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#### 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 minus 350 m.

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.

#### 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?

Given,

Marks for every correct answer =

Marks for every wrong answer =

(i) According to question,

Marks obtained for correct answers =

Marks obtained for incorrect answers = Total marks – Marks obtained for correct answers

Therefore, Radhika attempted 8 questions incorrectly.

(ii)

According to question,

Marks obtained by Mohini =

Marks obtained for correct answers =

Marks obtained for incorrect answers = Total marks – Marks obtained for correct answers

Therefore, Mohini attempted 13 questions incorrectly.

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#### 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 mid-night?

Given,

Temperature at 12 noon =

Final temperature =

Decrease in temperature =

Time taken for the temperature  to decrease by

Time taken for the temperature  to decrease by

Now,

Time until mignight =

Decrease in temperature in  =

Therefore, temparature at midnight =

Therefore, temperature at mid-night will be  below zero.

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

Five pairs of integers such that  are:

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#### 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

(a) Given,

A number divided by 1 gives the number itself.

(b)

The product is negative, therefore there must be odd number of negative integers.

(c)

A number divided by itself gives 1

(d)

The product is positive, therefore there must be even number of negative integers.

(e)

A number divided by 1 gives the number itself.

(f)

The product is negative, therefore there must be odd number of negative integers.

(g)

The product is negative, therefore there must be odd number of negative integers.

(h)

The product is negative, therefore there must be odd number of negative integers.

#### 2. Verify that 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

(a) a = 12, b = – 4, c = 2

L.H.S =

R.H.S =

Therefore.

Hence verified.

(b) a = (–10), b = 1, c = 1

L.H.S =

R.H.S =

Therefore.

Hence verified.

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(_24)divide5

#### Q. Is   (i) 1 ÷ a = 1?      (ii) a ÷ (–1) = – a? for any integer a. Take different values of a and check.

(i) is true only for .

(ii)

Taking,

Hence, this is true for every integer .

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#### Find:    (a) (–36) ÷ (– 4)        (b) (–201) ÷ (–3)        (c) (–325) ÷ (–13)

When we divide a negative integer by a negative integer, we first divide them as whole numbers and then put a positive sign (+).

(a)

(b)

(c)

#### Find:     (a) 125 ÷ (–25)        (b) 80 ÷ (–5)        (c) 64 ÷ (–16)

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.

(a)

(b)

(c)