CBSE Class 7 Mathematics/Integers/Chapter 1/Notes/Part 3/NCERT Textbook Solutions

Division of Integers:
When we divide a positive integer by a negative integer, we first divide them as whole numbers and then put a minus sign (-) before the quotient. That is, we get a negative integer.
Examples:
(- 48)÷ 8 = -6

• When we divide a negative integer by a negative integer, we first divide them as whole numbers and then put a positive sign. That is, we get a positive integer.
  Example: (-12) ÷ (-6) = 2
  Properties of Division of Integers:

1. Division is not commutative for whole numbers.
2. For any integer a, a ÷0 is not defined but 0÷a = 0 for a≠0.
3. When we divide a whole number by 1 it gives the same whole number.
4. Division is not associative for 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]
   Answers:
   a) -3
   b) -10
   c) 4
   d) -1
   e) -13
   f) 0
   g) 1
   h) -1
   i) 1
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
   b) a = (-10), b = 1, c = 1
   Answer:
   a) LHS = a ÷ (b + c) = 12 ÷ [(-4) + 2] = 12 ÷ (-2) = -6
   RHS = (a ÷ b) + (a ÷c) = [12 ÷ (-4)] + [12 ÷ 2] = (-3) + 6 = 3
   LHS ≠ RHS, Verified.
   b) LHS = a ÷ (b + c) = (-10) ÷ [1 + 1] = (-10) ÷ 2 = -5
   RHS = (a ÷ b) + (a ÷ c) = [(-10) ÷1] + [(-10) ÷1] = (-10) + (-10) = -20
   LHS ≠ RHS, Verified.
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
   Answers:
   a) 1
   b) 75
   c) -206
   d) -1
   e) -87
   f) -48
   g) -10
   h) -12
4. Write five pairs of integers (a, b) such that a ÷ b = -3. One such pair is (6, -2) because 6 ÷ (-2) = -3
   Answer:
   (-6, 2), (-12, 4), (12, -4), (9, -3), (-9, 3)
5. The temperature at 12 noon was 10℃ above zero. If it decreases at the rate of 2℃ per hour until midnight, at what time would the temperature be 8℃ below zero? What would be the temperature at midnight?
   Answer:
   The temperature at 12 noon = 10℃
   Rate of change of temperature = -2℃
   Temperature at 1 pm = 8℃
   Temperature at 2 pm = 6℃
   Temperature at 3 pm = 4℃
   Temperature at 4 pm = 2℃
   Temperature at 5 pm = 0℃
   Temperature at 6 pm = -2℃
   Temperature at 7 pm = -4℃
   Temperature at 8 pm = -6℃
   Temperature at 9 pm = -8℃
   Temperature at 10 pm = -10℃
   Temperature at 11 pm = -12℃
   Temperature in 12 hours = -14℃
   Therefore, at 9 pm, the temperature will be 8℃ below zero.
   At midnight temperature will be 14℃ below 0.
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?
   Answer:
   Marks given for 1 correct answer = 3
   Marks given for 1 incorrect answer = -2
   i) Radhika’s score = 20 marks
   Marks given for 12 correct answers = 12 × 3 = 36
   Marks obtained for incorrect answers= 20 – 36 = -16
   Number of incorrect answers = (-16) ÷ (-2) = 8
   ii) Mohini’s score = -5
   Marks given for 7 correct answers = 7 × 3 = 21
   Marks obtained for incorrect answers = (-5) – 21 = -26
   Number of incorrect answers = (-26) ÷ (-2) = 13
7. An elevator descends into a mine shaft at the rate of 6m/min. If the descent starts from 10m above the ground level, how long will it take to reach -350m.
   Answer:
   Initial height = 10m
   Final depth = -350m
   The total distance to descend by the elevator = (-350) – (10)
   = (-350) + (-10) = -360m
   Time taken to descend 6m = 1 minute
   Time taken to descend -360m = (-360) ÷ (-6) = 60 minutes = 1 hour