Maths solutions for NCERT class 7 chapter 1 Integers exercise 1.3
NCERT maths class 7 Chapter 1 Integers exercise 1.3 solutions are given.
You should study the textbook lesson integers chapter 1 very well.
You should also observe and practice all problems and solutions are given in the textbook.
You can observe the solutions and will be try them in your own method.
Integers exercise 1.3 solutions NCERT maths class 7
Chapter 1
Integers
Exercise 1.3
1. Evaluate each of the following:
a. (- 30) ÷ 10
b. 50 ÷ (- 5)
c. (- 36) ÷ (- 9)
d. (- 49) ÷ (49)
e. 13 ÷ [ (- 2) + 1]
f. 0 ÷ (- 12)
g. (- 31) ÷ [ (- 30) + (- 1)]
h. [ (- 36) ÷ 12] ÷ 3
i. [ (- 6 + 5)] ÷ (- 2) + 1]
Solutions:
a. (- 30) ÷ 10 = – 3
b. 50 ÷ (- 5) = – 10
c. (- 36) ÷ (- 9) = 4
d. (- 49) ÷ (49) – 1
e. 13 ÷ [ (- 2) + 1] = 13 ÷ (- 1) = – 13
f. 0 ÷ (- 12) = 0
g. (- 31) ÷ [ (- 30) + (- 1)] = – 31 ÷ (- 31) = 1
h. [ (- 36) ÷ 12] ÷ 3 = (- 3) ÷ 3 = – 1
i. [ (- 6 + 5)] ÷ [ (- 2) + 1] = (- 1) ÷ (- 1) = 1
Problem 2
2. Verify that a ÷ (b + c) is not equal to (a ÷ b) + (a ÷ c) for each of the following values of a, b and c.
a. a = 12, b = – 4, c = 2
b, a = (- 10), b = 1, c = 1
Solutions:
a. a = 12, b = – 4, c = 2
a ÷ (b + c) = 12 ÷ [ (- 4) + 2]
= 12 ÷ (- 2) = – 6
(a ÷ b) + (a ÷ c) = [ 12 ÷ (- 4)] + [ 12 ÷ 2]
= (- 3) + 6 = 3
Therefore, a ÷ (b + c) is not equal to (a ÷ b) + (a ÷ c)
b, a = (- 10), b = 1, c = 1
a ÷ (b + c) = – 10 ÷ (1 + 1)
= – 10 ÷ 2 = – 5
(a ÷ b) + (a ÷ c) = [(- 10) ÷ 1] + [ (- 10) ÷ 1]
= (- 10) + (- 1) = – 10 – 10 = – 20
Therefore, a ÷ (b + c) is not equal to (a ÷ b) + (a ÷ c)
Problem: 3
3. Fill in the blanks:
a. 369 ÷ ……. = 369
b. (- 75) ÷ ……… = – 1
c. (- 206) ÷ ………. = 1
d. – 87 ÷ ………. = 87
e. ………. ÷ 1 = – 87
f. …….. ÷ 48 = – 1
g. 20 ÷ ……… = – 2
h. ……… ÷ (4) = – 3
Solutions:
a. 369 ÷ 1 = 369
b. (-75) ÷ 75 = – 1
c. (-206) ÷ (-206) = 1
d. – 87 ÷ (-1) = 87
e. – 87 ÷ 1 = – 87
f. – 48 ÷ 48 = – 1
g. 20 ÷ (-10) = – 2
h. – 12 ÷ (4) = – 3
Problem: 4
4. Write five pairs of integers (a, b) such that a ÷ b = – 3. One such pair is (6, -2) because (6 ÷ -2) = (-3).
Solutions:
1. (a, b) = (24, -8)
a ÷ b = 24 ÷ (-8) = – 3
2. (a, b) = (-15, 5)
a ÷ b = – 15 ÷ (5) = – 3
3. (a, b) = (9, -3)
a ÷ b = 9 ÷ (-3) = – 3
4. (a, b) = (-12, 4)
a ÷ b = – 12 ÷ 4 = – 3
5. (a, b) = (21, – 7)
a ÷ b = 21 ÷ (-7) = – 3
Problem: 5
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 be the temperature at mid – night?
Solution:
Initial temperature at noon, 12: 00 = 8° C
Change in temperature per hour = – 2° C
The temperature at 1: 00PM = = 10° C – 2°C = 8°C
The temperature at 2: 00 PM = = 8° C – 2°C = 6°C
The temperature at 3: 00 PM = = 6° C – 2°C = 4°C
The temperature at 4: 00 PM = = 4° C – 2°C = 2°C
The temperature at 5: 00 PM= = 2° C – 2°C = 0°C
The temperature at 6: 00 PM = = 0° C – 2°C = – 2°C
The temperature at 7: 00 PM = – 2° C – 2°C = – 4°C
The temperature at 8: 00 PM = = – 4° C – 2°C = – 6°C
The temperature at 9: 00 PM = = – 6 ° C – 2°C = – 8°C
Therefore, the temperature will be 8°C below 0 at 9: 00 PM.
The temperature at 10: 00 PM = = – 8° C – 2°C = – 10°C
The temperature at 11: 00 PM = = – 10° C – 2°C = – 12°C
The temperature at 12: 00, midnight = – 12° C – 2°C = – 14°C
Therefore, the temperature at midnight will be 14°C below zero.
Solutions for exercise 1.3 NCERT maths class 7
Problem: 6
6. In a class test (+3) marks are given for every correct answer and (-2) marks are given for every incorrect answer and no marks for not attempting any question. i. Radhika scored 20 marks. If she has got 12 correct answers, how many questions has she attempted incorrectly? ii. Mohan scores – 5 marks in this test, though she has got 7 correct answers. How many questions has she attempted incorrectly?
Solution:
Marks obtained for one right answer = 3
Marks obtained for one wrong answer = – 2
i. For Radhika
The marks scored by Radhika = 20
Marks obtained for 12 correct answers = 12 × 3 = 36
Marks obtained for incorrect answers = total score – marks obtained for correct answers = 20 – 36 = – 16
The number of incorrect answers = – 16 ÷ (- 2) = 8
Therefore, she attempted 8 questions incorrectly.
ii. For Mohini
Marks scored by Mohini = – 5
Marks obtained for 7 correct answers = 7 × 3 = 21
Marks obtained for incorrect answers = total score – marks obtained for correct answers = – 5 – 21 = – 26
The number of incorrect answers = – 26 ÷ (-2) = 13
Therefore, she attempted 13 questions incorrectly.
Problem: 7
7. An elevator descends into a mine 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:
Initial height = 10 m
Final depth – – 350
The total distance descended by the elevator = (-360) – (+ 10) = – 360
Time taken by the elevator to descend 6 m = 1 minute
Time taken by the elevator to descend (-360) = – 369 ÷ (-6) = 60 minutes = 1 hour.
Note: Observe the solutions and try them in your own method.