## 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.
Temperature at the Lahulspiti = -8°C
Temperature at the Srinagar = -2°C
Temperature at the Shimla = 5°C
Temperature at the Ooty = 14°C
Temperature at the Bengaluru = 22°C

(b) What is the temperature difference between the hottest and the coldest places among the above?

The temperature at the hottest place (Bengaluru) = 22°C
The temperature at the coldest place (Lahulspiti) = -8°C
Temperature difference between hottest and coldest place = ?
= 22°C - (-8°C)
= 22°C + 8°C
= 30°C
Therefore, the temperature difference between the hottest and the coldest place is 30°C.

(c) What is the temperature difference between Lahulspiti and Srinagar?

The temperature at the Lahulspiti = -8°C
The temperature at the Srinagar = -2°C
The temperature difference between Lahulspiti and Srinagar = ?
= -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?

The temperature at Srinagar = -2°C
The temperature at Shimla = 5°C
The temperature sum of Srinagar and Shimla = ?
= -2°C + 5°C
= 3°C
5°C > 3°C
Therefore, the temperature of Srinagar and Shimla taken together is less than the temperature at Shimla.
3° > -2°
No, the temperature of Srinagar and Shimla taken together is not less than the temperature of 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?

Jack’s score in five successive rounds = 25, -5, -10, 15 and 10
The total score of Jack at the end will be = ?
= 25 + (-5) + (-10) + 15 + 10
= 25 - 5 - 10 + 15 + 10
= 50 - 15
= 35
Therefore, Jack’s total score at the end is 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?

Temperature on Monday at Srinagar = -5°C
Temperature on Tuesday at Srinagar = ?
= Temperature on Monday - 2°C
= -5°C - 2°C
= -7°C
Temperature on Wednesday at Srinagar = ?
= Temperature on Tuesday + 4°C
= -7°C + 4°C
= -3°C
Therefore, 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?

Plane is flying at the height = 5000 m
Depth of Submarine = -1200 m
The vertical distance between plane and submarine = ?
= 5000 m - (-1200) m
= 5000 m + 1200 m
= 6200 m
Therefore, the vertical height between the plane and submarine is 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.

(Withdrawal of amount from the account is represented by a negative integer while deposit of amount to the account is represented by a positive integer.)
Total amount deposited in bank account by the Mohan = ₹ 2000
Total amount withdrawn from the bank account by the Mohan = -₹ 1642
Balance in Mohan’s account after the withdrawal = ?
= Amount deposited + Amount withdrawn
= ₹ 2000 + (-₹ 1642)
= ₹ 2000 - ₹ 1642
= ₹ 358
Therefore, the balance in Mohan’s account after the withdrawal is ₹ 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 a positive integer then, how will you represent the distance travelled towards west? By which integer will you represent her final position from A?

(A positive integer represents the distance towards the east while the distance travelled towards the west will be represented by a negative integer.)
Rita travels a distance in east direction = 20 km
Rita travels a distance in west direction = -30 km
Therefore, distance travelled from A = ?
= 20 + (- 30)
= 20 - 30
= -10 km
Therefore, the distance travelled by Rita from point 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.

(i) By adding the numbers in each rows,
= 5 + (- 1) + (- 4) = 5 - 1 - 4 = 5 - 5 = 0
= -5 + (-2) + 7 = - 5 - 2 + 7 = -7 + 7 = 0
= 0 + 3 + (-3) = 3 - 3 = 0
By adding the numbers in each columns,
= 5 + (- 5) + 0 = 5 - 5 = 0
= (-1) + (-2) + 3 = -1 – 2 + 3 = -3 + 3 = 0
= -4 + 7 + (-3) = -4 + 7 - 3 = -7 + 7 = 0
By adding the numbers in diagonals,
= 5 + (-2) + (-3) = 5 - 2 - 3 = 5 - 5 = 0
= -4 + (-2) + 0 = - 4 - 2 = -6
Due to sum of one diagonal is not equal to zero, (i) is not a magic square

(ii) By adding the numbers in each rows,
= 1 + (-10) + 0 = 1 - 10 + 0 = -9
= (-4) + (-3) + (-2) = -4 - 3 - 2 = -9
= (-6) + 4 + (-7) = -6 + 4 - 7 = -13 + 4 = -9
By adding the numbers in each columns,
= 1 + (-4) + (-6) = 1 - 4 - 6 = 1 - 10 = -9
= (-10) + (-3) + 4 = -10 - 3 + 4 = -13 + 4
= 0 + (-2) + (-7) = 0 - 2 - 7 = -9
By adding the numbers in diagonals,
= 1 + (-3) + (-7) = 1 - 3 - 7 = 1 - 10 = -9
= 0 + (-3) + (-6) = 0 - 3 - 6 = -9
Therefore, (ii) is a magical square.

Question 8: Verify a – (– b) = a + b for the following values of a and b.
(i) a = 21, b = 18

a = 21
b = 18
Left Hand Side [a – (– b)]
= 21 - (- 18)
= 21 + 18
= 39
Right Hand Side [a + b]
= 21 + 18
= 39
Comparing LHS and RHS
LHS = RHS
39 = 39
Therefore, the value of a and b is verified.

(ii) a = 118, b = 125

a = 118
b = 125
Left Hand Side [a – (– b)]
= 118 - (- 125)
= 118 + 125
= 243
Right Hand Side [a + b]
= 118 + 125
= 243
Comparing LHS and RHS
LHS = RHS
243 = 243
Therefore, the value of a and b is verified.

(iii) a = 75, b = 84

a = 75
b = 84
Left Hand Side [a - (- b)]
= 75 - (- 84)
= 75 + 84
= 159
Right Hand Side [a + b]
= 75 + 84
= 159
Comparing LHS and RHS
LHS = RHS
159 = 159
Therefore, the value of a and b is verified.

(iv) a = 28, b = 11

a = 28
b = 11
Left Hand Side [a - (- b)]
= 28 - (- 11)
= 28 + 11
= 39
Right Hand Side [a + b]
= 28 + 11
= 39
Comparing LHS and RHS
LHS = RHS
39 = 39
Therefore, the value of a and b is verified.

Question 9: Use the sign of >, < or = in the box to make the statements true.
(a) (-8) + (-4) [ ] (-8) – (-4)

Left Hand Side = (-8) + (-4)
= -8 - 4
= -12
Right Hand Side = (-8) – (-4)
= -8 + 4
= -4
Comparing LHS and RHS
LHS < RHS
-12 < -4
Therefore, (-8) + (-4) [<] (-8) - (-4)

(b) (-3) + 7 – (19) [ ] 15 – 8 + (-9)

Left Hand Side = (-3) + 7 - 19
= -3 + 7 - 19
= -22 + 7
= -15
Right Hand Side = 15 - 8 + (-9)
= 15 - 8 - 9
= 15 - 17
= -2
Comparing LHS and RHS
LHS < RHS
-15 < -2
Therefore, (-3) + 7 - (19) [<] 15 - 8 + (-9)

(c) 23 – 41 + 11 [ ] 23 – 41 – 11

Left Hand Side = 23 - 41 + 11
= 34 - 41
= – 7
Right Hand Side = 23 - 41 - 11
= 23 - 52
= -29
Comparing LHS and RHS
LHS > RHS
-7 > -29
Therefore, 23 – 41 + 11 [>] 23 – 41 – 11

(d) 39 + (-24) – (15) [ ] 36 + (-52) – (- 36)

Left Hand Side = 39 + (-24) - 15
= 39 - 24 - 15
= 39 - 39
= 0
Right Hand Side = 36 + (-52) - (- 36)
= 36 - 52 + 36
= 72 - 52
= 20
Comparing LHS and RHS
LHS < RHS
0 < 20
Therefore, 39 + (-24) - (15) [<] 36 + (-52) - (- 36)

(e) -231 + 79 + 51 [ ] -399 + 159 + 81

Left Hand Side = -231 + 79 + 51
= -231 + 130
= -101
Right Hand Side (RHS) = – 399 + 159 + 81
= -399 + 240
= -159
Comparing LHS and RHS
LHS > RHS
-101 > -159
Therefore, -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 then jumps back 2 steps up. In how many jumps will he reach the water level?

(Let the steps moved down be represented by positive integers and steps moved up are represented by negative integers)
In 1st jump monkey will be at step = 1 + 3 = 4 steps
In 2nd jump monkey will be at step = 4 + (-2) = 4 - 2 = 2 steps
In 3rd jump monkey will be at step = 2 + 3 = 5 steps
In 4th jump monkey will be at step = 5 + (-2) = 5 - 2 = 3 steps
In 5th jump monkey will be at step = 3 + 3 = 6 steps
In 6th jump monkey will be at step = 6 + (-2) = 6 - 2 = 4 steps
In 7th jump monkey will be at step = 4 + 3 = 7 steps
In 8th jump monkey will be at step = 7 + (-2) = 7 - 2 = 5 steps
In 9th jump monkey will be at step = 5 + 3 = 8 steps
In 10th jump monkey will be at step = 8 + (-2) = 8 - 2 = 6 steps
In 11th jump monkey will be at step = 6 + 3 = 9 steps
Therefore, Monkey took 11 jumps to 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?

(Let the steps moved down be represented by positive integers and then, steps moved up are represented by negative integers)
In 1st jump monkey will be at step = 9 + (-4) = 9 - 4 = 5 steps
In 2nd jump monkey will be at step = 5 + 2 = 7 steps
In 3rd jump monkey will be at step = 7 + (-4) = 7 - 4 = 3 steps
In 4th jump monkey will be at step = 3 + 2 = 5 steps
In 5th jump monkey will be at step = 5 + (-4) = 5 - 4 = 1 step
Therefore, monkey took 5 jumps to reach back to the first 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?

(Let the number of steps moved down be represented by negative integers and the number of steps moved up by positive integers)
Monkey moves in part (i)
= -3 + 2 - ……….. = -8
Then LHS = - 3 + 2 - 3 + 2 - 3 + 2 - 3 + 2 - 3 + 2 - 3
= -18 + 10
= -8
RHS = -8
Therefore, moves in part (i) represents monkey is going down 8 steps because negative integer.
Monkey moves in part (ii)
= 4 - 2 + ……….. = 8
Then LHS = 4 - 2 + 4 - 2 + 4
= 12 - 4
= 8
RHS = 8
Therefore, moves in part (ii) represents monkey is going up 8 steps. Because positive integer.