## NCERT Solutions for Class 7 Maths Chapter 1 Integers Ex 1.3

- Class 7 Maths Integers Exercise 1.1
- Class 7 Maths Integers Exercise 1.2
- Class 7 Maths Integers Exercise 1.3
- Class 7 Maths Integers Exercise 1.4

**NCERT Solutions for Class 7 Maths Chapter 1 Integers Exercise 1.3**

Ex 1.3 Class 7 Maths Question 1.

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)

Solution:

(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) = 0 [∵ a × 0 = a]

(f) (-12) × (-11) × (10)

= (-) × (-) × 12 × 11 × 10 = 1320

(g) 9 × (-3) × (-6) = (-3) × (-6) × 9

= (—) × (-) × 3 × 6 × 9 = 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

Ex 1.3 Class 7 Maths Question 2.

Verify the following:

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

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

Solution:

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

LHS = 18 × [7 + (-3)] = 18 × 4 = 72

RHS = [18 × 7] + [18 × (-3)] = 126 + (-54)

= 126 – 54 = 72

LHS = RHS

Hence, verified.

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

LHS = (-21) × [(-4) + (-6)]

= (-21) × (-10)

= (-) × (-) × 21 × 10 = 210

RHS = [(-21) × (-4)] + [(-21) × (-6)]

= (84) + (126) = 84 + 126 = 210

LHS = RHS

Hence, verified.

Ex 1.3 Class 7 Maths Question 3.

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

(ii) Determine the integer whose product with (-1) is 0.

(a) -22

(b) 37

(c) 0

Solution:

(i) (-1) × a = -a

(ii) (-1) × 0 = 0 [∵ a × 0 = 0]

Hence (c) 0 is the required integer.

Ex 1.3 Class 7 Maths 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

Ex 1.3 Class 7 Maths Question 5.

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

Solution:

(a) 26 × (-48) + (-48) × (-36)

= -48 × [26 + (-36)] = -48 × [26 – 36] = -48 × -10 = 480 [Distributive property of multiplication over

addition]

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

[Associative property of multiplication] = 53 × (-1000) = -53000

(c) 15 × (-25) × (-4) × (-10)

= [(-25) × (-4)] × [15 × (-10)]

[Regrouping the terms] = 100 × (-150) = -15000

(d) (-41) × 102 = (-41) × [100 + 2]

= (-41) × 100 + (-41) × 2

[Distributive property of multiplication over addition] = -4100 – 82 = -4182

(e) 625 × (-35) + (-625) × 65

= 625 × [(-35) + (-65)]

[Distributive property of multiplication over addition]

= 625 × (-100) = -62500

(f) 7 × (50 – 2) = 7 × 48 = 336 or

7 × (50 – 2) = 7 × 50 -7 × 2 = 350 – 14 = 336 [Distributive property of multiplication over addition]

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

= (-17) × 30 + (-17) × (-1)

= -510 + 17 = -493

[Distributive property of multiplication over addition]

(h) (-57) × (-19) + 57 = 57 × 19 + 57

= 57 × 19 + 57 × 1 [Y (-) × (-) = (+)] [Distributive property of multiplication over addition]

= 57 × (19 + 1) = 57 × 20 = 1140

Ex 1.3 Class 7 Maths 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:

Temperature of the room in the beginning = 40°C

Temperature after 1 hour

= 40°C – 1 × 5°C = 40°C – 5°C – 35°C

Similarly, temperature of the room after 10 hours

= 40°C – 10 × 5°C = 40°C – 50°C = -10°C

Ex 1.3 Class 7 Maths 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 and si× 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?

Solution:

(i) Marks awarded to Mohan = 4 × 5

=20 for correct answers Marks awarded to Mohan = 6 × (-2)

= -12 for incorrect answers.

∴ Total marks obtained by Mohan

= 20 + (-12) = 20 – 12 = 8

(ii) Marks awarded to Reshma for correct answers

= 5 × 5 = 25

Marks awarded to Reshma for incorrect answers

= 5 × (-2) = -10

∴ Total marks obtained by Reshma

= 25 + (-10) = 25 – 10 = 15

(iii) Marks awarded to Heena for correct answers

= 2 × 5 = 10

Marks awarded to Heena for incorrect answers

= 5 × (-2) = -10

Number of question not attempted by Heena

= 10 – (2 + 5) = 10 – 7 = 3

Marks awarded to Heena for non-attempted questions

=3×0=0

∴ Total marks obtained by Heena

= 10 + (-10) + 0 = 10-10+ 0 = 0

Ex 1.3 Class 7 Maths 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 sold 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.

Solution:

(a) Profit on one white cement bag = ₹ 8

loss on one grey cement bag = ₹ – 5

Profit on 3,000 bags of white cement

= ₹ (8 × 3,000) = ₹ 24,000

Loss on 5,000 bags of grey cement

= ₹ (-5 × 5000) = – ₹ 25,000

Total loss = – ₹ 25,000 + ₹ 24,000

= – ₹ 1000 i.e. ₹ 1000

(b) Selling price of grey bags at a loss of ₹ 5

= ₹ (5 × 6,400) – ₹ 32,000

For no profit and no loss, the selling price of white bags = ₹ 32,000

Rate of selling price of white bags at a profit of ₹ 8 per bag.

∴ Number of white cement bags sold

Hence, the required number of bags = 4,000

Ex 1.3 Class 7 Maths Question 9.

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

(a) (-3) × __ = 27

(b) 5 × __ = -35

(c) __ × (-8) = -56

(d) __ × (-12) = 132

Solution:

(a) (-3) × __ = 27 = (-3) × (-9) = 27 [∵ (-) × (-) = (+)]

(b) 5 × __ = -35 = 5 × (-7) = -35 [∵ (+) × (-) = (-)]

(c) __ × (-8) = -56 = 7 × (-8) = -56 [∵ (+) × (-) = (-)]

(d) __ × (-12) = 132 = (-11) × (-12) = 132 [∵ (-) × (-) = (+)]

NCERT SolutionsMathsScienceSocialEnglishSanskritHindiRD Sharma

MANSI JAISWAL says

THANKS FOR HELPING US

Dilpreet kaur says

Thanks

Sandeep saini says

Thank you learncbse.in for your hepl.this is best websIte ever

AFIFA says

THANK YOU SOOOO MUCH

Saumya Tiwari says

Thankuu very much for helping me in solutions .

Muskan Nagpal says

Thanks…… this help my child to do his maths homework

Rocky says

Thanks u had make my future

Shreyas says

Thanks to you for helping me in Homework

billings says

nice one

Ram lal meena says

Thanks sir ji

Anjali says

Thanks for your this Help again and again thanks google

Shriya rai says

Thanks to help me

Anil says

Thank you for helping me

Alok.sahu says

It’s too good anytime anyway

tahaa husain says

thanks soo easy answers and hard introduction about properties

Apurv says

Thanks for helping me

Kanaka says

Thanks

Melon21 says

Thanks a great help by learncbse ………..HOMEWORK FRIEND LEARNCBSE…..

Shalini says

I am very thankful to you..its help me to teach my elder brother.. Thanks again

Swatipatanwar says

Thank-you soooooooooooooo much

Bhawana says

Oh its ossum

Karthik says

Thank you soooo much because of thise I have not punished from my teacher it’s best Web site ever

Prince singh says

Prince

Singh

Digaru sonapur Kamrup ‘metro’

Explain chapter of all subject with question and answer

Vivek says

Thanks for helping me in my homework