Below are the details you should keep in mind when solving the Integers chapter EXERCISE 1.3. The questions are easy to solve but you need to have a closer look at question 5, 6 and 7.
In this Class 7 Maths chapter on Integers primarily exercise 1.3, you’ll learn two big ideas. First, you’ll get to know how to do multiplication with integers. Second, you’ll understand the special rules for multiplying integers. Also, you’ll find out that when you divide integers, the order can’t be switched around. Plus, dividing any number by 1 doesn’t change the number.
- Division Order Matters: When you divide one integer by another, the order is important. For example, 6÷3 is not the same as 3÷6.
- No Division by Zero: You can’t divide a number by zero. It’s like a rule in math that you just can’t break.
- Dividing by 1: Any number divided by 1 stays the same. So, 7÷1 is still 7.
- Dividing by -1: When you divide a number by -1, it becomes the opposite. So, 7 ÷ −1 becomes -7.
| Class: | 7 |
| Chapter and Exercise: | 1 – 1.3 |
| Chapter Name: | Integers |
| Academic Session: | 2023-24 (CBSE) |
| Medium: | English |
| Book Name: | NCERT: Mathematics (Textbook for Class VII) |
| Edition: | December 2022 Agrahayana 1944 (latest) |
| Page Number: | 18 |
NCERT Class 7 Maths Chapter 1 Other Exercises
NCERT Solutions Class 7 Maths Chapter 1 Exercise 1.3 Integers
Question 1: Evaluate each of the following:
(a) (-30) ÷ 10:
-30 ÷ 10 = -3
(b) 50 ÷ (-5):
50 ÷ -5 = -10
(c) (-36) ÷ (-9):
-36 ÷ -9 = 4
(d) (-49) ÷ 49:
-49 ÷ 49 = -1
(e) 13 ÷ [(-2) + 1]:
13 ÷ (-2 + 1) = 13 ÷ -1 = -13
(f) 0 ÷ (-12):
0 ÷ -12 = 0
(g) (-31) ÷ [(-30) + (-1)]:
-31 ÷ (-30 – 1) = -31 ÷ -31 = 1
(h) [(-36) ÷ 12] ÷ 3:
(-36 ÷ 12) ÷ 3 = -3 ÷ 3 = -1
(i) [(-6) + 5] ÷ [(-2) + 1]:
(-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.
(a) a = 12, b = -4, c = 2:
Left-hand side (LHS): a ÷ (b + c) = 12 ÷ (-4 + 2) = 12 ÷ (-2) = -6.
Right-hand side (RHS): (a ÷ b) + (a ÷ c) = (12 ÷ -4) + (12 ÷ 2) = -3 + 6 = 3.
LHS ≠ RHS: -6 ≠ 3.
(b) a = -10, b = 1, c = 1:
LHS: a ÷ (b + c) = -10 ÷ (1 + 1) = -10 ÷ 2 = -5.
RHS: (a ÷ b) + (a ÷ c) = (-10 ÷ 1) + (-10 ÷ 1) = -10 – 10 = -20.
LHS ≠ RHS: -5 ≠ -20.
Question 3: Fill in the blanks:
(a) 369 ÷ _____ = 369:
369 ÷ 1 = 369
Blank = 1 (since any number divided by 1 is the number itself).
(b) (-75) ÷ _____ = -1:
(-75) ÷ 75 = -1
Blank = 75 (since -75 divided by 75 gives -1).
(c) (-206) ÷ _____ = 1:
(-206) ÷ 206 = 1
Blank = -206 (since -206 divided by -206 gives 1).
(d) -87 ÷ _____ = 87:
-87 ÷ (-1) = 87
Blank = -1 (since -87 divided by -1 gives 87).
(e) _____ ÷ 1 = -87:
-87 ÷ 1 = -87
Blank = -87 (since any number divided by 1 is the number itself).
(f) _____ ÷ 48 = -1:
-48 ÷ 48 = -1
Blank = -48 (since -48 divided by 48 gives -1).
(g) 20 ÷ _____ = -2:
20 ÷ (-10) = -2
Blank = -10 (since 20 divided by -10 gives -2).
(h) _____ ÷ (4) = -3
-12 ÷ (4) = -3:
Blank = -12 (since -12 divided by 4 gives -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.
(6, -2) [given example]
(-9, 3) [since -9 ÷ 3 = -3]
(15, -5) [since 15 ÷ -5 = -3]
(-12, 4) [since -12 ÷ 4 = -3]
(21, -7) [since 21 ÷ -7 = -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?
Temperature decreases by 2°C per hour.
To find when the temperature reaches -8°C:
Initial temperature = 10°C.
Final temperature = -8°C.
Total temperature drop = 10°C – (-8°C) = 18°C.
Time to drop = Total drop / Rate of drop = 18°C / 2°C per hour = 9 hours.
Since the change starts at 12 noon, the temperature will be -8°C at 12 noon + 9 hours = 9 PM.
To find the temperature at midnight:
From 12 noon to midnight = 12 hours.
Temperature drop by midnight = 12 hours * 2°C/hour = 24°C.
Temperature at midnight = 10°C – 24°C = -14°C.
The temperature would be 8°C below zero at 9 PM. The temperature at midnight would be -14°C.
Question 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?
For each correct answer, Radhika earns 3 marks. So, for 12 correct answers, she earns 12 * 3 = 36 marks.
Since her total score is 20 marks, and each incorrect answer deducts 2 marks, the number of incorrect answers can be found from the difference.
Total marks from incorrect answers = 36 – 20 = 16 marks.
Number of incorrect answers = 16 / 2 = 8.
Radhika attempted 8 questions incorrectly.
(ii) Mohini scores –5 marks in this test, though she has got 7 correct answers. How many questions has she attempted incorrectly?
For each correct answer, Mohini earns 3 marks. So, for 7 correct answers, she earns 7 * 3 = 21 marks.
Since her total score is -5 marks, and each incorrect answer deducts 2 marks, the number of incorrect answers can be found from the difference.
Total marks from incorrect answers = 21 – (-5) = 26 marks.
Number of incorrect answers = 26 / 2 = 13.
Mohini attempted 13 questions incorrectly.
Question 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.
The total distance the elevator needs to travel = 10 m (above ground) + 350 m (below ground) = 360 m.
Since the elevator descends at a rate of 6 m/min, the time taken to descend 360 m is:
Time = Distance / Speed = 360 m / 6 m/min = 60 minutes.
It will take the elevator 60 minutes to reach –350 m.
