NCERT Solutions for Class 7 Maths Chapter 1 Integers Ex 1.1, are part of NCERT Solutions for Class 7 Maths. Here we have given NCERT Solutions for Class 7 Maths Chapter 1 Integers Ex 1.1.
NCERT Solutions for Class 7 Maths Chapter 1 Integers Ex 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 Lahul-Spiti 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?
Solution:
(a)
(b) Temperature difference between the hottest and the coldest places
= Temperature of Bangalore – Temperature of Lahul-Spiti
= 22°C-(-8°C)
= 22°C + 8°C
= 30°C
(c) Temperature difference between Lahul-Spiti and Srinagar
= Temperature of Srinagar
– Temperature of Lahul-Spiti
= – 2°C – (- 8°C)
= – 2°C + 8°C
= 6°C
(d) Temperature of Srinagar and Shimla together
= Temperature of Srinagar
+ Temperature of Shimla
= – 2° + 5°C
= 3°C
Temperature at Shimla = 5°C
Temperature at Srinagar = – 2°C.
Therefore, we can say that temperature of Srinagar and Shimla together is less than the temperature at Shimla but the temperature of Srinagar and Shimla together 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?
Solution:
Total at the end
= 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 Tues¬day. What was the temperature of Srinagar on Tuesday? On Wednesday, it rose by 4°C. What was the temperature on this day?
Solution:
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
= – (7 – 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 e×actly above a submarine floating 1200 m below the sea level. What is the vertical distance between them?
Solution:
Vertical distance between the plane and submarine.
= 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.
Solution:
Amount deposited = + ₹2000
Balance in Mohan’s account after the withdrawal
= ₹ 2000 – ₹ 1642
= ₹ (2000 – 1642)
= ₹ 358.
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 positive integer then, how will you represent the distance travelled towards west?
By which integer will you represent her final position from A?
Solution:
The distance towards west
= – 30 km
Her final position from A
= + 20 km + (- 30) km
= – (30 – 20) 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.
Solution:
I. Row, Sum = 5 + (- 1) + (- 4)
= 5 + (- 5) = 0
II. Row, Sum = (- 5) + (- 2) + 7
= (- 7) + 7 = 0
III. Row, Sum = 0 + 3 + (- 3)
= 0 + 0 = 0
I. Column, Sum = 5 + (- 5) + 0
= 0 + 0 = 0
II. Column, Sum = (- 1) + (- 2) + 3
= (- 3) + 3 = 0
III. Column, Sum = (- 4) + 7 + (- 3)
= 7 + (- 4) + (- 3)
= 7 + (- 7) = 0
One Diagonal, Sum = 5 + (- 2) + (- 3) = 5 + (- 5) = 0
Other Diagonal, Sum = 0 + (- 2) + (- 4) = 0 + (- 6) = -6 ≠ 0
Therefore, the given square is not a magic square.
I. Row, Sum = 1 + (- 10) + 0 = – 9
II. Row, Sum = (- 4) + (- 3) + (- 2) = – 9
III. Row, Sum = (- 6) + 4 + (- 7)
= 4 + (- 6) + (- 7)
= 4 + (- 13)
= – (13-4) = -9
I. Column, Sum = 1 + (- 4) + (- 6)
= 1 + (- 10)
= -(10 – 1) = – 9
II. Column, Sum = (- 10) + (- 3) + 4
= (-13)+ 4
= – (13-4) = -9
III. Column, Sum = 0 + (- 2) + (- 7)
= 0 + (- 9) = – 9
One Diagonal, Sum = 1 + (- 3) + (- 7)
= 1 + (- 10)
= -(10-1) = -9
Other Diagonal, Sum = (- 6) + (- 3) + 0
= (- 9) + 0 = – 9
Since each row, column and diagonal ‘ have the same sum, therefore, the given square is a 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.
Solution:
(i) a = 21, b = 18
L.H.S. = a – (- b) = 21 – (- 18) = 21 + 18 = 39 …..(1)
R.H.S. = a + b = 21 + 18 = 39 …..(2)
From (1) and (2), we get a -(-b) = a + b
(ii) a = 118, b = 125
L.H.S. = a – (- b) = 118 – (- 125) = 118 + 125 = 243 …(1)
R.H.S. = a + b = 118 + 125 = 243 …(2)
From (1) and (2), we get a -(- b) = a + b
(iii) a = 75, b = 84
L.H.S. = a – (- b) = 75 – (- 84) = 75 + 84 = 159 …(1)
R.H.S. = a + b = 75 + 84 = 159 …(2)
From (1) and (2), we get a – (- b) = a + b
(iv) a = 28, b = 11
L.H.S. = a – (- b) = 28 -(-11) = 28 + 11 = 39 …(1)
R.H.S. = a + b = 28 + 11 = 39 …(2)
From (1) and (2), we get a – (- b) = a + b.
Question 9.
Use the sign of >, < or = in the bo× to make the statements true.
(a) (- 8) + (-4) …… (- 8) – (- 4)
(b) (-3) +7 – (19) …… 15-8 +(-9)
(c) 23 – 41 + 11 …… 23-41- 11
(d) 39 + (-24) – (15) …… 36+ (-52) – (- 36)
(e) – 231 + 79 + 51 …… -399 + 159 + 81.
Solution:
(a) L.H.S. = (- 8) + (- 4)
= – (8 + 4) = – 12
R.H.S. = (- 8) – (- 4)
= – 8 + 4 = – (8 – 4) = – 4
∴ (-8) + (-4) < (-8)-(-4)
(b) L.H.S. = (-3) + 7 – (19)
= + 4 – (19)
= + 4 – 19
= -15
R.H.S. = 15 – 8 + (- 9)
= 7 + (-9) = 7- 9 = -2
∴ (- 3) + 7 – (19) < 15 – 8 + (- 9)
(c) L.H.S. = 23 – 41 + 11
= 23 + 11- 41
= 34 – 41 = – (41 – 34)
= – 7
R.H.S. = 23 – 41 – 11
= 23 – (41 + 11)
= 23 – 52
= – (52 – 23)
= – 29
∴ 23 – 41 + > 23 – 41 – 11
(d) L.H.S. = 39 + (- 24) – (15)
= 39 – 24 – (15)
= 15 – (15) = 0
R.H.S. = 36 + (- 52) – (- 36)
= – (52 – 36) – (- 36)
= – 16 – (- 36)
= – 16 + 36 = 20
∴ 39 + (- 24) – (15) < 36 + (- 52) – (- 36)
(e) L.H.S. = – 231 + 79 + 51
= – 231 + 130
= – (231 – 130) = – 101
R.H.S. = – 399 + 159 + 81
= – 399 + 240
= – (399 – 240)
= – 159
∴ – 231 + 79 + 51 > – 399 + 159 + 81.
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 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 com pleting the following;
(a) -3 + 2 – …………. = -8
(b) 4 – 2 + = 8.
In (a) the sum (-8) represent going down by eight steps. So, what will the sum 8 in (b) represent?
Solution:
(i) To reach the water level his jump will be as follows:
(- 3) + 2 + (- 3) + 2 + (- 3) + 2
+ (- 3) + 2 + (- 3) + 2 + (- 3) = – 8.
Hence in 11 jumps he will reach the water level.
(ii) To reach back the top step his jumps will be as follows:
4 + (- 2) + 4 + (- 2) + 4 = 8
Therefore, he will be out of the tank in 5 jumps.
(iii) (a) – 3 + 2 + (- 3) + 2 + (- 3) + 2
+ (- 3) + 2 + (T 3) + 2 + (- 3) = – 8
(6) 4 – 2 + 4 – 2 + 4 = 8
The sum 8 in (b) will represent going up.
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