Students can Download Chapter 1 Integers Ex 1.4, Question and Answers, Notes Pdf, KSEEB Solutions for Class 7 Maths, Karnataka State Board Solutions help you to revise complete Syllabus and score more marks in your examinations.

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

Question 1.

Evaluate each of the following

a) (-30) ÷ 10

Solution:

b) 50 ÷ (-5)

Solution:

c) (-36) ÷ (-9)

Solution:

= 4

d) (-49) ÷ (49)

Solution:

= -1

e) 13 ÷ [(-2) + 1]

Solution:

= 13 ÷ (-2 + 10)

= 13 ÷ (-1)

\(=\frac{13}{-1}\)

= -13

f) 0 ÷ (-12)

= 0

g) (-31) ÷ [(-30) + (-1)]

= (-31) ÷ [-30 – 1]

= (-31) ÷ (-31)

= 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)

∴ LHS ≠ RHS

hence verified

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

∴ LHS ≠ RHS

hence verified

Question 3.

Fill in the blanks :

a) 369 ÷ ___ = 369

369 ÷ __1__ = 369

Let number be x

x = 1

b) (-75) ÷ ___ = -1

(-75) ÷ __75__ = -1

Let number be x

x = 75

c) (-206) ÷ ___ = 1

(-206) ÷ __-206__ = 1

Let number be x

x = -206

d) -87 ÷ ___ = 87

-87 ÷ __-1__ = 87

let the number be x

x = -1

e) ___ ÷ 1 = -87

__87__ ÷ 1 = -87

Let the number be x

1 × -87 = x

-87 = x

x = -87

f) ___ ÷ 48 = -1

__48__ ÷ 48 = -1

Let number be x

– 1 × 48 = x

-48 = x

∴ x = -48

g) 20 ÷ ___ = -2

20 ÷ __-10__ = (-2)

x = -10

h) __ ÷ (4) = -3

__-12__ ÷ (4) = -3

Let number be x

x = -3 × 4

x=-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)

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, thought 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.