## Integers

__EXERCISE 1.3__

*CBSE Class 7 Maths*

**Q1: Find each of the following products:**

(a) 3 × (–1)

(b) (–1) × 225

(c) (–21) × (–30)

(d) (–316) × (–1)

(e) (–15) × 0 × (–18)

(f) (–12) × (–11) × (10)

(g) 9 × (–3) × (– 6)

(h) (–18) × (–5) × (– 4)

(i) (–1) × (–2) × (–3) × 4

(j) (–3) × (–6) × (–2) × (–1)

Answer:

(a) 3 × (–1) = = –3

(b) (–1) × 225 = -225

(c) (–21) × (–30) = 630

(d) (–316) × (–1) = 316

(e) (–15) × 0 × (–18) = 0

(f) (–12) × (–11) × (10) = 132 × 10 = 1320

(g) 9 × (–3) × (– 6) = 9 × 18 = 162

(h) (–18) × (–5) × (– 4) = 90 × (–4) = –360

(i) (–1) × (–2) × (–3) × 4 = –6 × 4 = -24

(j) (–3) × (–6) × (–2) × (–1) = 18 × 2 = 36

**Q2: Verify the following:**

**(a) 18 × [7 + (–3)] = [18 × 7] + [18 × (–3)]**

**(b) (–21) × [(– 4) + (– 6)] = [(–21) × (– 4)] + [(–21) × (– 6)]**

Answer:

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

⇒ 18 × 4 = 126 + (–54)

⇒ 72 = 72

LHS = RHS

Hence verified.

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

⇒ (–21) × (–10) = 84 + 126

⇒ 210 = 210

LHS = RHS

Hence verified.

**Q3: (i) For any integer a, what is (–1) × a equal to?**

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

**(a) –22**

**(b) 37**

**(c) 0**

Answer:

(i) -1 × a = -a

(ii)

(a) -1 × -22 = 22

(b) -1 × 37 = -37

(b) -1 × 0 = 0

**Q4: Starting from (–1) × 5, write various products showing some pattern to show (–1) × (–1) = 1.**

Answer:

(-1) × 5 = -5

(-1) × 4 = -4

(-1) × 3 = -3

(-1) × 1 = -1

(-1) × 0 = 0

(-1) × (-1) = 1

(-1) × (-2) = 2

**Q5: Find the product, using suitable properties:**

**(a) 26 × (– 48) + (– 48) × (–36)**

**(b) 8 × 53 × (–125)**

**(c) 15 × (–25) × (– 4) × (–10)**

**(d) (– 41) × 102**

**(e) 625 × (–35) + (– 625) × 65**

**(f) 7 × (50 – 2)**

**(g) (–17) × (–29)**

**(h) (–57) × (–19) + 57**

Answer:

(a) 26 × (– 48) + (– 48) × (–36)

= (-48) × [26 + (-36)] [Distributive property]

= (-48) × [26 - 36]

= (-48) × (-10)

= 480

(b) 8 × 53 × (–125)

= 53 × [8 × (–125)] [Commutative Property]

= 53 × -1000

= -53000

(c) 15 × (–25) × (– 4) × (–10)

= 15 × (–10) × (–25) × (– 4) [Commutative Property]

= [15 × (–10)] × [(–25) × (– 4)]

= -150 × 100

= -15000

(d) (– 41) × 102

= (-41) × [100 + 2] [Distributive Property]

= (-41 × 100) + (-41 × 2)

= -4100 + (-82)

= -4100 - 82

= -4182

(e) 625 × (–35) + (– 625) × 65

= 625 × (–35) + 625 × (–65)

= 625 × [(–35) + (-65)] [Distributive Property]

= 625 × [-100]

= -62500

(f) 7 × (50 – 2)

= 7 × (50 – 2) [Distributive Property]

= (7 × 50) - (7 × 2)

= 350 - 14

= 336

(g) (–17) × (–29)

= (–17) × [(-30) + 1] [Distributive Property]

= (-17) × (-30) + (-17) × 1

= 510 + (-17)

= 510 - 17

= 493

(h) (–57) × (–19) + 57

= 57 × 19 + 57

= 57 × (19 + 1)

= 57 × 20

= 1140

**Q6: 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?**

Answer: Present room temperature = 40°C

Decreasing in temperature per hour = 5°C

Room temperature after 10 hours = 40°C + 10 × (–5 o C )

= 40°C – 50°C

= –10°C

Thus, the room temperature after 10 hours is –10°C.

**Q7: 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 and six incorrect answers. What is his score?**

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

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

Answer:

Marks given for correct answer = +5

Marks deducted for incorrect = -2

(i) Mohan's correct answers = 4

Marks for correct answers = 4 × (+5) = 20

Mohan's incorrect answers = 6

Marks for incorrect = 6 × (-2) = -12

Total marks for Mohan = 20 + (-12) = 20 - 12 = 8

(ii) Reshma's correct answers = 5

Marks for correct answers = 5 × (+5) = 25

Reshma's incorrect answers = 5

Marks for incorrect = 5 × (-2) = -10

Total marks for Reshma = 25 + (-10) = 25 - 10 = 15

(iii) Heena's correct answers = 2

Marks for correct answers = 2 × (+5) = 10

Heena's incorrect answers = 5

Marks for incorrect = 5 × (-2) = -10

Total marks for Heena = 10 + (-10) = 10 - 10 = 0

**Q8: A cement company earns a profit of Rs 8 per bag of white cement sold and a loss of Rs 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?**

**(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.**

Answer: Given,

Profit per white cement bag = ₹ +8

Loss per grey cement bag = ₹ -5

(a) Profit on 3000 white cement bags = 3000 × ₹ +8 = ₹ +24,000

Loss on 5000 grey cement bags = 5000 × ₹ -5 = ₹ -25,000

Total Profit or Loss = +24,000 + (-25,000)

= ₹ -1000

-ve value indicates it is a loss of ₹ 1000

(b) Let number of white cement bags = y

Profit = y × 8

Number of grey bags = 6400

Loss on grey cement bags = ₹-5 ×6,400

∵ Profit + Loss = 0

∴ y × 8 + (-5 × 6,400) = 0

y × 8 = 5 × 6,400

y = (5 × 6400)/8 = 5 × 800 = 4000 bags

**Q9: Replace the blank with an integer to make it a true statement.**

**(a) (–3) × _____ = 27**

**(b) 5 × _____ = –35**

**(c) _____ × (– 8) = –56**

**(d) _____ × (–12) = 132**

Answer:

(a) (–3) × (-9) = 27

(b) 5 × (-7) = –35

(c) 7 × (– 8) = –56

(d) (-11) × (–12) = 132

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