NCERT Solutions for Class 7 Maths Chapter 1 Integers Exercise 1.1
NCERT Solutions for Class 7 Maths Chapter 1 Integers Ex 1.1
Class 7 Maths Integers Exercise 1.1
Class 7 Maths Integers Exercise 1.2
Class 7 Maths Integers Exercise 1.3
Class 7 Maths Integers Exercise 1.4
Exercise 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 Lahulspriti 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 following temperatures.
Cities Temperature
Lahulspriti -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
Difference in temperature of hottest and coldest place = 22°C – (-8°C) = 22°C + 8°C = 30°C
(c) Temperature of Lahulspriti = -8°C
Temperature of Srinagar = -2°C
∴ Temperature difference between Lahulspriti and Srinagar = -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 Srinagar and Shimla taken together is less than the temperature at Shimla (3°C < 5°C) by 5°C - 3°C = 2°C.
And it is not less than the temperature at Srinagar (-2°C < 3°C)
Exercise 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:
Given scores are 25, -5, -10, 15, 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
Exercise 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 (∴dropped by 2°C)
Temperature on Wednesday = -7°C + 4°C = -3°C (∴rose by 4°C)
Exercise 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?
Height of the flying plane = 5000 m
Depth of the submarine = -1200 m
∴ Distance between them = 5000 m – (-1200 m) = 5000 m + 1200 m = 6200 m
Hence, the vertical distance = 6200 m
Exercise 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 = ₹ 2000.
Amount withdrawn = ₹ 1,642
∴ Balance in the account = ₹ 2,000 – ₹ 1,642 = ₹ 358
Exercise 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?
Distances travelled towards east from point A will be represented by positive integer i.e. +20 km.
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 (negative sign represents towards the west)
Hence, the required position of Rita will be presented by a negative number, i.e., -10.
Exercise 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?
(i) 1st Row sum = 5 + (-1) + (—4) =5 – 1 – 4 = 5 – 5 = 0
2nd Row sum = (-5) + (-2) + 7 = -5 – 2 + 7 = -7 + 7 = 0
3rd Row sum = 0 + 3 + (-3) = 0 + 3- 3 = 0
1st Column sum = 5 + (-5) + 0 = 5 – 5 + 0 = 0
2nd column sum = (-1) + (-2) + (3) =-1 – 2 + 3 = -3 + 3 = 0
3rd column sum = (-4) + 7 + (-3) = -4 + 7 – 3 = 7 – 7 = 0
1st Diagonal sum = 5 + (-2) + (-3) = 5 – 2- 3 = 5 – 5 = 0
2nd Diagonal sum = (-4) + (-2) + 0 = -4 – 2 + 0 = -6 + 0 = -6
Here, the sum of the integers of 2nd diagonal is different from the others.
Hence, it is not a magic square.
(ii) 1st Row sum = 1 + (-10) + 0 = 1 – 10 + 0 = -9
2nd Row sum = (-4) + (-3) + (-2) = -4 – 3 – 2 = -9
3rd Row sum = (-6) + (4) + (-7) = -6 + 4 – 7 = -9
1st Column sum = 1 + (-4) + (-6) = 1 – 4 – 6 = -9
2nd column sum = (-10) + (-3) + 4 = -10 – 3 + 4 = -9
3rd column sum = 0 + (-2) + (-7) = 0 – 2 -7 = -9
1st Diagonal sum = 1 + (-3) + (-7) = 1 – 3 – 7 = 1 – 10 = -9
2nd Diagonal sum = 0 + (-3) + (-6) = 0 – 3- 6 = -9
Here, sum of the integers column wise, row wise and diagonally is same i.e. -9.
Hence, (ii) is a magic square.
Exercise 1.1 Class 7 Maths Question 8.
Verify a – (-b) = a + b for the following values of a and 6.(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 = a – (-b) = 21 – (-18) = 21 + 18 = 39
RHS = a + b = 21 + 18 = 39
LHS = RHS Hence, verified.
(ii) a – (-b) = a + b
LHS = a – (-b) = 118 – (-125) = 118 + 125 = 243
RHS = a + b = 118 + 125 = 243
LHS = RHS Hence, verified.
(iii) a – (-b) = a + b
LHS = a – (-b) = 75 – (-84) = 75 + 84 = 159
RHS = a + b = 75 + 84 = 159
LHS = RHS Hence, verified.
(iv) a – (-b) = a + b
LHS = a – (-b) = 28 – (-11) = 28 + 11 = 39
RHS = a + b = 28 + 11 = 28 + 11 = 39
LHS = RHS Hence, verified.
Exercise 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 + 1 = -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
Exercise 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 (t) 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) As the monkey is sitting on the step = 1
The position of monkey after the 1st jump = 1 + 3 = 4th step
2nd jump = 4 - 2 = 2nd step
3rd jump = 2 + 3 = 5th step
4th jump = 5 - 2 = 3rd step
5th jump = 3 + 3 = 6th step
6th jump = 6 - 2 = 4th step
7th jump = 4 + 3 = 7th step
8th jump = 7 - 2 = 5th step
9th jump = 5 + 3 = 8th step
10th jump = 8 - 2 = 6th step
11th jump = 6 + 3 = 9th step (Water level)
Hence the required number of jumps = 11.
(ii) As the monkey is sitting at water level = 9
Monkey’s position after the 1st jump = 9 - 4 = 5th step
2nd jump = 5 + 2 = 7th step
3rd jump = 7 - 4 = 3rd step
4th jump = 3 + 2 = 5th step
5th jump = 5 - 4 = 1st step
Hence, the required number of jumps = 5.
(iii) According to the given conditions we have the following tables
Jumps 1 2 3 4 5 6 7 8 9 10 11
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
Jumps 1 2 3 4 5
Number of steps + 4 -2 +4 -2 +4
Therefore (b) Total number of steps = +4 – 2 + 4 – 2 + 4 = 8
Here, the monkey is going up by 8 steps.