## Chapter 1 Integers Exercise 1.4

**Question 1: Evaluate each of the following:(a) (–30) ÷ 10 Answer:**

= (-30) ÷ 10

= -3

**(b) 50 ÷ (–5)**

Answer:

Answer:

= (50) ÷ (-5)

= -10

**(c) (–36) ÷ (–9)**

Answer:

Answer:

= (-36) ÷ (-9)

= 4

**(d) (– 49) ÷ (49)**

Answer:

Answer:

= (-49) ÷ 49

= -1

**(e) 13 ÷ [(–2) + 1]**

Answer:

Answer:

= 13 ÷ [(-2) + 1]

= 13 ÷ (-1)

= -13

**(f) 0 ÷ (–12)**

Answer:

Answer:

= 0 ÷ (-12)

= 0

**(g) (–31) ÷ [(–30) + (–1)]**

Answer:

Answer:

= (-31) ÷ [(-30) + (-1)]

= (-31) ÷ [-30 - 1]

= (-31) ÷ (-31)

= 1

**(h) [(–36) ÷ 12] ÷ 3**

Answer:

Answer:

= [(-36) ÷ 12]

= (-36) ÷ 12

= -3

= (-3) ÷ 3

= -1

**(i) [(– 6) + 5)] ÷ [(–2) + 1]**

Answer:

Answer:

= [-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

Answer:

(a) a = 12, b = – 4, c = 2

Answer:

= a ÷ (b + c) ≠ (a ÷ b) + (a ÷ c)

a = 12

b = -4

c = 2

Left Hand Side = a ÷ (b + c)

= 12 ÷ (-4 + 2)

= 12 ÷ (-2)

= -6

Right Hand Side = (a ÷ b) + (a ÷ c)

= (12 ÷ (-4)) + (12 ÷ 2)

= (-3) + (6)

= 3

Comparing LHS and RHS

= -6 ≠ 3

= LHS ≠ RHS

Therefore, the given values are verified.

**(b) a = (–10), b = 1, c = 1**

Answer:

Answer:

= a ÷ (b + c) ≠ (a ÷ b) + (a ÷ c)

a = (-10)

b = 1

c = 1

Left Hand Side = a ÷ (b + c)

= (-10) ÷ (1 + 1)

= (-10) ÷ (2)

= -5

Right Hand Side = (a ÷ b) + (a ÷ c)

= ((-10) ÷ (1)) + ((-10) ÷ 1)

= (-10) + (-10)

= -10 - 10

= -20

Comparing LHS and RHS

= -5 ≠ -20

= LHS ≠ RHS

Therefore, the given values are verified.

**Question 3: Fill in the blanks:**

(a) 369 ÷ _____ = 369

Answer:

(a) 369 ÷ _____ = 369

Answer:

Let the missing integer be x.

= 369 ÷ x = 369

= x = (369/369)

= x = 1

**(b) (–75) ÷ _____ = –1**

Answer:

Answer:

Let the missing integer be x.

= (-75) ÷ x = -1

= x = (-75/-1)

= x = 75

**(c) (–206) ÷ _____ = 1**

Answer:

Answer:

Let the missing integer be x.

= (-206) ÷ x = 1

= x = (-206/1)

= x = -206

**(d) – 87 ÷ _____ = 87**

Answer:

Answer:

Let the missing integer be x.

= (-87) ÷ x = 87

= x = (-87)/87

= x = -1

**(e) _____ ÷ 1 = – 87**

Answer:

Answer:

Let the missing integer be x.

= (x) ÷ 1 = -87

= x = (-87) × 1

= x = -87

**(f) _____ ÷ 48 = –1**

Answer:

Answer:

Let the missing integer be x.

= (x) ÷ 48 = -1

= x = (-1) × 48

= x = -48

**(g) 20 ÷ _____ = –2**

Answer:

Answer:

Let the missing integer be x.

= 20 ÷ x = -2

= x = (20)/ (-2)

= x = -10

**(h) _____ ÷ (4) = –3**

Answer:

Answer:

Let the missing integer be x.

= (x) ÷ 4 = -3

= x = (-3) × 4

= x = -12

**Question 4: Write five pairs of integers (a, b) such that a ÷ b = –3. One such pair is (6, –2) because 6 ÷ (–2) = (–3).**

Answer:

Answer:

1. (15, -5) as, 15 ÷ (-5) = (-3)

2. (-15, 5) as, (-15) ÷ (5) = (-3)

3. (18, -6) as, 18 ÷ (-6) = (-3)

4. (-18, 6) as, (-18) ÷ 6 = (-3)

5. (21, -7) as, 21 ÷ (-7) = (-3)

**Question 5: The temperature at 12 noon was 10°C above zero. If it decreases at the rate of 2**

Answer:

**°**C per hour until midnight, at what time would the temperature be 8°C below zero? What would be the temperature at mid-night?Answer:

Temperature at the beginning = 10

**°**C

Rate of change of temperature = -2

**°**C per hour

Temperature at 1 PM = 10 + (-2) = 8

**°**C

Temperature at 2 PM = 8 + (-2) = 6

**°**C

Temperature at 3 PM = 6 + (-2) = 4

**°**C

Temperature at 4 PM = 4 + (-2) = 2

**°**C

Temperature at 5 PM = 2 + (-2) = 0

**°**C

Temperature at 6 PM = 0 + (-2) = -2

**°**C

Temperature at 7 PM = -2 + (-2) = -4

**°**C

Temperature at 8 PM = -4 + (-2) = -6

**°**C

Temperature at 9 PM = -6 + (-2) = -8

**°**C

Therefore, at 9 PM the temperature will be -8

**°**C.

The temperature at mid-night = -2oC × 12 = -24

**°**C

At midnight temperature will be = 10 + (-24) = -14

**°**C

Therefore, at midnight temperature will 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?

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

Answer:

(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 awarded for 1 correct answer = + 3

Marks awarded for 1 wrong answer = -2

(i) Radhika’s score = 20 marks

Total marks awarded for 12 correct answers = 12 × 3 = 36

Marks awarded for incorrect answers = Total score - Total marks awarded for 12 correct answers

= 20 - 36

= -16

Therefore, the number of incorrect answers made by Radhika = (-16) ÷ (-2) = 8

(ii) Mohini’s score = -5 marks

Total marks awarded for 7 correct answers = 7 × 3 = 21

Marks awarded for incorrect answers = Total score - Total marks awarded for 12 correct answers

= -5 - 21

= -26

Therefore, the number of incorrect answers made by Mohini = (-26) ÷ (-2) = 13

**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.**

Answer:

Answer:

The initial height of the elevator = 10 m

Final depth of elevator = -350 m (as distance descended is denoted by a negative integer]

The total distance to descended by the elevator = (-350) - (10)

= -360 m

Time taken by the elevator to descend -6 m = 1 min

So, time taken by the elevator to descend -360 m = (-360) ÷ (-60)

= 60 minutes

= 1 hour

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