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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.

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:

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.     ...

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.

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]

Points to keep in mind:  When we divide a negative integer by a positive integer, we first divide them as whole numbers and then put a minus sign (–) before the quotient. 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. When we divide a negative integer by a negative integer, we first divide them as...
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