NCERT Solutions Class 7th Maths Chapter – 1 Integers Exercise – 1.3

Question 1. Evaluate each of the following:
(a) (-30) ÷ 10
Solution:
(-30) ÷ 10
= −30 ÷ 10
= -3

(b) 50 ÷ (-5)
Solution:
50 ÷ (-5)
= 50 ÷ −5 
= -10

(c) (-36) ÷ (-9)
Solution:
(-36) ÷ (-9)
= −36 ÷ 9 
= 4

(d) (-49) ÷ (49)
Solution:
(-49) ÷ (49)
= −49 ÷ 49 
= -1

(e) 13 ÷ [(-2) + 1]
Solution:
13 ÷ [(-2) + 1]
= 13 ÷ -1
= -13

(f) 0 ÷ (-12)
Solution:
0 ÷ (-12)
= 0 ÷ −12 
= 0

(g) (-31) ÷ [(-30) + (-1)]
Solution:
(-31) ÷ [(-30) + (-1)]
= (-31) ÷ (-31)
= −31 ÷ −31 
= 1

(h) [(-36) ÷ 12] ÷ 3
Solution:
[(-36) ÷ 12] ÷ 3
= -3 ÷ 3
= -1

(i) [(-6) + 5] ÷ [(-2) + 1]
Solution:
[(-6) + 5] ÷ [(-2) + 1]
= (-1) ÷ (-1)
= −1

Question 2. Verify that: a ÷ (b + c) ≠ (a ÷ b) + (a ÷ c) for each of the following values of a, b and c.

(а) a = 12, b = – 4, c = 2

Solution: 

a = 12, b = – 4, c = 2
a ÷ (b + c) = 12 ÷ [(-4) + 2]
= 12 ÷ (-2) = 12/−2 = -6
(a ÷ b) + (a ÷ c) = [12 ÷ (-4)] + [12 ÷ 2]
= 12/−4 + 12/2 = − 3 + 6 = 3
Since, (-6) + 3
hence ÷ (b + c) + (a ÷ b) + (a ÷ c)

(b) a = (-10), b = 1, c = 1

Solution:

a = (-10), b = 1, c = 1
a ÷ (b + c) = (-10) ÷ (1 + 1)
=(-10) ÷ 2 = −10/2 = -5
(a ÷ b) + (a ÷ c)
=[(-10) ÷ 1] + [(-10) ÷ 1]
=(−10)/1 + (−10)/1
= (-10) + (-10) = -20
Since (-5) ≠ (-20)
Hence, a ÷ (b + c) ≠ (a ÷ b) + (a ÷ c)

Question 3. Fill in the blanks:

(a) 369 ÷ ___ = 369
Solution:
369 ÷ ___ = 369
= 369 ÷ 1
= 369

(b) (-75) ÷ ___ = -1
Solution:
(-75) ÷ ___ = -1
= (-75) ÷ 75
= -1

(c) (-206) ÷ ___ =1
Solution:
(-206) ÷ ___ = 1
= (-206) ÷ (-206)
= 1

(d) -87 ÷ ___ = -87
Solution:
87 ÷ ___ = 87
= -87 ÷ (-1)
= 87

(e) ___ ÷ 1 = -87
Solution:
___ ÷ 1 = -87
= -87 ÷ 1
= -87

(f) ___ ÷ 48 = -1
Solution:
___ ÷ 48 = -1
= (-48) ÷ 48
= -1

(g) 20 + ___ = -2
Solution:
20 + ___ = -2
= 20 ÷ (-10)
= -2

(h) ___ + (4) = -3
Solution:
___ + (4) = -3
= (-12) ÷ (4)
= -3

Question 4. Write five pairs of integers (a, b) such that a ÷ b = -3. One such pair is (6, -2) because 6 + (-2) = -3.

Solution:

(a) (24, -8) because 24 ÷ (-8) = -3
(b) (-12, 4) because (-12) ÷ 4 = -3
(c) (15, -5) because 15 ÷ (-5) = -3
(d) (18, -6) because 18 ÷ (-6) = -3
(e) (60, -20) because 60 ÷ (-20) = -3

Question 5. The temperature at 12 noon was 10°C above zero. If it decreases at the rate of 2°C per hour until midnight, at what time would the temperature be 8°C below zero? What would be the temperature at midnight?

Solution:

Temperature at 12 noon was 10°C above zero i.e. +10°C
Rate of decrease in temperature per hour = 2°C
Number of hours from 12 noon to midnight = 12
∴ Change in temperature in 12 hours
= 12 × (-2°C) = -24°C
∴ Temperature at midnight
= +10°C + (-24°C) = -14°C
Hence, the required temperature at midnight =-14°C
Difference in temperature between + 10°C and -8°C
= +10°C – (-8°C) = +10°C + 8°C = 18°C
Number of hours required = 18^∘C/2^∘C = 9 hours
∴ Time after 9 hours from 12 noon = 9 pm.

(i) Radhika scored 20 marks. If she has got 12 correct answers, how many questions has she attempted incorrectly?

Solution:

Marks given for every correct answer = 3 marks
Marks given for every incorrect answer = -2
Marks for not attempting any question = 0
The total score of Radhika = 20 marks
Number of correct answers given by Radhika = 12 answers
Marks obtained for correct answers = 3 × 12 = 36 marks
Marks obtained for incorrect answers = Total score – Marks obtained for 12 correct answers
= 20 – 36 = -16 marks
Marks obtained for every incorrect answer = -2 marks
Thus, number of incorrect answers = (-16) ÷ (-2) = 8
she attempted 8 incorrect questions

(ii) Mohini scores -5 marks in this test, though she has got 7 correct answers. How many questions has she attempted incorrectly?

Solution:

Total score of Mohini = -5
Number of correct answers given by Mohini = 7
Marks obtained for correct answers = 7 × 3 = 21 marks
Marks obtained for incorrect answers = Total score – marks obtained for correct answers
= – 5 – 21
= – 26
Marks obtained for every incorrect answer = -2 marks
Thus, number of incorrect answers = (-26) ÷ (-2) = 13
she attempted 13 incorrect questions

Question 7. An elevator descends into a nine shaft at the rate of 6 m/min. If the descent starts from 10 m above the ground level, how long will it take to reach -350 m.

Solution:

The present position of the elevator is at 10 in above the ground level.
Distance moved by the elevator below the ground level = 350 m
∴ Total distance moved by the elevator = 10 – (−350) = 360m
Rate of descent = 6 m/min.
Total time taken by the elevator
=360m/6m = 60m
= 60 minutes = 1 hour
Hence, the required time = 1 hour.