NCERT Solutions for Class 7 Maths Chapter 1 Integers Exercise 1.4

NCERT Solutions for Class 7 Maths Chapter 1 Integers Ex 1.4

Class 7 Maths Integers Exercise 1.1
Class 7 Maths Integers Exercise 1.2
Class 7 Maths Integers Exercise 1.3
Class 7 Maths Integers Exercise 1.4

Exercise 1.4 Class 7 Maths Question 1.

Evaluate each of the following:

(a) (-30) ÷ 10

(b) 50 ÷ (-5)

(d) (-49) ÷ (49)

(e) 13 ÷ [(-2) + 1]

(f) 0 ÷ (-12)

(g) (-31) ÷ [(-30) + (-1)]

(h) [(-36) ÷ 12] ÷ 3

(i) [(-6) + 5] ÷ [(-2) + 1]

Solution:

(a) (-30) ÷ 10 = \({-30 \over 10} = -3 \)

(b) 50 ÷ (-5) = \({50 \over -5} = -10 \)

(d) (-49) ÷ (49) = \({-49 \over 49} = -1 \)

(e) 13 ÷ [(-2) + 1] = 13 ÷ -1 = \({13 \over -1} = -13 \)

(f) 0 ÷ (-12) = \({0 \over -12} = 0 \)

(g) (-31) ÷ [(-30) + (-1)] = (-31) ÷ (-31) = \({-31 \over -31} = 1 \)

(h) [(-36) ÷ 12] ÷ 3 = \({-36 \over 12} ÷ 3 = -3 ÷ 3 = {-3 \over 3} =-1 \)

(i) [(-6) + 5] + [(-2) + 1] = (-1) – (-1) = \({-1 \over -1} = 1

Exercise 1.4 Class 7 Maths 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

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

Solution:

(a) a = 12, 6 = – 4, c = 2

a ÷ (b + c) = 12 ÷ [(-4) + 2] = 12 ÷ (-2) = \({12 \over -2} = -6 \)

(a ÷ b) + (a ÷ c) = [12 ÷ (-4)] + [12 ÷ 2] =\({12 \over -4} + {12 \over 2}=-3+6=3 \)

Since, (-6) ≠ 3

Hence, a ÷ (b + c) ≠ (a ÷ b) + (a ÷ c)

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

a ÷ (b + c) = (-10) ÷ (1 + 1) =(-10) ÷ 2 = \({-10 \over 2} = -5 \)

(a ÷ b) + (a ÷ c) =[(-10) ÷ 1] + [(-10) ÷ 1] =\({-10 \over1} + {-10 \over 1} = (-10) + (-10) = -20 \)

Since (-5) ≠ (-20)

Hence, a ÷ (b + c) ≠ (a ÷ b) + (a ÷ c)

Exercise 1.4 Class 7 Maths Question 3.

Fill in the blanks:

(a) 369 ÷ ___ = 369

(b) (-75) ÷ ___ = -1

(d) -87 ÷ ___ = -87

(e) ___ ÷ 1 = -87

(g) 20 ÷ ___ = -2

Solution:

(a) 369 ÷ ___ = 369

369 ÷ 1 = 369

(b) (-75) ÷ ___ = -1

(-75) ÷ 75 = -1

(-206) ÷ (-206) = 1

(d) 87 ÷ ___ = 87

-87 ÷ (-1) = 87

(e) ___ ÷ 1 = -87

-87 ÷ 1 = -87

(f) ___ ÷ 48 = -1

(-48) ÷ 48 = -1

(g) 20 + ___ = -2

20 ÷ (-10) = -2

(h) ___ + (4) = -3

(-12) ÷ (4) = -3

Exercise 1.4 Class 7 Maths 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)

24 ÷ (-8) = -3

(b) (-12, 4)

(-12) ÷ 4 = -3

15 ÷ (-5) = -3

(d) (18, -6)

18 ÷ (-6) = -3

(e) (60, -20)

60 ÷ (-20) = -3

Exercise 1.4 Class 7 Maths 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

Initial temperature = 10°C

Final temperature = -8°C (according to question)

Temperature difference = 10°C - (-8°C) = 18°C

Rate of decrease in temperature per hour = 2°C

Time taken in change of temperature from 10°C to -8°C = \( 18 \over 2 \) = 9 hours

∴ Time after 9 hours from 12 noon = 9 pm.

Exercise 1.4 Class 7 Maths 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?

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

Solution:

Given that:

+3 marks are given for each correct answer. (-2) marks are given for each incorrect answer. Zero marks for not attempted questions.

(i) Radhika's marks for 12 correct answers = (+3) × 12 = 36

Total marks obtained by Radhika = 20

∴ Radhika's marks for incorrect answers = 20 – 36 = -16

Number of incorrect answers = \({-16 \over -2} =8 \)

Hence, the required number of incorrect answers = 8

(ii) Marks scored by Mohini = -5

Number of correct answers = 7

∴ Marks obtained by Mohini for 7 correct answers = 7 × (+3) – 21

Marks obtained for incorrect answers = -5 – 21 = (-26)

∴ Number of incorrect answers = (-26) ÷ (-2) = 13

Hence, the required number of incorrect answers – 13.

Exercise 1.4 Class 7 Maths 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 = 350 m + 10 m = 360 m

Rate of descent = 6 m/min.

Total time taken by the elevator =\({360 \over 6} \) = 60 minutes = 1 hour

Hence, the required time = 1 hour.

NCERT Solutions for Class 7 Maths Chapter 1 Integers Exercise 1.4