdrawn from the bank account by the Mohan is = – ₹ 1642
Final Balance in Mohan’s account after the withdrawal = amount deposited + amount is withdrawn
= ₹ 2000 + (-₹ 1642)
= ₹ 2000 – ₹ 1642
= ₹ 358
Hence, the total balance in Mohan’s account after the withdrawal is ₹ 358
Question :2
In the following quiz, positive marks are given for every correct answer and negative marks are given for each incorrect answer. If Jack’s scores in the quiz for five successive rounds were 25, – 5, – 10, 10, and 15 so, what was his total at the end?
Solution
From the above question,
Jack’s scores in the five successive rounds are 25, -5, -10, 15 and 10
Hence, Their total score of Jack at the end will be = 25 + (-5) + (-10) + 15 + 10
= 25 – 5 – 10 + 15 + 10
= 50 – 15
= 35 marks
∴ Now, Jack’s total score at the end is 35.
Question : 3
In the city of Srinagar, temperature was – 5°C on Monday, and then it dropped by two °C on Tuesday. What was the temperature of the city of Srinagar on Tuesday? On Wednesday, the temperature rose by 4°C. What was the temperature on this day?
solution
From the above question,
The temperature on Monday at Srinagar is = -5C
The temperature on Tuesday at the city of Srinagar is dropped by 2C = Temperature on Monday – 2C
= -5C – 2C
= -7 celsius
The temperature on Wednesday at the city Srinagar rose by 4C = Temperature on Tuesday + 4C.
= -7C + 4C
= -3 celsius
Thus, the temperature on days Tuesday and Wednesday was found to be -7C and -3C, respectively.
Question :4
Verify a – (– b) is equal to a + b for the following values of alphabets a and b.
(i) a = 21, b = 18 (ii) a = 118, b = 125 (iii) a = 75, b = 84 (iv) a = 28, b = 11
Solution
From the above question,
a = 21 and b = 18
So To verify a – (- b) is equal to a + b
Let us take the Left Hand Side (LHS) = a – (- b)
= 21 – (- 18)
= 21 + 18
= 39
Now, lets take Right Hand Side (RHS) = a + b
= 21 + 18
= 39
By comparing both the LHS and the RHS.
LHS = RHS
39 = 39
Hence, the value of a and b are verified.
(ii) a = 118, b = 125
Answer:-
From the above question,
a = 118 and b = 125
To verify this a – (- b) = a + b
Let us take the Left Hand Side (LHS) = a – (- b)
= 118 – (- 125)
= 118 + 125
= 243
Now, take the Right Hand Side (RHS) = a + b
= 118 + 125
= 243
By comparing both the LHS and the RHS
LHS = RHS
243 = 243
Hence, the values of a and b are verified.
(iii) a = 75, b = 84
Answer:-
From the above question,
a = 75 and b = 84
To verify that the a – (- b) = a + b
Let us take the Left Hand Side (LHS) = a – (- b)
= 75 – (- 84)
= 75 + 84
= 159
Now, the Right Hand Side (RHS) = a + b
= 75 + 84
= 159
By comparing both LHS and RHS, we find that,
LHS = RHS
159 = 159
Hence, the value of a and b is verified as.
(iv) a = 28, b = 11
Answer:-
From the above question,
a = 28 and b = 11
To verify that a – (- b) = a + b
Let us now take Left Hand Side (LHS) = a – (- b)
= 28 – (- 11)
= 28 + 11
= 39
Now, Right Hand Side (RHS) = a + b
= 28 + 11
= 39
By comparing both the LHS and the RHS
LHS = RHS
39 = 39
Hence, the value of a and b are verified.