Ncert Solutions For Class 7 Maths Ex 1.3

Ncert Solutions For Class 7 Maths Chapter 1 Ex 1.3

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 40oC at the rate of 5oC every hour. What will be the room temperature after 10 hours?

Answer:

Given:

Room temperature at present = 40oC

Rate = 5o per hour

Decrease in temperature in 10 hours = 50oC

Room temperature after 10 hours = 40oC – 50oC = -10oC

Thus, the room temperature after 10 hours, after the process begins, is -10oC.

 

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) x (-9) = -81

iv)(-1)x (-12) = 12

 

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