Haryana State Board HBSE 7th Class Maths Solutions Chapter 1 Integers Ex 1.3 Textbook Exercise Questions and Answers.

## Haryana Board 7th Class Maths Solutions Chapter 1 Integers Exercise 1.3

Question 1.

Find each of the following products :

(a) 3 x (- 1)

(b) (- 1) x 225

(c) (-21) x (-30)

(d) (-316) x (- 1)

(e) (- 15) x 0 x (- 18)

(f) (-12) x(-11)x (10)

(g) 9 x(- 3) x (- 6)

(h) (-18) x (-5) x (-4)

(i) (- 1) x (- 2) x (- 3) x 4

(j) (- 3) x (- 6) x (- 2) x (- 1)

Solution:

(a) 3 x (- 1) = – 3

(b) (-1) x (225)=-225

(c) (- 21) x (- 30) = +(21×30)= + 630

(d) (-316) x (-1) = +(316 x 1) = + 316

(e) (-15) x 0 x (-18) = 0 x – 18 = 0

(f) (-12) x (-11) x 10 = + 132x 10 = 1320

(g) 9 x (- 3) x (- 6) = 9 x 18 = 162

(h) (- 18) x (- 5) x (- 4)=- 18 x 20 = – 360

(i) (- 1) x (- 2) x (- 3) x 4=2 x (- 12) = – 24

(j) (- 3) x (- 6) x (- 2) x (- 1)= 18 x 2 = 36

Question 2.

Verify the following:

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

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

Solution:

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

18 x [7 – 3] = 126 + (- 54)

18 x 4 = 126 – 54

72 =72

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

– 21 x (- 10) = 84 + 126

210 =210

Question 3.

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

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

(a) -22 (6) 37 (c) 0

Solution:

(i) 1 x (-1) = -1

2 x (- 1) = – 2

– 2 x (- 1) = 2 etc.

(ii) (a) 22 x (- 1) = – 22

(b) (- 37) x (- 1) = 37

(c) 0 x (- 1) = 0

Question 4.

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

Solution:

– 1 x 5 = – 5

– 1 x 4 = – 4

-1 x 3 =-3

-1 x 2 = -2

-1 x 1 =-1

– 1 x 0 = 0

-1 x -1 = 1

Question 5.

Find the product, using suitable properties :

(a) 26 x (- 48) + (-48 x- 36)

(b) 8 x 53 x (- 125)

(c) 15 x (- 25) x (-4) x (- 10)

(d) (-41) x 102

(e) 625 x (- 35) + (- 625) x 65

(f) 7 x [50 – 2]

(g) (- 17) x (- 29)

(h) (-57) x (-19) + 57

Solution:

(a) 26 x (-48) + (-48 x – 38)

= -48[26-36] – 48 [26 – 36]

= – 48 x [-10] – 48 x [-10]= 480

(b) 8 x [53 x (- 125)]

= [8 x 53] x (- 125) 8 x (- 6625)

= 424 x(-125)-53000

= -53000

(c) 15 x [(- 25) x (- 4)] x – 10

= (15 x 100) x (- 10)

= 1500 x (- 10) = – 15000

(d) (- 41) x 102 =(- 41) x (100 + 2)

= (-41×100)+ (-41×2)

= -4100+ (-82) = -4182

(e) 625 x (- 35) + (- 625) x 65

= 625 [(- 35) + (- 1) x 65]

= 625 [-35-65]

= 625 x – 100 = – 62500

if) 7 x [50-2]

= [7 x 50] – [7 x 2]

= 350-14 = 336

(g) (- 17) x (- 29) = – 17 x [- 30 + 1]

= [(- 17) x (- 30)] + [(- 17) x 1]

= 510+ (-17) = 510-17 = 493

(h) (- 57) x (- 19) + 57

= 57 [(- 1) x (- 19) + 1]

= 57 [19 + 1] = 57 x 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:

After 10 hours room temperature = 40°C – (5°C x 10) = 40°C – 50°C = – 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 questions not attempted.

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

(ii) Reshma gest five cored answers and five incorrect answer, what is her score?

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

Solution:

(i) 4 x 5 + 6 x (- 2) = 20 – 18 Mohan score = 2

(ii) 5 x 5 + 5 x (- 2) = 25-10 Reshma’s score = 15

(iii) 2 x 5 + 5 x (- 2) = 10-10 Heena’s score = 0

Question 8.

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

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

(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:

(a) = (3,000 x 8) – (5,000 x 5)

= 24,000-25,000 = -1000 loss = Rs. 1000 (b) No. of grey bags cement bags = 6,400

loss = 6,400 x 5 = Rs. 32,000 profit of white cement bags = Rs. 32,000

hence no. of white cement bags = 32000 ÷ 8 = 4000

Question 9.

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

(a) (- 3) x …………….. = 27

(b) 5 x …………….. =(-35)

(c) …………….. x(-8) = (-56)

(d) …………….. x (- 12) = 132

Solution:

(a) (- 3) x (- 9) = 27

(6) 5 x (- 7) =-35

(c) 7 x (-8) =-56

id) (- 11) x (— 12) = 132