NCERT Solutions for Class 7 Maths Chapter 1 Integers Ex 1.1

NCERT Solutions for Class 7 Maths Chapter 1 Integers Ex 1.1 are the part of NCERT Solutions for Class 7 Maths. Here you can find the NCERT Solutions for Class 7 Maths Chapter 1 Integers Ex 1.1.

Ex 1.1 Class 7 Maths 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?

Solution:
(a) From the given number line, we observe the temperature of the places as follows.

Cities	Temperature
Lahulspiti	-8°C
Srinagar	-2°C
Shimla	5°C
Ooty	14°C
Bengaluru	22°C

(b) The temperature of the hottest place = 22°C
The temperature of the coldest place = -8°C
Temperature difference = 22°C – (-8°C)
= 22°C + 8°C = 30°C
(c) Temperature of Lahulspiti = -8°C
Temperature of Srinagar = -2°C
∴ Temperature difference = -2°C – (-8°C)
= -2°C + 8°C = 6°C
(d) Temperature of Srinagar = -2°C
Temperature of Shimla = 5°C
∴ Temperature of the above cities taken together
= -2°C + 5°C = 3°C
Temperature of Shimla = 5°C
Hence, the temperature of Srinagar and Shimla taken together is less than that of the temperature of Shimla by 2°C.
i.e., (5°C – 3°C) = 2°C

Ex 1.1 Class 7 Maths 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:
Jack’s scores are 25, -5, -10, 15 and 10.
Marks given for correct answers = 25 + 15 + 10 = 50
Marks given for incorrect answers = (-5) + (-10) = -15
∴ Total marks given at the end = 50 + (-15) = 50 – 15 = 35

Ex 1.1 Class 7 Maths 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?

Solution:
Temperature of Srinagar on Monday = -5°C
Temperature on Tuesday = -5°C – 2°C = -7°C
Temperature was increased by 4°C on Wednesday.
∴ Temperature on Wednesday = -7°C + 4°C = -3°C

Ex 1.1 Class 7 Maths 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 flowing 1200 m below the sea level. What is the vertical distance between them?

Solution:
Height of the plane above the sea level = 5000 m
Depth of the submarine below the sea level = -1200 m
∴ Distance between the plane and the submarine
= + 5000 m – (-1200 m)
= 5000 m + 1200 m = 6200 m
Hence, the vertical distance between them = 6200 m

Ex 1.1 Class 7 Maths Question 5.

Mohan deposits ₹ 2,000 in a 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:
The deposited amount is represented by a positive integer, i.e., + ₹ 2000.
Amount withdrawn from the account = ₹ 1,642
∴ Balance in the account = ₹ 2,000 – ₹ 1,642 = ₹ 358
Hence, the balance in Mohan’s account after the withdrawal = ₹ 358

Ex 1.1 Class 7 Maths 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 her final position from A?

Solution:
The distance travelled towards east from point A is represented by positive integer, i.e., +20 km.
The distance travelled towards the west from point B will be represented by negative integer, i.e., –30 km.
Final position of Rita from A = 20 km – 30 km = –10 km
Hence, the final position of Rita will be presented by a negative integer, i.e., -10 km.

Ex 1.1 Class 7 Maths Question 7.

In a magic square each row, column and the diagonal have the same sum. Check which of the following is a magic square?

Solution:
(i) Sum of the first row = 5 + (-1) + (–4)
= 5 – 1 – 4 = 5 – 5 = 0
Sum of the second row = (-5) + (-2) + 7
= -5 – 2 + 7 = -7 + 7 = 0
Sum of the third row = 0 + 3 + (-3)
= 0 + 3 – 3 = 0
Sum of the first column = 5 + (-5) + 0
= 5 – 5 + 0 = 0
Sum of the second column = (-1) + (-2) + (3)
= -1 – 2 + 3 = -3 + 3 = 0
Sum of the third column = (-4) + 7 + (-3)
= -4 + 7 – 3 = 7 – 7 = 0
Sum of the first diagonal = 5 + (-2) + (-3)
= 5 – 2 – 3 = 5 – 5 = 0
Sum of the second diagonal = (-4) + (-2) + 0
= -4 – 2 + 0 = -6 + 0 = -6
Here, the sum of the integers of second diagonal is different from the others.
Hence, it is not a magic square.

(ii) Sum of the first row = 1 + (-10) + 0
= 1 – 10 + 0 = -9
Sum of the second row = (-4) + (-3) + (-2)
= -4 – 3 – 2 = -9
Sum of the third row = (-6) + (4) + (-7)
= -6 + 4 – 7 = -9
Sum of the first column = 1 + (-4) + (-6)
= 1 – 4 – 6 = -9
Sum of the second column = (-10) + (-3) + 4
= -10 – 3 + 4 = -9
Sum of the third column = 0 + (-2) + (-7)
= 0 – 2 – 7 = -9
Sum of the first diagonal = 1 + (-3) + (-7)
= 1 – 3 – 7 = 1 – 10 = -9
Sum of the second diagonal = 0 + (-3) + (-6)
= 0 – 3 – 6 = -9
Here, the sum of the integers in each row, each column and each diagonal is the same, i.e., -9. Hence, square (ii) is a magic square.

Ex 1.1 Class 7 Maths 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

Solution:
(i) a – (-b) = a + b
LHS = 21 – (-18) = 21 + 18 = 39
RHS = 21 + 18 = 39
LHS = RHS. Hence, verified.

(ii) a – (-b) = a + b
LHS = 118 – (-125) = 118 + 125 = 243
RHS = 118 + 125 = 243
LHS = RHS. Hence, verified.

(iii) a – (-b) = a + b
LHS = 75 – (-84) = 75 + 84 = 159
RHS = 75 + 84 = 159
LHS = RHS. Hence, verified.

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

Ex 1.1 Class 7 Maths 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 □ 23 – 41 – 11
(d) 39 + (-24) – (15) □ 36 + (-52) – (-36)
(e) -231 + 79 + 51 □ -399 + 159 + 81

Solution:
(a) (-8) + (-4) □ (-8) – (-4)
LHS = (-8) + (-4) = -8 – 4 = – 12
RHS = (-8) – (-4) = -8 + 4 = -4
Here, – 12 < -4
Hence, (-8) + (-4) < (-8) – (-4)

(b) (-3) + 7 – (19) □ 15 – 8 + (-9)
LHS = (-3) + 7 – (19) = -3 + 7 – 19
= -3 – 19 + 7
= -22 + 7 = -15
RHS = 15 – 8 + (-9)
= 15 – 8 – 9
= 15 – 17 = -2
Here, -15 < -2
Hence, (-3) + 7 – (19) < 15 – 8 + (-9)

(c) 23 – 41 + 11 □ 23 – 41 – 11
LHS = 23 – 41 + 11 = 23 + 11 – 41 = 34 – 41 = -7
RHS = 23 – 41 – 11 = 23 – 52 = -29. Here, -7 > -29
Hence, 23 – 41 + 11 > 23 – 41 – 11

(d) 39 + (-24) – (15) □ 36 + (-52) – (-36)
LHS = 39 + (-24) – (15)
= 39 – 24 – 15
= 39 – 39 = 0
RHS = 36 + (-52) – (-36) = 36 – 52 + 36
= 36 + 36 – 52
= 72 – 52 = 20
Here 0 < 20
Hence, 39 + (-24) – (15) < 36 + (-52) – (-36)

(e) -231 + 79 + 51 □ -399 + 159 + 81
LHS = -231 + 79 + 51 = -231 + 130 = -101
RHS = -399 + 159 + 81 = -399 + 240 = -159
Here, -101 > -159
Hence, -231 + 79 + 51 > -399 + 159 + 81

Ex 1.1 Class 7 Maths 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 move 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?

Solution:

(i) The position of monkey after the

1^st jump J₁ is at 4^th step ↓
2^nd jump J₂ is at 2^nd step ↑
3^rd jump J₃ is at 5^th step ↓
4^th jump J₄ is at 3^rd step ↑
5^th jump J₅ is at 6^th step ↓
6^th jump J₆ is at 4^th step ↑
7^th jump J₇ is at 7^th step ↓
8^th jump J₈ is at 5^th step ↑
9^th jump J₉ is at 8^th step ↓
10^th jump J₁₀ is at 6^th step ↑
11^th jump J₁₁ is at 9^th step ↓ (Water level)
Hence, the required number of jumps to reach the water level is 11.

(ii) Monkey’s position after the

1^st jump J₁ is at 5^th step ↑
2^nd jump J₂ is at 7^th step ↓
3^rd jump J₃ is at 3^rd step ↑
4^th jump J₄ is at 5^th step ↓
5^th jump J₅ is at 1^st step ↑
Hence, the required number of jumps to reach at the top is 5.

(iii) According to the given conditions we have the following tables

Jumps	J₁	J₂	J₃	J₄	J₅	J₆	J₇	J₈	J₉	J₁₀	J₁₁
Number of steps	-3	+2	-3	+2	-3	+2	-3	+2	-3	+2	-3

Therefore (a) Total number of steps
= -3 + 2 – 3 + 2 – 3 + 2 – 3 + 2 – 3 + 2 – 3
= -8 which represents the monkey goes down by 8 steps.
In case (ii), we get