**Question 1:**

**Find the product of the following:**

**(a) 4 x (–1)**

= -4

**(b) (–1) x 345**

= -345

**(c) (–12) x (–20)**

= 240

**(d) (–136) x (–1)**

= 136

**(e) (–13) x 0 x (–17)**

= 0

**(f) (–11) x (–13) x (10)**

= 1430

**(g) 10 x (–4) x (–8)**

= 320

**(h) (–16) x (–5) x (–2)**

= – 160

**(i) (–2) x (–1) x (–4) x 4**

= – 32

**(j) (–4) x (–5) x (2) x (–1)**

= – 40

**Question 2:**

**Verify:**

**i) 16 x [4 + (–3)] = [16 x 4] + [16 x (–3)]**

**ii) (–22) x [(–6) + (–4)] = [(–22) x (-6)] + [(–22) x (–4)]**

**Answer:**

i) 16 x [4 + (–3)] = [16 x 4] + [16 x (–3)]

16 x 1 = 64 + (-48)

16 = 16

L.H.S. = R.H.S.

Hence, verified.

ii) (–22) x [(–6) + (–4)] = [(–22) x (-6)] + [(–22) x (–4)]

(-22) x (-10) = 132 + 88

220 = 220

L.H.S. = R.H.S.

Hence, verified.

**Question 3:**

**a) For any integer b, what is****(-1****)*** ***x b equal to?**

**b) Determine the integer whose product with****(-1)****is:**

**i) –12**

**ii) 47**

**iii) 0**

**Answer:**

a) (-1) x b = -b, where b is an integer.

b)

i) (-1) x (-12) = 12

ii) (-1) x 47 = -47

iii) (-1) x 0 = 0

**Question 4:**

**Starting from (-1) x 7, write various products showing some patterns to show (-1) x (-1) = 1.**

**Answer:**

(-1) x 7 = -7 (-1) x 3 = -3 (-1) x (-1) = 0

(-1) x 6 = -6 (-1) x 2 = -2

(-1) x 5 = -5 (-1) x 1 = -1

(-1) x 4 = -4 (-1) x 0 = 0

Thus, we can conclude that it shows that if we multiply a negative integer with a positive integer the outcome is a negative integer whereas if we multiply a negative integer with another negative integer number then the outcome is a positive integer.

**Question 5:**

**Using suitable properties, find the product of the following:**

**i) (-48) x 26 + 26 x (-15)**

**ii) 7 x 53 x (-145)**

**iii) (-55) x (-18) +57**

**Answer:**

i) (-48) x 26 + 26 x (-15)

26 x [(-48) + (-15)] [Distributive property]

26 x (-63) = -1638

ii) 7 x 53 x (-145)

7 x [53 x (-145)] [Commutative property]

7 x (-7685) = -53795

iii) (-55) x (-18) + 55

(-55) x (-18) + 55 x 1

55 x 18 + 55 x 1

55 x (18+1) [Distributive property]

55 x 19 = 1045

**Question 6:**

**A certain freezing process requires the room temperature to be lowered from 40 ^{o}C at the rate of 5^{o}C every hour. What will be the room temperature after 10 hours?**

**Answer:**

Given:

Room temperature at present = 40^{o}C

Rate = 5^{o} per hour

Decrease in temperature in 10 hours = 50^{o}C

Room temperature after 10 hours = 40^{o}C – 50^{o}C = -10^{o}C

Thus, the room temperature after 10 hours, after the process begins, is -10^{o}C.

** **

**Question 7:**

**A class test is taken comprising of 10 questions. For every correct answer 5 marks is awarded, for every incorrect answer (-2) marks is awarded and 0 marks is awarded for questions not attempted. Calculate the total score when:**

**a) Vipul gets seven correct and three incorrect answers.**

**b) Ankesh gets five correct answers and five incorrect answers.**

**Answer:**

a) Marks for correct answers = 7 x 5 = 35

Marks for incorrect answers = 3 x (-2) = -6

Total score = 35 + (-6) = 29

Thus, Vipul gets 29 marks in a class test.

b) Marks for correct answers = 5 x 5 = 25

Marks for incorrect answers = 5 x (-2) = -10

Toatal score = 25 + (-10) = 15

Thus, Ankesh gets 15 marks in a class test.

**Question 8:**

** A cement company earns a profit of Rs 10 per bag of white cement sold and loss of Rs 6 per bag of grey cement sold.**

**i) What is its profit or loss when the company sells 2,000 bags of white cements and 4,000 bags of grey cement in a month?**

**ii) The number of grey cement bags sold is 6,500 bags. How many white cement bags the company must sell to have neither profit nor loss?**

**Answer:**

Given:

Profit of 1 white cement bag = Rs 10

Loss of 1 grey cement bag = Rs 6

i) Profit on selling 2,000 bags of white cement bags = 2000 x 10 = Rs 20000

Loss on selling 4,000 bags of grey cement = 4000 x 6 = Rs 24000

Since, Profit < Loss

Therefore, company’s total loss = Loss – Profit = 24000 – 20000 = Rs 4,000

Thus, company’s lost is Rs 4,000.

ii) Let the number of bags of white cement be x.

Loss on selling 6,500 bags of grey cement = 6500 x 6 = Rs 39000

According to the question, Profit = Loss

Therefore, 10x = 39000

x = 39000/10 = 3,900

Thus, company must sell 3,900 bags of white cement to have neither profit nor loss.

**Question 9:**

**Fill up the blanks with suitable integer.**

**i) (-4) x ________ = 24**

**ii) (-5) x _______ = 45**

**iii) _______ x (-9) = -81**

**iv) _______ x (-12) = 12**

**Answer:**

i) (-4) x__(-6)__= 24

ii) (-5) x__(-9)__= 45

iii)__ ____9 __x (-9) = -81

iv)__(-1)__x (-12) = 12