NCERT Solutions for Class 7 Maths Chapter 1 Integers Ex 1.1
NCERT Solutions for Class 7 Maths Chapter 1 Integers Ex 1.1
These NCERT Solutions for Class 7 Maths Chapter 1 Integers Ex 1.1 Questions and Answers are prepared by our highly skilled subject experts.
NCERT Solutions for Class 7 Maths Chapter 1 Integers Exercise 1.1
Question 1.
Following number line shows the temperature in degree Celsius (°C) at different places on a particular day.
(a) Observe this number line and write the temperature of the places marked on it.
(b) What is the temperature difference between the hottest and the coldest places among the above?
(c) What is the temperature difference between Lahulspiti and Srinagar?
(d) Can we say temperature of Srinagar and Shimla taken together is less than the temperature at Shimla? Is it also less than the temperature at Srinagar?
Answer:
(b) Temperature difference between the hottest and the coldest places
= Temperature of Bengaluru – Temperature of Lahulspiti
= 22°C – (- 8°C) = 22°C + 8°C
= 30°C
(c) Temperature difference between Lahulspiti and Srinagar
= Temperature of Srinagar – Temperature of Lahulspiti
= – 2°C – (- 8°C) = – 2°C + 8°C = 6°C
(d) Temperature of Srinagar and Shimla together
= Temperature of Srinagar + Temperature of Shimla
= – 2°C + 5°C = 3°C
3°C < 5°C
Yes, sum of temperatures at Srinagar and Shimla is less than the temperature at Shimla. Now, temperature of Srinagar = – 2°C
Also 3°C > – 2°C
No, sum of the temperatures at Srinagar and Shimla is not less than the temperature at Srinagar.
Question 2.
In a quiz, positive marks are given for correct answers and negative marks are given for incorrect answers. If Jack’s scores in five successive rounds were 25, – 5,- 10, 15 and 10, what was his total at the end?
Answer:
Score in 1st round = 25
Score in 2nd round = – 5
Score in 3rd round = – 10
Score in 4th round = 15
Score in 5th round = 10
Total score at the end
= 25 + (-5) + (-10) + 15 + 10
= 25 – 5 – 10 + 15 + 10
= 25 + 15 + 10 – 5 – 10
= 50 – 15 = 35
Question 3.
At Srinagar temperature was – 5°C on Monday and then it dropped by 2°C on Tuesday. What was the temperature of Srinagar on Tuesday? On Wednesday, it rose by 4°C. What was the temperature on this day?
Answer:
Temperature at Srinagar on Monday = -5°C
Drop in temperature at Srinagar on Tuesday = 2°C
∴ Temperature at Srinagar on Tuesday = – 5°C – 2°C = – 7°C
Rise in temperature at Srinagar on Wednesday = 4°C
∴ Temperature at Srinagar on Wednesday = – 7°C + 4°C = – 3°C
Question 4.
A plane is flying at the height of 5000 m above the sea level. At a particular point, it is exactly above a submarine floating 1200 m below the sea level. What is the vertical distance between them?
Answer:
Since the sea level is at 0 m and the plane is 5000 m above the sea level. Also the submarine is 1200 m below the sea level, so vertical distance between the plane and submarine is
= 5000 m – (- 1200 m)
= 5000 m + 1200 m
= 6200 m
Question 5.
Mohan deposits ₹ 2,000 in his bank account and withdraws ₹ 1, 642 from it, the next day. If withdrawal of amount from the account is represented by a negative integer, then how will you represent the amount deposited? Find the balance in Mohan’s account after the withdrawal.
Answer:
Amount deposited = ₹ 2000
Amount withdrawn = ₹ 1642
Balance in Mohan’s account = ₹ 2000 – ₹ 1642
after withdrawal = ₹ 358
Amount deposited is represented by positive integer.
Question 6.
Rita goes 20 km towards east from a point A to the point B. From B, she moves 30 km towards west along the same road. If the distance towards east is represented by a positive integer then, how will you represent the distance travelled towards west? By which integer will you represent her final position from A?
Answer:
Distance towards west is represented by negative integer
The directions east and west are opposite to each other
Distance moved towards west = – 30 km
Distance moved towards east = + 20 km
Her final position from A = + 20 km + (- 30 km) = 20 km – 30 km
= – 10 km
Question 7.
In a magic square each row, column and diagonal have the same sum. Check which of the following is a magic square?
(i)
| 5 | – 1 | – 4 |
| – 5 | – 2 | 7 |
| 0 | 3 | – 3 |
(ii)
| 1 | – 10 | 0 |
| – 4 | – 3 | – 2 |
| – 6 | 4 | – 7 |
Answer:
(i) Sum of the digits along
1st row = 5 + (- 1) + (- 4)
= 5 – 1 – 4 = 0
2nd row = – 5 + (- 2) + 7
= -5 – 2 + 7 = 0
3rd row = 0 + 3 + (- 3)
=0 + 3 – 3 = 0
1st column = 5 + (- 5) + 0
= 5 – 5 + 0 = 0
2nd column = -1 + (- 2) + 3
= -1 -2 + 3 = 0
3rd column = – 4 + 7 + (- 3)
= – 4 + 7- 3 = 7 – 7 = 0
1st diagonal = 5 + (- 2) + (- 3)
= 5 – 2 – 3 = 0
2nd diagonal = – 4 + (- 2) + 0
= – 4 – 2 + 0
= – 6 ≠ 0
∴ Square (i) is not a magic square.
(ii) Sum of the digits along
1st row = 1 + (- 10) + 0
= 1 – 10 + 0 = – 9
2nd row = – 4 + (- 3) + (- 2)
= – 4 – 3 – 2 = -9
3rd row = – 6 + 4 + (- 7)
= – 6 + 4 – 7 = – 13 + 4 = -9
1st column = 1 + (- 4) + (- 6)
= 1 – 4 – 6 = 1 – 10 = -9
2nd column = (- 10 ) + (- 3) + 4
= -10 -3 + 4 = – 13 + 4 = – 9
3rd column = 0 + (-2) + (-7)
= 0 – 2 – 7 = 0 – 9 = – 9
1st diagonal = 1 + (- 3) + (- 7)
= 1 – 3 -7 = 1 – 10 = – 9
2nd diagonal= – 6 + (- 3) + 0
= -9 + 0 = -9
∴ Sum of each row, column and diagonal is the same.
∴ The square (ii) is the magic square.
Question 8.
Verify a – (- b) = a + b for the following values of a and b.
(i) a = 21, b = 18
(ii) a = 118, b = 125 .
(iii) a = 75, b = 84
(iv) a = 28, b = 11
Answer:
(i) L.H.S = a – (-b) = 21 – (-18)
= 21 + 18 = 39
R.H.S = a + b = 21 + 18 = 39
∴ a – (- b) = a + b
(ii) L.H.S = a – (- b) = 118 – (-125)
= 118 + 125 = 243
R.H.S = a + b = 118 + 125 = 243
∴ a – (- b) = a + b
(iii) L.H.S = a – (- b) = 75 – (- 84)
= 75 + 84 = 159
R.H.S = a + b = 75 + 84 = 159
∴ a – (-b) = a + b
(iv) L.H.S = a – (- b) = 28 – (- 11)
= 28 + 11 = 39
R.H.S = a + b = 28 +11 = 39
∴ a – (- b) = a + b
Question 9.
Use the sign of >, < or = in the box make the statements true.
Answer:
(a) (- 8) + (- 4) = – 8 – 4 = -12
(- 8) – (- 4) = – 8 + 4 = – 4
∴ – 12 < – 4
(b) (-3) + 7 – (19) = -3 + 7 – 19
= – 22 + 7 = – 15
15 – 8 + (- 9) = 15 – 8 – 9
= 15 – 17 = – 2
∴ -15 < – 2
(c) 23 – 41 + 11 = 34 – 41 = – 7
23 – 41 – 11 = 23 – 52 = – 29
∴ – 7 > – 29
(d) 39 + (- 24) – (15) = 39 – 24 – 15
= 39 – 39 = 0
36 + (- 52) – (- 36) = 36 – 52 + 36
= 72 – 52 = 20
∴ 0 < 20
(e) – 231 + 79 + 51 = – 231 + 130 = – 101
– 399 + 159 + 81 = – 399 + 240 = – 159
∴ -101 > -159
Question 10.
A water tank has steps inside it. A monkey is sitting on the topmost step (i.e., the first step). The water level is at the ninth step.
(i) He jumps 3 steps down and then jumps back 2 steps up. In how many jumps will he reach the water level?
(ii) After drinking water, he wants to go back. For this, he jumps 4 steps up and then jumps back 2 steps down in every move. In how many jumps will he reach back the top step?
(iii) If the number of steps moved down is represented by negative integers and the number of steps moved up by positive integers, represent his moves in part (i) and (ii) by completing the 1 following:
(a) – 3 + 2 -… = – 8
(b) 4 – 2 + … = 8.
In (a) the sum (- 8) represents going down by eight steps. So, what will the sum 8 in (b) represent?
Answer:
(i) To reach the water level his jumps will T be as follows:
(- 3) + 2 + (- 3) + 2 + (- 3) + 2 + (- 3) + 2 + (- 3) + 2 + (- 3) = – 8
Hence, in 11 jumps he will reach the 1 ninth step (water level)
(ii) To reach back the top step his jumps will be as follows:
4 + (-2) + 4 +(-2) + 4 = 8
Therefore, he will reach back the top step in 5 jumps.
(iii) (a) (- 3) + 2 + (- 3) + 2 + (- 3) + 2 + (- 3) + 2 + (- 3 + 2) + (- 3) = – 8
(b)4 – 2 + 4 – 2 + 4 – 2 + 4 – 2 = 8
Also in (a) the sum (- 8) represent going down by 8 steps and in (b) the sum (+ 8) will represent going up by 8 steps.
OR
(i) The position of the monkey after the:
(a) 1st jump is at the fourth step.
(b) 2nd jump is at the 2nd step.
(c) 3rd jump is at the 5th step.
(d) 4th jump is at the 3rd step.
(e) 5th jump is at the 6th step.
(f) 6th jump is at the 4th step.
(g) 7th jump is at the 7th step.
(h) 8th jump is at the 5th step.
(i) 9th jump is at the 8th step.
(j) 10th jump is at the 6th step.
(k) 11th jump is at the 9th step.
∴ Required number of jumps = 11.
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