![NCERT Solutions for Class 7 Maths Chapter 1 Integers Exercise 1.4
Ex 1.4 Class 7 Maths Question 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]
Solution:
(a) (-30) ÷ 10 = −3010 = -3 50
(b) 50 ÷ (-5) = 50−5 = -10
(c) (-36) ÷ (-9) = −36−9 = 4
(d) (-49) ÷ (49) = −4949 = -1
(e) 13 ÷ [(-2) + 1] = 13 ÷ -1 = 13−1 = -13
(f) 0 ÷ (-12) = 0−12 = 0
(g) (-31) ÷ [(-30) + (-1)] = (-31) ÷ (-31) = −31−31 = 1
(h) [(-36) + 12] ÷ 3 = [−3612] ÷ 3 = -3 ÷ 3
= −33 =-1
(i) [(-6) + 5] + [(-2) + 1] = (-1) – (-1) = −1−1 = 1
Ex 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) = 12−2 = -6
(a ÷ b) + (a ÷ c) = [12 ÷ (-4)] + [12 ÷ 2]
=12−4+122=−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 = −102 = -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)
Ex 1.4 Class 7 Maths Question 3.
Fill in the blanks:
(a) 369 ÷ ___ = 369
(b) (-75) ÷ ___ = -1](https://image.slidesharecdn.com/ncertsolutionsforclass7mathschapter1integersexercise1-201213083542/85/Ncert-solutions-for-class-7-maths-chapter-1-integers-exercise-1-4-1-320.jpg)
Ncert solutions for class 7 maths chapter 1 integers exercise 1.4
- 1. NCERT Solutions for Class 7 Maths Chapter 1 Integers Exercise 1.4 Ex 1.4 Class 7 Maths Question 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] Solution: (a) (-30) ÷ 10 = −3010 = -3 50 (b) 50 ÷ (-5) = 50−5 = -10 (c) (-36) ÷ (-9) = −36−9 = 4 (d) (-49) ÷ (49) = −4949 = -1 (e) 13 ÷ [(-2) + 1] = 13 ÷ -1 = 13−1 = -13 (f) 0 ÷ (-12) = 0−12 = 0 (g) (-31) ÷ [(-30) + (-1)] = (-31) ÷ (-31) = −31−31 = 1 (h) [(-36) + 12] ÷ 3 = [−3612] ÷ 3 = -3 ÷ 3 = −33 =-1 (i) [(-6) + 5] + [(-2) + 1] = (-1) – (-1) = −1−1 = 1 Ex 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) = 12−2 = -6 (a ÷ b) + (a ÷ c) = [12 ÷ (-4)] + [12 ÷ 2] =12−4+122=−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 = −102 = -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) Ex 1.4 Class 7 Maths Question 3. Fill in the blanks: (a) 369 ÷ ___ = 369 (b) (-75) ÷ ___ = -1
- 2. (c) (-206) ÷ ___ =1 (d) -87 ÷ ___ = -87 (e) ___ ÷ 1 = -87 (g) 20 ÷ ___ = -2 Solution: (a) 369 ÷ ___ = 369 = 369 ÷ 1 = 369 (b) (-75) ÷ ___ = -1 = (-75) ÷ 75 = -1 (c) (-206) ÷ ___ = 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 Ex 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) 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 Ex 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 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∘C2∘C= 9 hours ∴ Time after 9 hours from 12 noon = 9 pm. Ex 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:
- 3. 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) Marks obtained by Radhika for 12 correct answers = (+3) × 12 = 36 Marks obtained by Radhika for correct answers = 12 × 3 = 36 Total marks obtained by Radhika = 20 ∴ Marks obtained by Radhika for incorrect answers = 20 – 36 = -16 Number of incorrect answers =(−16)÷(−2)=(−16)(−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. Ex 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 =360m6m/min = 60 minutes = 1 hour Hence, the required time = 1 hour.