 # NCERT Solutions for Class 7 Maths Exercise 1.1 Chapter 1 Integers

NCERT Solutions for Class 7 Maths Exercise 1.1 Chapter 1 Integers in simple PDF are given in this article. The NCERT Solutions for Class 7 Chapter 1 Exercise 1.1 contains topics related to the introduction of integers. We know that integers form a bigger collection of numbers, which includes whole numbers and negative numbers. Our expert teachers have formulated these solutions in precise, comprehensive and in a detailed form. Learn more about these topics by solving the questions of NCERT Solutions for Class 7 Maths Chapter 1 Integers with the help of solutions provided here.

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1. Following number line shows the temperature in degree celsius (co) at different places on a particular day. (a) Observe this number line and write the temperature of the places marked on it.

Solution:-

By observing the number line, we can find the temperature of the cities as follows,

The temperature at Lahulspiti is -8oC

The temperature at Srinagar is -2oC

The temperature at Shimla is 5oC

The temperature at Ooty is 14oC

The temperature at Bengaluru is 22oC

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

Solution:-

From the number line, we observe that,

The temperature at the hottest place, i.e. Bengaluru, is 22oC

The temperature at the coldest place, i.e., Lahulspiti, is -8oC

Temperature difference between hottest and coldest place is = 22oC – (-8oC)

= 22oC + 8oC

= 30oC

Hence, the temperature difference between the hottest and the coldest place is 30oC.

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

Solution:-

From the given number line,

The temperature at Lahulspiti is -8oC

The temperature at Srinagar is -2oC

∴ The temperature difference between Lahulspiti and Srinagar is = -2oC – (8oC)

= – 2OC + 8oC

= 6oC

(d) Can we say the temperature of Srinagar and Shimla, taken together, is less than the

temperature at Shimla? Is it also less than the temperature at Srinagar?

Solution:-

From the given number line,

The temperature at Srinagar =-2oC

The temperature at Shimla = 5oC

The temperature of Srinagar and Shimla, taken together, is = – 2oC + 5oC

= 3oC

∴ 5oC > 3oC

So, the temperature of Srinagar and Shimla, taken together, is less than the temperature at Shimla.

Then,

3o > -2o

Hence, the temperature of Srinagar and Shimla, taken together, is not less than the temperature of Srinagar.

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:-

From the question,

Jack’s scores in five successive rounds are 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

∴ Jack’s total score at the end is 35.

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:-

From the question,

The temperature on Monday at Srinagar = -5oC

The temperature on Tuesday at Srinagar has dropped by 2oC = Temperature on Monday –2oC

= -5oC – 2oC

= -7oC

The temperature on Wednesday at Srinagar rose by 4oC = Temperature on Tuesday + 4oC

= -7oC + 4oC

= -3oC

Thus, the temperature on Tuesday and Wednesday was -7oC and -3oC, respectively.

4. A plane is flying at a height of 5000 m above 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? Solution:-

From the question,

The 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

5. Mohan deposits ₹ 2,000 in his bank account and withdraws ₹ 1,642 from it the next day. If the withdrawal of the 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:-

Withdrawal of the amount from the account is represented by a negative integer.

Then, the deposit of the amount to the account is represented by a positive integer.

From the question,

Total amount deposited in bank account by the Mohan = ₹ 2000

The total amount is 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

Hence, the balance in Mohan’s account after the withdrawal is ₹ 358

6. Rita goes 20 km towards the east from point A to point B. From B, she moves 30 km towards the west along the same road. If the distance towards the east is represented by a positive integer, then how will you represent the distance travelled towards the west? By which integer will you represent her final position from A? Solution:-

From the question, it is given that

A positive integer represents the distance towards the east.

Then, the distance travelled towards the west will be represented by a negative integer.

Rita travels a distance in the east direction = 20 km

Rita travels a distance in the west direction = – 30 km

∴ Distance travelled from A = 20 + (- 30)

= 20 – 30

= -10 km

Hence, we will represent the distance travelled by Rita from point A by a negative integer, i.e., –10 km

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

First, we consider the square (i)

By adding the numbers in each row, we get

= 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 column, we get

= 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, we get

= 5 + (-2) + (-3) = 5 – 2 – 3 = 5 – 5 = 0

= -4 + (-2) + 0 = – 4 – 2 = -6

Because the sum of one diagonal is not equal to zero,

(i) is not a magic square

Now, we consider the square (ii)

By adding the numbers in each row, we get

= 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 column, we get

= 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, we get

= 1 + (-3) + (-7) = 1 – 3 – 7 = 1 – 10 = -9

= 0 + (-3) + (-6) = 0 – 3 – 6 = -9

This (ii) square is a magic square because the sum of each row, each column and the diagonal is equal to -9.

8. Verify a – (– b) = a + b for the following values of a and b.

(i) a = 21, b = 18

Solution:-

From the question,

a = 21 and b = 18

To verify a – (- b) = a + b

Let us take Left Hand Side (LHS) = a – (- b)

= 21 – (- 18)

= 21 + 18

= 39

Now, Right Hand Side (RHS) = a + b

= 21 + 18

= 39

By comparing LHS and RHS

LHS = RHS

39 = 39

Hence, the value of a and b is verified.

(ii) a = 118, b = 125

Solution:-

From the question,

a = 118 and b = 125

To verify a – (- b) = a + b

Let us take Left Hand Side (LHS) = a – (- b)

= 118 – (- 125)

= 118 + 125

= 243

Now, Right Hand Side (RHS) = a + b

= 118 + 125

= 243

By comparing LHS and RHS

LHS = RHS

243 = 243

Hence, the value of a and b is verified.

(iii) a = 75, b = 84

Solution:-

From the question,

a = 75 and b = 84

To verify a – (- b) = a + b

Let us take Left Hand Side (LHS) = a – (- b)

= 75 – (- 84)

= 75 + 84

= 159

Now, Right Hand Side (RHS) = a + b

= 75 + 84

= 159

By comparing LHS and RHS

LHS = RHS

159 = 159

Hence, the value of a and b is verified.

(iv) a = 28, b = 11

Solution:-

From the question,

a = 28 and b = 11

To verify a – (- b) = a + b

Let us take Left Hand Side (LHS) = a – (- b)

= 28 – (- 11)

= 28 + 11

= 39

Now, Right Hand Side (RHS) = a + b

= 28 + 11

= 39

By comparing LHS and RHS

LHS = RHS

39 = 39

Hence, the value of a and b is verified.

9. Use the sign of >, < or = in the box to make the statements true.

(a) (-8) + (-4) [ ] (-8) – (-4)

Solution:-

Let us take Left Hand Side (LHS) = (-8) + (-4)

= -8 – 4

= -12

Now, Right Hand Side (RHS) = (-8) – (-4)

= -8 + 4

= -4

By comparing LHS and RHS

LHS < RHS

-12 < -4

∴ (-8) + (-4) [<] (-8) – (-4)

(b) (-3) + 7 – (19) [ ] 15 – 8 + (-9)

Solution:-

Let us take Left Hand Side (LHS) = (-3) + 7 – 19

= -3 + 7 – 19

= -22 + 7

= -15

Now, Right Hand Side (RHS) = 15 – 8 + (-9)

= 15 – 8 – 9

= 15 – 17

= -2

By comparing LHS and RHS

LHS < RHS

-15 < -2

∴ (-3) + 7 – (19) [<] 15 – 8 + (-9)

(c) 23 – 41 + 11 [ ] 23 – 41 – 11

Solution:-

Let us take Left Hand Side (LHS) = 23 – 41 + 11

= 34 – 41

= – 7

Now, Right Hand Side (RHS) = 23 – 41 – 11

= 23 – 52

= – 29

By comparing LHS and RHS

LHS > RHS

– 7 > -29

∴ 23 – 41 + 11 [>] 23 – 41 – 11

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

Solution:-

Let us take Left Hand Side (LHS) = 39 + (-24) – 15

= 39 – 24 – 15

= 39 – 39

= 0

Now, Right Hand Side (RHS) = 36 + (-52) – (- 36)

= 36 – 52 + 36

= 72 – 52

= 20

By comparing LHS and RHS

LHS < RHS

0 < 20

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

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

Solution:-

Let us take Left Hand Side (LHS) = – 231 + 79 + 51

= – 231 + 130

= -101

Now, Right Hand Side (RHS) = – 399 + 159 + 81

= – 399 + 240

= – 159

By comparing LHS and RHS

LHS > RHS

-101 > -159

∴ – 231 + 79 + 51 [>] -399 + 159 + 81

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?

Solution:-

Let us consider steps moved down are represented by positive integers, and steps moved up are represented by negative integers.

Initially, the monkey is sitting on the topmost step, i.e., the first step

In the 1st jump the monkey will be at step = 1 + 3 = 4 steps

In the 2nd jump the monkey will be at step = 4 + (-2) = 4 – 2 = 2 steps

In the 3rd jump the monkey will be at step = 2 + 3 = 5 steps

In the 4th jump the monkey will be at step = 5 + (-2) = 5 – 2 = 3 steps

In the 5th jump the monkey will be at step = 3 + 3 = 6 steps

In the 6th jump the monkey will be at step = 6 + (-2) = 6 – 2 = 4 steps

In the 7th jump the monkey will be at step = 4 + 3 = 7 steps

In the 8th jump the monkey will be at step = 7 + (-2) = 7 – 2 = 5 steps

In the 9th jump the monkey will be at step = 5 + 3 = 8 steps

In the 10th jump the monkey will be at step = 8 + (-2) = 8 – 2 = 6 steps

In the 11th jump the monkey will be at step = 6 + 3 = 9 steps

∴ The monkey took 11 jumps (i.e., the 9th step) to reach the water level.

(ii) After drinking water, the monkey wants to go back. For this, he jumps 4 steps up and then jumps back 2 steps down with every move. In how many jumps will he reach back to the top step?

Solution:-

Let us consider steps moved down are represented by positive integers, and then steps moved up are represented by negative integers.

Initially, the monkey is sitting on the ninth step, i.e., at the water level

In the 1st jump the monkey will be at step = 9 + (-4) = 9 – 4 = 5 steps

In the 2nd jump the monkey will be at step = 5 + 2 = 7 steps

In the 3rd jump the monkey will be at step = 7 + (-4) = 7 – 4 = 3 steps

In the 4th jump the monkey will be at step = 3 + 2 = 5 steps

In the 5th jump the monkey will be at step = 5 + (-4) = 5 – 4 = 1 step

∴ The monkey took 5 jumps to reach back to the top step, i.e., 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 parts (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:-

From the question, it is given that

If the number of steps moved down is 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

∴ Moves in part (i) represent that the monkey is going down 8 steps because of a negative integer.

Now,

Monkey moves in part (ii)

= 4 – 2 + ……….. = 8

Then LHS = 4 – 2 + 4 – 2 + 4

= 12 – 4

= 8

RHS = 8

∴ Moves in part (ii) represent that the monkey is going up 8 steps because of a positive integer.

### Access Other Exercises of NCERT Solutions for Class 7 Chapter 1 – Integers

Exercise 1.2 Solutions

Exercise 1.3 Solutions

Exercise 1.4 Solutions

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