**Integers Class 7 Ex. 1.3;**

**New Ncert Solution for Class 7 Maths Chapter 1 Integers Free Solution;**

**Exercise 1.3**

**Question 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]**

**Solution 1:-**

(a) (-30) ÷ 10 = −30/10 = -3 ;

(b) 50 ÷ (-5) = 50/−5 = -10 ;

(c) (-36) ÷ (-9) = −36/−9 = 4 ;

(d) (-49) ÷ (49) = −49/49 = -1 ;

(e) 13 ÷ [(-2) + 1] = 13 ÷ -1 = 13/−1 = -13

(f) 0 ÷ (-12) = 0/−12 = 0 ;

(g) (-31) ÷ [(-30) + (-1)] = (-31) ÷ (-31) = −31/−31 = 1 ;

(h) [(-36) ÷ 12] ÷ 3 = [−(36/12)] ÷ 3 = -3 ÷ 3 = −(3/3) =-1 ;

(i) [(-6) + 5] ÷ [(-2) + 1] = (-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.**

**(а) a = 12, b = – 4, c = 2 ;**

**(b) a = (-10), b = 1, c = 1 ;**

**Solution 2:-**

(a) From given, a = 12, b = – 4, c = 2 ;

For R.H.S, a ÷ (b + c) =

12 ÷ [(-4) + 2] = 12 ÷ (-2) = 12÷(-2) = -6 ;

For L.H.S, (a ÷ b) + (a ÷ c) =

[12 ÷ (-4)] + [12 ÷ 2] =12÷(−4)+(12÷2) = −3+6 = 3 ;

Since, L.H.S ≠ R.H.S

Hence, a ÷ (b + c) ≠ (a ÷ b) + (a ÷ c), verified.

(b) From given, a = (-10), b = 1, c = 1 ;

For L.H.S, a ÷ (b + c) =

(-10) ÷ (1 + 1) =(-10) ÷ 2 = −10/2 = -5 ;

For R.H.S, (a ÷ b) + (a ÷ c) =

[(-10) ÷ 1] + [(-10) ÷ 1] =(−10)/1+(−10)/1 = (-10) + (-10) = -20 ;

Since, L.H.S ≠ R.H.S

Hence, a ÷ (b + c) ≠ (a ÷ b) + (a ÷ c) , verified.

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

**(a) 369 ÷ ___ = 369**

**(b) (-75) ÷ ___ = -1**

**(c) (-206) ÷ ___ =1**

**(d) -87 ÷ ___ = 87**

**(e) ___ ÷ 1 = -87**

**(g) 20 ÷ ___ = -2**

**(h) ____÷ (4) = -3**

**Solution 3:-**

(a) 369 ÷ ___ = 369

369 ÷ 1 = 369 .

(b) (-75) ÷ ___ = -1

(-75) ÷ 75 = -1 .

(c) (-206) ÷ ___ = 1

(-206) ÷ (-206) = 1.

(d) -87 ÷ ___ = 87

-87 ÷ (-1) = 87.

(e) ___ ÷ 1 = -87

-87 ÷ 1 = -87.

(f) ___ ÷ 48 = -1

(-48) ÷ 48 = -1.

(g) 20 + ___ = -2

20 ÷ (-10) = -2.

(h) ___ + (4) = -3

(-12) ÷ (4) = -3.

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

**Solution 4:-**

(a) (9, -3) because 9 ÷ (-3) = -3 ;

(b) (-36, 12) because (-36) ÷ 12 = -3 ;

(c) (21, -7) because 21 ÷ (-7) = -3 ;

(d) (18, -6) because 18 ÷ (-6) = -3 ;

(e) (24, -8) because 24 ÷ (-8) = -3 ;

**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?**

**Solution 5:-**

The temperature at 12 noon, was 10°C above zero = +10°C ;

Rate of decrease, in temperature per hour = 2°C ;

Number of hours, from 12 noon to midnight = 12 hours;

Since, the change in temperature in 12 hours

= 12 × (-2°C) = -24°C

So, the temperature at midnight

= +10°C + (-24°C) = -14°C

Hence, the required temperature at midnight =-14°C

Temperature decrease 2°C = 1 hour ;

Temperature decrease 1°C = 1/2 hour ;

Temperature decrease 18°C = (1/2) x 18 hour = 9 hour ;

Total time = 12 noon + 9 hour = 21 hour = 9 pm;

So, at 9 pm the temprature would be 8°C below 0°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?**

**Solution 6:-**

Given that,

For each-correct answer marks given = +3 marks;

For each incorrect answer marks given = -2 marks;

Zero marks for not attempted questions.

(i) Marks obtained by Radhika for 12 correct answers = (+3) × 12 = 36

Marks obtained by Radhika for correct answers = 12 × 3 = 36

Total marks obtained by Radhika = 20

Since, marks obtained by Radhika for incorrect answers = 20 – 36 = -16

So, number of incorrect answers = (−16)÷(−2) = 16/2 = 8;

Therefore, the number of incorrect answers = 8.

(ii) Marks scored by Mohini = -5

Number of correct answers = 7

Since, marks obtained by Mohini for 7 correct answers = 7 × (+3) = + 21;

Since, marks obtained for incorrect answers = -5 – 21 = (-26)

So, the number of incorrect answers = (-26) ÷ (-2) = 13;

Therefore, the number of incorrect answers = 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.**

**Solution 7:-**

The present position of the elevator is at 10 m above the ground level.

Since, the distance moved by the elevator below the ground level = 350 m

So, the total distance moved by the elevator = 350 m + 10 m = 360 m

Rate of descent = 6 m/min.

Total time taken by the elevator =360/6 = 60 minutes = 1 hour

Hence, the required time = 1 hour.

**Chapter-1, Integer Class-7 Exercise-1.3 for Free**