**NCERT Solutions for Class 7 Maths Chapter 1 Integers Ex 1.1****NCERT Solutions for Class 7 Maths Chapter 1 Integers Ex 1.2****NCERT Solutions for Class 7 Maths Chapter 1 Integers Ex 1.3**

**NCERT Solutions for Class 7 Maths Chapter 1 Integers Ex 1.3 ****(Rationalised Contents)**

**Ex 1.3 Class 7 Maths 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:**(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/−1 = 1

**Ex 1.3 Class 7 Maths Question 2.**

### Verify that a ÷ (b + c) ≠ (a ÷ b) + (a ÷ c) for each of the following values of a, b and c.

(Ð°) a = 12, b = – 4, c = 2

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

**Solution:**(a) a = 12, 6 = – 4, c = 2

a ÷ (b + c) = 12 ÷ [(-4) + 2]

= 12 ÷ (-2) = 12/−2 = -6

(a ÷ b) + (a ÷ c) = [12 ÷ (-4)] + [12 ÷ 2]

= 12/−4 + 12/2 = −3 + 6 = 3

Since, (-6) ≠ 3

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

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

a ÷ (b + c) = (-10) ÷ (1 + 1)

=(-10) ÷ 2 = −10/2 = -5

(a ÷ b) + (a ÷ c)

=[(-10) ÷ 1] + [(-10) ÷ 1]

=(−10)/1 + (−10)/1

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

Since (-5) ≠ (-20)

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

**Ex 1.3 Class 7 Maths Question 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

**Solution:**(a) 369 ÷ _____ = 369 Hence, 369 ÷

**= 369**

__1__(b) (-75) ÷ _____ = -1 Hence, (-75) ÷

**= -1**

__75__(c) (-206) ÷ _____ = 1 Hence, (-206) ÷ (

**) = 1**

__-206__(d) -87 ÷ _____ = 87 Hence, -87 ÷ (

**) = 87**

__-1__(e) _____ ÷ 1 = -87 Hence,

**÷ 1 = -87**

__-87__(f) _____ ÷ 48 = -1 Hence, (

**) ÷ 48 = -1**

__-48__(g) 20 + _____ = -2 Hence, 20 ÷ (

**) = -2**

__-10__(h) _____ + (4) = -3 Hence, (

**) ÷ (4) = -3**

__-12__

**Ex 1.3 Class 7 Maths 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:**(i) (9, -3) because 9 ÷ (-3) = -3

(ii) (-12, 4) because (-12) ÷ 4 = -3

(iii) (15, -5) because 15 ÷ (-5) = -3

(iv) (21, -7) because 21 ÷ (-7) = -3

(v) (30, -10) because 30 ÷ (-10) = -3

**Ex 1.3 Class 7 Maths 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:**The temperature at 12 noon was 10°C above zero, i.e., +10°C

Rate of decrease in temperature per hour = 2°C

Number of hours from 12 noon to midnight = 12

∴ Change in temperature in 12 hours

= 12 × (-2°C) = -24°C

∴ Temperature at midnight = +10°C + (-24°C) = -14°C

Hence, the temperature at midnight = -14°C

Difference in temperature between +10°C and -8°C

= +10°C – (-8°C) = +10°C + 8°C = 18°C

Number of hours required = 18°C/2°C = 9 hours

∴ Time after 9 hours from 12 noon = 9 pm.

**Ex 1.3 Class 7 Maths 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:**It is given that +3 marks are given for each correct answer and (-2) marks are given for each incorrect answer. Zero marks are given for not attempting questions.

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

Total marks obtained by Radhika = 20

∴ Marks obtained by Radhika for incorrect answers = 20 – 36 = -16

Number of incorrect answers = (−16) ÷ (−2) = (−16)/(−2) = 8

Hence, the required number of incorrect answers is 8.

(ii) Marks scored by Mohini = -5

Number of correct answers by Mohini = 7

∴ Marks obtained by Mohini for 7 correct answers = 7 × (+3) = 21

Marks obtained for incorrect answers = -5 – 21 = (-26)

∴ Number of incorrect answers = (-26) ÷ (-2) = 13

Hence, the required number of incorrect answers is 13.

**Ex 1.3 Class 7 Maths Question 7.**

### An elevator descends into a nine 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:**The current position of the elevator is at 10 m above the ground level.

Distance moved by the elevator below the ground level = 350 m

∴ 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 min

= 60 minutes = 1 hour

Hence, the required time is 1 hour.

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