NCERT Maths solutions for class 7th, Questions and answers of NCERT class 7th Mathematics, NCERT Class 7th Mathematics Chapter 1 – Integers Solutions Exercise 1.3 Solutions, Class 7th maths solutions.
Please find the detailed Solutions for class 7th Maths chapter 1 exercise 1.1, you can check all the solutions from here chapter wise
NCERT Class 7th Mathematics Chapter 1 – Integer Solutions Exercise 1.3 Solutions
Exercise 1.3
1. Find each of the following products:
(a) 3 × (–1)
Ans. 3 × (–1) = -3
(b) (–1) × 225
Ans. (–1) × 225 = -225
(c) (–21) × (–30)
Ans. -21 x (-30) = 630
(d) (–316) × (–1)
Ans. (–316) × (–1) =316
(e) (–15) × 0 × (–18)
Ans. (–15) × 0 × (–18) = 0
(f) (–12) × (–11) × (10)
Ans. (–12) × (–11) × (10) = 132
(g) 9 × (–3) × (– 6)
Ans. 9 × (–3) × (– 6) = 162
(h) (–18) × (–5) × (– 4)
Ans. (–18) × (–5) × (– 4) = -360
(i) (–1) × (–2) × (–3) × 4
Ans. (–1) × (–2) × (–3) × 4 = -24
(j) (–3) × (–6) × (–2) × (–1)
Ans. (–3) × (–6) × (–2) × (–1) = 36
2. Verify the following:
(a) 18 × [7 + (–3)] = [18 × 7] + [18 × (–3)]
Ans.18 × [7 + (–3)] =18 x 4 = 72
[18 × 7] + [18 × (–3)] = 126 + (-54) = 72
So, 18 × [7 + (–3)] = [18 × 7] + [18 × (–3)]
(b) (–21) × [(– 4) + (– 6)] = [(–21) × (– 4)] + [(–21) × (– 6)]
Ans.(–21) × [(– 4) + (– 6)] =(-21) x (-10) = 210
[(–21) × (– 4)] + [(–21) × (– 6)] = 84 + 126 = 210
So, (–21) × [(– 4) + (– 6)] = [(–21) × (– 4)] + [(–21) × (– 6)]
3. (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
Ans. a) (-1) x a = -a, where a is an integer.
b)i) (-1) x (22) = -22
ii) (-1) x (-37) = 37
iii) (-1) x 0 = 0
4. Starting from (–1) × 5, write various products showing some pattern to show (–1) × (–1) = 1. Ans.(-1) x 5 = -5
(-1) x 4 = -4 = -5 + 1
(-1) x 3 = -3 = -4 + 1
(-1) x 2 = -2 = -3 + 1
(-1) x 1 = -1 = -2 + 1
(-1) x 0 = 0 = -1 + 1
(-1) x (-1) = 0 + 1 = 1
5. Find the product, using suitable properties:
(a) 26 × (– 48) + (– 48) × (–36)
Ans. 26 × (– 48) + (– 48) × (–36)
=(-48) x [26 + (-36)]
=(-48) x (-10) = 480
(b) 8 × 53 × (–125)
Ans. 8 x 53 x (-125)
= 8 x [53 x (-125)]
= 8 x (-6625)
= -53000
(c) 15 × (–25) × (– 4) × (–10)
Ans. 15 × (–25) × (– 4) × (–10)
= [15 x (-25)] x [(-4) x (-10)]
= (-375) x 40
= -15000
(d) (– 41) × 102
Ans.(-41) x 102
= -4182
(e) 625 × (–35) + (– 625) × 65
Ans. 625 × (–35) + (– 625) × 65
= 625 x [(-35) + (-65)]
= 625 x [-100]
= -62500
(f) 7 × (50 – 2)
Ans. 7 × (50 – 2)
= 7 x 48
= 336
(g) (–17) × (–29)
Ans. (–17) × (–29)
= 493
(h) (–57) × (–19) + 57
Ans. (–57) × (–19) + 57
= (–57) × (–19) + 57 x 1
= 57 x {[-(-19)] + 1}
= 57 x {19 + 1}
= 57 x 20
= 1140
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?
Ans.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.
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 six incorrect answers. What is his score?
(ii) Reshma gets five correct answers and five incorrect answers, what is her score?
Ans. a) Marks for correct answers = 4 x 5 = 20
Marks for incorrect answers = 6 x (-2) = -12
Total score = 20 + (-12) = 20 – 12 = 8
Thus, Mohan gets 10 marks in a class test.
(ii) Reshma gets five correct answers and five incorrect answers, what is her score?
Ans.b) Marks for correct answers = 5 x 5 = 25
Marks for incorrect answers = 5 x (-2) = -10
Toatal score = 25 + (-10) = 15
Thus, Reshma gets 15 marks in a class test.
(iii) Heena gets two correct and five incorrect answers out of seven questions she attempts. What is her score?
Ans. ) Marks for correct answers = 2 x 5 = 10
Marks for incorrect answers = 5 x (-2) = -10
Toatal score = 10 + (-10) = 10 – 10 = 0
Thus, Heena gets 0 marks in a class test
8. 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.
Ans. Given:
Profit of 1 white cement bag = Rs 8
Loss of 1 grey cement bag = Rs 5
i) Profit on selling 3,000 bags of white cement bags = 3000 x 8 = Rs 24000
Loss on selling 5,000 bags of grey cement = 5000 x 5 = Rs 25000
Since, Profit < Loss
Therefore, company’s total loss = Loss – Profit = 25000 – 24000 = Rs 1,000
Thus, company’s loss is Rs 1,000.
ii) Let the number of bags of white cement be x.
Loss on selling 6,400 bags of grey cement = 6400 x 5 = Rs 32000
According to the question, Profit = Loss
Therefore, 8x = 32000
x = 32000/8 = 4000
Thus, company must sell 4000 bags of white cement to have neither profit nor loss.
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
Ans. (a) (–3) × (-9) = 27
(b) 5 x (-7) = –35
(c) 7 × (– 8) = –56
(d) (-11) × (–12) = 132
You can find the solutions for previous exercise from here
You can find solution for whole chapter here –
