RBSE Solutions for Class 7 Maths Chapter 1 Integers Ex 1.1

Rajasthan Board RBSE Solutions for Class 7 Maths Chapter 1 Integers Ex 1.1 Textbook Exercise Questions and Answers.

RBSE Class 7 Maths Solutions Chapter 1 Integers Ex 1.1

Question 1.
Following number line shows the temperature in degrees Celsius (°C) at different places on a particular day.

(a) Observe this number line and write the temperature of the places marked on it.
Answer:

(b) What is the temperature difference between the hottest and the coldest place among the above?
Answer:
Temperature of the hottest place,
Bengaluru = 22°C
Temperature of the coldest place.
Lahuispiti = - 8°C
Difference in temperature
= 22°C - (- 8°C)
= 22°C + 8°C = 30°C

(c) What is the temperature difference between Lahulspiti and Srinagar?
Answer:
Temperature of Lahulspiti = - 8°C
Temperature of Srinagar = - 2°C
Difference in temperature
= - 2°C - (- 8°C)
= - 2°C + 8°C = 6°C

(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:
Temperature of Srinagar = - 2°C
Temperature of Shimla = + 5°C
Temperature of Srinagar and Shimla
= - 2°C + 5°C = 3°C
Since, 5°C > 3°C
Temperature of Srinagar and Shimla taken together is less than the temperature at Shimla.
Also - 2°C < 3°C
No, it 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:
Jack's scores in 5 rounds = 25, - 5, - 10, 15, 10
Jack's total score
= 25 + (- 5) + (- 10) + 15 + 10
= 25 - 5 - 10 + 15 + 10 = 50 - 15 = 35
So, Jack's score is 35 at the end.

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 of Srinagar on Monday = - 5°C
Temperature drop on Tuesday = 2°C
Temperature on Tuesday = - 5°C - 2°C = - 7°C -
Temperature rise on Wednesday = 4°C
Temperature on Wednesday = - 7°C + 4°C = - 3°C
So, the temperature on Tuesday and Wednesday was - 7°C and - 3°C respectively.

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:
Height of plane = 5000 m
Depth of submarine = 1200 m
Vertical distance between plane and sub-marine = 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 = ₹ 2,000
Amount withdrawn = ₹ 1,642
Balance in account = ₹ 2,000 - ₹ 1,642 = ₹ 358
If withdrawl is represented by negative integer, then amount deposited will be represent 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 east from AtoB = 20 km
Distance from B towards west = - 30 km
Final position from A = 20 km + (- 30) km = -10 km
So, Rita's final position front A is - 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?

Answer:
(i) Sum of rows
I = (5) + (- 1) + (- 4)
= 5 - 5 = 0
II = (- 5) + (- 2) + 7
= - 7 + 7 = 0
III = 0 + 3 + (- 3) = 0
Sum of columns
1 = 5 +(- 5)+ 0 = 0
II = (- 1) + (- 2) + 3 = - 3 + 3 = 0
III = (- 4) + 7 + (- 3) = 3 - 3 = 0
Sum of diagonal one
= 5 + (- 2) + (- 3) = 5 - 5 = 0
other = (- 4) + (- 2) + 0 = - 6
Since, all the sums are not equal, then given square isn't a magic square.

(ii) Sum of rows
I = 1 + (- 10) + 0 = - 9
II = (- 4) + (- 3) + (- 2) = - 9 .
III = (-6) + 4 + (-7)
= -13 + 4 = -9
Sum of columns
I = 1 + (- 4) + (- 6) = 1 - 10 = - 9
II = (- 10) +(-3) +4 = - 13 + 4 = - 9
III = 0 + (- 2) + (- 7) = - 9
Sum of diagonal one
= 1 + (- 3) + (- 7) = 1 - 10 = - 9
other = 0 + (- 3) + (- 6) = - 9
Since, all the sum are equal then 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 = 28,6 = 11
Answer:
(i) LHS = a - (- 6)
= 21 - (- 18)
= 21 + 18 = 39
RHS = a + b = 21 + 18 = 39
∴ LHS = RHS

(ii) LHS = a - (- 6)
= 118 - (- 125)
= 118 + 125 = 243 RHS =a + b
= 118 + 125 = 243
∴ LHS = RHS

(iii) LHS = a - ( - b)
= 75 - (-84)
= 75 + 84 = 159
RHS = a + b = 75 + 84 = 159
∴ LHS = RHS

(iv) LHS = a - (- b)
= 28 - (- 11) = 28 + 11 = 39
RHS = a + b = 28 + 11 = 39
∴ LHS = RHS
Hence verified.

Question 9.
Use the sign of >, < or = in the box to make the statements true:
(a) (- 8) + (- 4) __________ (- 8) - (- 4)
(b) ( - 3) + 7 - (19) _________ 15 - 8 + (- 9)
(c) 23 - 41 + 11 ___________ 36 + (- 52) - (- 36)
(d) 39 + (- 24) - (15) _________ 36 + (- 52) - (- 36)
(e)- 231 + 79 + 51 _________ - 399 + 159 + 81
Answer:
(a) - 8 + (- 4) _________ (- 8) - (- 4)
⇒ - 8 - 4 _________ (- 8) + 4
⇒ - 12 < - 4

(b) - 3 + 7 - (19) _________ 15 - 8 + (- 9)
⇒ - 22 + 7 _________ 15 - 7
⇒ - 15 < - 2

(c) 23 - 41 + 11 _________ 23 - 41 - 11
⇒ 34 - 41 _________ 23 - 52
⇒ - 7 > - 29

(d) 39 + (- 24) - (15) _________ (36) + (- 52) - (- 36)
⇒ 39 - 39 _________ 72 - 52
⇒ 0 < 20

(e) - 231 + 79 + 51 ________ 399 + 159 + 81
⇒ 231 + 130 _________ - 399 + 240
⇒ 101 > - 159

Question 10.
A water tank has steps inside it. A monkey is sitting on the topmost step (i.ethe 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 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) He jumps 3 steps down and jumps back 2 steps up. Following table shows the jumps of monkey :
I Jump = 1 + 3 = 4 steps
II Jump = 4 - 2 = 2 steps
III Jump = 2 + 3 = 5 steps
IV Jump = 5 - 2 = 3 steps
V Jump = 3 + 3 = 6 steps
VI Jump = 6 - 2 = 4 steps
VII Jump = 4 + 3 = 7 steps
VIII Jump = 7 - 2 = 5 steps
IX Jump = 5 + 3 = 8 steps
X Jump = 8 - 2 = 6 steps
XI Jump = 6 + 3 = 9 steps
The monkey will reach the water tank in 11 jumps.

(ii) I Jump = 9 - 4 = 5 steps
II Jump = 5 + 2 = 7 steps
III Jump = 7 - 4 = 3 steps
IV Jump = 3 + 2 = 5 steps
V Jump = 5 - 4 = 1 steps
The monkey will reach back the top step in 5 jumps.

(iii) (a) - 3 + 2 - 3 + 2 - 3 + 2 - 3 + 2
- 3 + 2 - 3 + 2 - 3 + 2 - 3 + 2 = - 8
(b) 4 - 2 + 4 - 2 + 4 - 2 + 4 - 2 = 8
The sum 8 represents going up by 8 steps.