Students can Download Chapter 1 Integers Ex 1.3, 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 1.3

Question 1.

Find each of the following products

a) 3 × (-1)

3 × (-1) = -3

b) (-1) × 225

(-1) × 225 = – 225

c) (-21) × (-30)

(-21) × (-30) = 630

d) (-316) × (-1)

(-316) × (-1) = 316

e) (-15) × 0 × (-18)

(-15) × 0 × (-18)

f) (-12) × (-11) × (10)

(-12) × (-11) × (10) = 1320

g) 9 × (-3) × (-6)

9 × (-3) × (-6) = 162

h) (-18) × (-5) × (-4)

(-18) × (-5) × (-4) = – 360

i) (-1) × (2) × (-3) × 4

(-1) × (-2) × (-3) × 4 = -24

j) (-3) × (-6) × (-2) × (-1)

(-3) × (-6) × (-2) × (-1) = 36

Question 2.

Verify the following :

a) 18 × [7 + (-3)] = [18 × 7] + [18 × (-3)]

Solution:

18 × [7 – 3] = [126] + [18 × -3]

18 × [4] = 126 + [-54]

72 = 72 (verified)

b) (-21) × [(-4) + (-6)] = [(-21) × (-4)] + [(-21) × (-6)]

Solution:

-21 × [-4 + -6] = [-21 × -4] + [-21 × -6]

-21 × -10 = [84]+[126]

+ 210 = 210

LHS = RHS (verified)

Question 3.

i) For any integer a, what is (-1) × a equal to?

-1 × a = -a

ii) Determine the integer whose product with (-1) is

a) -22

-1 × -22 = +22

b) 37

-1 × 37 = -37

c) 0

-1 × 0 = 0

Question 4.

Starting from (-1) × 5, write various products showing some pattern to show (-1) × (-1) = 1.

Solution:

(-1) × 5 = -5

(-1) × 4 = -4 [= (-5) + 1]

(-1) × 3 = -3 [= (-4) + 1]

(-1) × 2 = -2 [= (-3) + 1]

(-1) × 1 = -1 [= (-2) + 1]

(-1) × 0 = 0 [= (-1) + 1]

(-1) × (-1) = 1 [= 0 + 1]

Question 5.

End the product, using suitable properties:

a) 26 × (-48) + (-48) × (-36)

= 26 × (-48)+ (-36) × (-48)

= [26 + (-36)] × (-48) ∵ Distributive Property = (-10) × (-48)

= + 480

b) 8 × 53 × (-125)

= 8 × (-125) × 53

= [8 × (-125)] × 53

= [-(8 × 125)] × 53 ∵ a × (-b) = -(a × b)

= (-1000) × 53 = -(1000 x 53) ∵ (-a) × (b) = -(a × b)

= -53000

c) 15 × (-25) × (-4) × (-10)

= 15 × (-25) × (-10) × (-4)

∵ commutativity of multiplication

= 15 × (-10) × (-25) × (-4)

= [15 × (-10)] × [(-25) × (-4)]

= [-(15 × 10)] × [25 × 4] (∵ a × (-b) = -(a × b)

= -150 × 100 (-a) × (-b) = a × b

= -15000

d) (-41) × 102

= -(41 × 102) ∵ (-a) × b = -(a × b)

=-[41 × (100 + 2)]

= -[41 × 100 + 41 × 2]

Distributivity of multiplication over addition.

= -[4100 + 82]

= -4182

e) 625 × (-35) + (-625) × 65

= 625 × (-35) + 625 × (-65) ∵ (-a) × b = a × (-b)

= 625 × [(-35) + (-65)] ∵ Distributivity of multiplication over addition

= 625 × (-100)

= -(625 × 100)

f) 7 × (50 – 2)

= 7 × 50 – 7 × 2 ∵ Distributivity of multiplication over subtraction

= 350 – 14 = 336

g) (-17) × (-29)

= 17 × 29 ( ∵ (-a) × (-b) = a × b)

= 17 × (30 – 1)

= 17 × 30 – 17 × 1

∴ Distributivity of multiplication over subtraction

= 510 – 17

= 493

h) (-57) × (-19) + 57

= 57 × 19 + 57 ∵ (-a) × (-b) = a × b

= 57 × 19 + 57 × 1 ∵ (a × 1 = a)

= 57 × (19 + 1)

∴ Distributivity of multiplication over subtraction.

= 57 × 20 = 1140

Question 6.

A certain freezing process requires that room temperature be lowered from 40°C at the rate of 5°C every hour. What will be the room temperature 10 hours after the process begins?

Solution:

Initial temperature = 40°C

Room temperature decreases at 5°C per hour

Temperature change in 1 hour = – 5°C

Temperature change in 10 hour = – 5 × 10°C = – 50°C

Room temperature after 10 hours = Initial temperature + Temperature change in 10 hour

= 40 + (- 50)

= 40 – 50

∴ Room temperature after 10 hours = – 10°C

Question 7.

In a class test containing 10 questions, 5 marks are awarded for every correct answer, and (-2) marks are awarded for every incorrect answer and 0 for question not attempted.

i) Mohan gets four correct and six incorrect answers. What is his score?

Solution:

Total questions = 10

Marks for correct answer = + 5

Marks for incorrect answer = – 2

Marks for no attempt = 0

Mohan marks for 4 correct answers = 4 × 5 = 20

Mohan marks for 6 incorrect answers= 6 × (- 2) = 12

∴ Total marks = 20 + (- 12) = 20 – 12 = 8

Total marks scored by Mohan is = 8

ii) Reshma gets five correct answers and five incorrect answers, what is her score?

Solution:

Reshma marks for 5 correct answers = 5 × 5

= 25

Reshma marks for 5 incorrect answers

= 5 × (-2) = -10

∴ Total marks = 25 + (-10)

= 25 – 10

= 15

∴ Total marks scored by Reshma = 15

iii) Heena gets two correct and five incorrect answers out of seven questions she attempts. What is her score ?

Solution:

Heena marks for 2 correct answers = 2 × 5 = 10

Heena marks for 5 incorrect answers = 5 × (- 2) = -10

∴ Heena total marks = 10 + (- 10) = 10 – 10 = 0

∴ Total marks scored by Heena = 0

Question 8.

A cement company earns a profit of 8 per bag of white cement sold and a loss of 5 per bag of grey cement sold.

a) The company sells 3,000 bags of white cement and 5,000 bags of grey cement in a month. What is its profit or loss?

Solution:

Profit on white cement = Rs + 8

Loss on grey cement = Rs – 5

∴ Profit on 1 bag of white cement = Rs 8

Profit on 3,000 bags of white cement

= Rs 8 × 3000 = Rs 24,000

Loss on 1 bag cement = Rs – 5

Loss on 5000 bags grey cement

= Rs -5 × 5000 = Rs – 25000

Total profit / loss = Total profit + Total loss

= 24000 + (- 2500)

= 24000 – 25000

∴ Total loss = – 1000

b) What is the number of white cement bags it must sell to have neither profit nor loss, if the number of grey bags sold is 6,400 bags.

Solution:

Loss on 1 bag grey cement bag = Rs -5

Loss on 6400 bag grey cement =Rs -5 × 6400

= Rs -32000

Let number of bags of white cement = n

profit on 1 bag white cement = Rs 8

Profit on n bags white cement = Rs 8n

∴ Total profit / loss = 0

Total profit + Total loss = 0

8n + (-32000) = 0

8n – 32000 = 0

⇒ 8n = 32000

n = 4000

∴ Number of white cement bags = n = 4000

Question 9.

Replace the blank with integer to make it a true statement.

a) (-3) × ___ = 27

(-3) × __-9__ = 27

WKT,

3 × 9 = 27

and -1 × -1 = 1

∴ (-3) × (-9) = 27

b) 5 × ___ = -35

5 × __-7__ = -35

WKT,

5 × 7 = 35 and 1 × -1 = -1

∴ 5 × (-7) = -35

c) __ × (-8) = -56

__7__ × (-8) = -56

WKT,

7 × 8 = 56

and 1 × -1 = -1

∴ 7 × (-8) = -56

d) __ × (-12) = 132

__-11__ × (-12)= 132

WKT,

11 × 12 = 132 and -1 × -1 = 1

∴ (-11) × (-12)= 132