# Integers

## NCERT Exercise 1.4

**Question 1:** Evaluate each of the following:

- `( - 30) ÷10`
- `50 ÷ ( - 5)`
- `( - 36) ÷ ( - 9)`
- `( - 49) ÷ (49)`
- `13 ÷[( - 2) + 1]`
- `0 ÷ ( - 12)`
- `( - 31) ÷ [( - 30) + ( - 1)]`
- `[( - 36)÷12`
- `[( - 6) + 5]÷[( - 2) + 1]`

**Answer:**(a) -3, (b) -10, (c) 4,(d) -1, (e) -13, (f) zero, (g) 1, (h) -3, (i) 1

**Question 2:** Verify that `a ÷ (b +c) ≠ (a ÷b) + (a÷c)` for each of the following values of a, b and c.

(i) `a = 12`, `b = - 4`, `c = 2`

**Answer:** `a ÷ ( b + c)`

`= 12 ÷ ( - 4 + 2) = 12 ÷ ( - 2) = - 6`

Now, `(a÷b) + (a÷c)`

v`= 12 ÷ ( - 4) + 12 ÷ 2`

`= - 3 + 6 = 3`

Results are different in these cases. This shows `a ÷ (b +c) ≠ (a ÷b) + (a÷c)`

(ii) `a = ( - 10)`, `b = 1`, `c = 1`

**Answer:** `a ÷ ( b + c)`

`= - 10 ÷ ( 1 + 1) = - 10 ÷ 2 = - 5`

Now, `(a÷b) + (a÷c)`

`- 10 ÷ 1 + ( - 10) ÷1`

`= ( - 10) + ( - 10) = 20`

Results are different in these cases. This shows `a ÷ (b +c) ≠ (a ÷b) + (a÷c)`

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

- `369 ÷ ……… = 369`
- `( - 75) ÷ ……… = - 1`
- `( - 206) ÷ ……… = 1`
- `– 87 ÷ …… = 87`
- `………… ÷1= - 87`
- `………… ÷ 48 = - 1`
- `20 ÷ …… = - 2`
- `………… ÷ 4 = 3`

**Answer:** (a) 1, (b) 75, (c) -206, (d) -1, (e) -87, (f) -48, (g) -10, (h) 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:** (3, - 1), (9, - 3), (12, - 4), (15, - 5), (- 18, 6)

**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?

**Answer:** Difference in temperatures `= 10 – ( -8) = 10 + 8 = 18`

Time taken for reduction of `8°C = 8÷2 = 4` hours

At 4 PM the temperature would be 8°C below zero.

From 12 noon to midnight, 12 hours elapse

Hence, reduction in temperature `= 12 xx ( -2) = - 24`

Hence, temperature at midnight `= 10 - 24 = - 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 got 12 correct answers, how many questions 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:** Radhika’s score for 12 correct answers `= 12 xx 3 = 36`

Radhika’s score for incorrect answer `= 36 – 20 = 16`

Hence, number of incorrect answer `= 16 ÷ 2 = 8`

Mohini’s score for 7 correct answers `= 7 xx 3 = 21`

Mohini’s score for incorrect answers `= 21 – ( - 5) = 31 + 5 = 26`

Hence, number of incorrect answers `= 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:** Total distance covered `= 10 – ( - 350) = 360 m`

Time taken to cover the distance `= 360 ÷ 6 = 60 min = 1 hour`