Students can Download Class 7 Maths Chapter 1 Integers Ex 1.4 Questions and Answers, Notes Pdf, KSEEB Solutions for Class 7 Maths helps you to revise the complete Karnataka State Board Syllabus and to clear all their doubts, score well in final exams.

## Karnataka State Syllabus Class 7 Maths Chapter 1 Integers Ex 1.4

Question 1.

Evaluate each of the following

a) (- 30) ÷ 10

Solution:

(- 30) ÷ 10 = – 3

b) 50 ÷ (- 5)

Solution:

\(\frac{50}{-5}=-10\)

c) (- 36) ÷ (- 9)

Solution:

\(\frac{-36}{-9}=4\)

= 4

d) (- 49) ÷ (49)

Solution:

\(\frac{-49}{+49}=-1\)

= – 1

e) 13 ÷ [(- 2) + 1]

Solution:

= 13 ÷ (- 2 + 10)

= 13 ÷ (- 1)

= -13

f) 0 ÷ (- 12)

= 0

g) (- 31) ÷ [(- 30) + (- 1)]

= (- 31) ÷ [- 30 – 1]

= (- 31) ÷ (- 31)

\(\frac{-31}{-31}=+1\)

= 1

h) [(- 36) ÷ 12] ÷ 3

Solution:

= -1

i) [(- 6) + 5] ÷ [(- 2) + 1]

=[- 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.

a) a = 12, b = – 4, c = 2

Solution:

a) a = 12, b = – 4, c = 2

To verify a ÷ (b + c) ≠ (a ÷ b) + (a ÷ c)

⇒ 12 ÷ (- 4 + 2) ≠ [12 ÷ (- 4)] + (12 ÷ 2 )

⇒ 12 ÷ (- 2) ≠ – 3 + 6

⇒ – 6 ≠ 3

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

⇒ (- 10) ÷ (1 + 1) ≠ [(- 10) ÷ 1] + (- 10 ÷ 1)

⇒ – 10 ÷ 2 ≠ – 10 + (-10)

⇒ – 5 ≠ – 20

Question 3.

Fill in the blanks :

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:

a ÷ b = – 3

∴ The other five pairs are (- 6, 2), (- 3, 1), (- 9, 3), (- 12, 4), (- 15, 5)

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 mid-night?

Solution:

Temperature at 12pm = 10°C

Temperature decreases at 2°C per hour

we need to find, time when temperature is 8°C below zero, ie., – 8°C

∴ Total decrease = Final temperature – initial temperature = – 8°C – 10°C

= – 8 – 10 = -18°C

Now,

Temperature decrease in 1 hour × Total number of hours = Total decrease

So, temperature becomes – 8°C = 9 hours

∴ Temperature is -8°C at 9PM

Now,

We need to find temperature at mid – night temperature at 12AM = Temperature at 12PM

Temperature change in 12 hours

Temperature change in 1 hour = – 2°C

Temperature change in 12 hour = – 2 × 12°C = – 24°C

Now,

Temperature at 12AM – Temperature at 12PM = Temperature change in 12 hours. Temperature at 12AM – 10°C = – 24°C

Temperature at 12AM = – 24°C + 10°C

Temperature at 12 AM = – 14°C

∴ Temperature at Mid – night = – 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.

Solution:

Marks given for correct answer = + 3

Marks given for incorrect answer = – 2

Marks given for not attempting = 0

i) Radhika scored 20 marks. If she has got 12 correct answers, how many questions has she attempted incorrectly?

Solution:

Total marks scored = 20

Number of correct answer = 12

Marks of for correct answer = 12 × 3 = 36

Also

Marks for incorrect answer = (- 2) × Number of incorrect answer

Marks for not attempt answer = 0 × Number of not attempt = 0

Now,

Total marks = marks for correct answer + marks for incorrect answer + marks for not attempt

20 = 36 + (- 2) × No of incorrect answers + 0

20 – 36 = (- 2) × No of incorrect answers

– 16 = (- 2) × No of incorrect answer

\(\frac{-16}{-2}\) = No of incorrect answers

8 = No of incorrect answers

So, Radhika attempted 8 questions incorrectly

ii) Mohini scores -5 marks in this test, though she has got 7 correct answers. How many questions has she attempted incorrectly?

Solution:

Total marks = -5

No of correct answers = 7

Marks for correct answers = 7 × 3 = 21

Also,

Marks for incorrect answer = (-2) × No. of incorrect answers

Marks for not attempt answer = 0 × No of not attempt answers

Now,

Total marks = marks for correct answer + marks for incorrect answer + marks for not attempt

-5 = 21 + (-2) × No. of incorrect answers + 0

-5 – 21 = (-2) × No. of incorrect answers

-26 = -2 × No. of incorrect answers

\(\frac{-26}{-2}\) = No. of incorrect answers

13 = No, of incorrect answers.

∴ Mohini attempted 13 questions incorrectly

Question 7.

An elevator descends into a mine shaft at the rate of 6m/min. If the descent starts from 10m above the ground level, how long will it take to reach – 350 m.

Solution:

Initial position = 10m final position = -350 m

Total distance elevator has to travel = initial position – final position

= 10 – (-350)

= 10 + 350 = 360 m

Now,

Elevator descends at rate 6m/min

∴ Elevator travels 6m in = 1 minute

Elevator travels 1 m in: = \(\frac{1}{6}\)

Elevator travels 360m in = \(\frac{1}{6}\) × 360 minutes

= 60 minutes

= 1 hour

∴ It will take the elevator 1 hour.