Mathematics Class 7 – Chapter 1 – Integers – NCERT Exercise 1.1 Solutions

Mathematics Class 7 – Chapter 1 – Integers – NCERT Exercise 1.1 Solutions (Question- Answer) is provided below. Total 10 Questions are in this CBSE NCERT Exercise, all are solved here.

Q1. 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.

Answer: By observing the number line, we find the temperature of the marked places,

Temperature at the Lahulspiti = -8oC

Temperature at the Srinagar = -2oC

Temperature at the Shimla = 5oC

Temperature at the Ooty = 14oC

Temperature at the Bengaluru = 22oC

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

Answer: According to given number line we observe that-

The temperature at the hottest place = 22oC (Bengaluru)

The temperature at the coldest place = -8oC (Lahulspiti)

Temperature difference between hottest (Bengaluru) and coldest (Lahulspiti) place is

                                                          = 22oC – (-8oC)

                                                            = 22oC + 8oC

                                                            = 30oC

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

Answer: According to given number line-

The temperature at the Lahulspiti = -8oC

The temperature at the Srinagar = -2oC

Hence, 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?

Answer: According to 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

Hence, 5oC > 3oC

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

Then,

3o > -2o

No, the temperature of Srinagar and Shimla have taken together is not less than the temperature of Srinagar.

Q2. 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:

According to the given question:

Jack’s score in five successive rounds are 25, -5, -10, 15 and 10

The total score of Jack at the end,

                                         = 25 + (-5) + (-10) + 15 + 10

                                          = 25 – 5 – 10 + 15 + 10

                                           = 50 – 15

                                           = 35

Hence, Jack’s total score at the end is 35.

Q3. 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:

According to the given question:

Temperature on Monday at Srinagar = -5oC

Temperature on Tuesday at Srinagar is dropped by 2oC

Temperature on Tuesday = Temperature on Monday – 2oC

                                                    = -5oC – 2oC

                                                    = -7oC

Temperature on Wednesday at Srinagar is rose by 4oC

Temperature on Wednesday = Temperature on Tuesday + 4oC

                                                         = -7oC + 4oC

                                                          = -3oC

Q4. 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?

(attach fig )

Answer:

According to the given question:

Plane is flying above the sea level at the height = 5000 m

Depth of Submarine below the sea level = -1200 m

The vertical distance between plane and submarine = 5000 m – (- 1200) m

                                                                                   = 5000 m + 1200 m

                                                                                    = 6200 m

Q5. Mohan deposits Rs 2,000 in his bank account and withdraws Rs 1,642 from it, the next day. If the 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:

Given, Withdrawal of amount from the account is represented by a negative integer ( – ).

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

According to the question:

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

Total amount withdrawn from the bank account by the Mohan = – Rs 1642

After the withdrawal the left amount in Mohan’s account = amount deposited – amount withdrawn

                                                                                = Rs 2000 – Rs1642

                                                                                  = Rs 2000 – Rs 1642

                                                                                   = Rs 358

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

Q6. 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:

Given, distance towards the east represented by positive integer ( + )

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

Rita travels a distance towards east = 20 km

Rita travels a distance towards west = – 30 km

A/Q, 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

Q7.  In a magic square each row, column and diagonal have the same sum. Check which of the following is a magic square.

Answer:

First we consider the square (i)

By adding the numbers in each columns we get,

C1 = 5 + (- 5) + 0 = 5 – 5 = 0

C2 = (-1) + (-2) + 3 = -1 – 2 + 3 = -3 + 3 = 0

C3 = -4 + 7 + (-3) = -4 + 7 – 3 = -7 + 7 = 0

By adding the numbers in each rows we get,

R1 = 5 + (- 1) + (- 4) = 5 – 1 – 4 = 5 – 5 = 0

R2 = -5 + (-2) + 7 = – 5 – 2 + 7 = -7 + 7 = 0

R3 = 0 + 3 + (-3) = 3 – 3 = 0

By adding the numbers in diagonals we get,

D1 = 5 + (-2) + (-3) = 5 – 2 – 3 = 5 – 5 = 0

D2 = -4 + (-2) + 0 = – 4 – 2 = -6

The sum of one diagonal is not equal to zero,

So, square (i) is not a magic square

Now, we consider the square (ii)

By adding the numbers in each columns we get,

‘C1 = 1 + (-4) + (-6) = 1 – 4 – 6 = 1 – 10 = -9

‘C2 = (-10) + (-3) + 4 = -10 – 3 + 4 = -13 + 4

‘C3 = 0 + (-2) + (-7) = 0 – 2 – 7 = -9

By adding the numbers in each rows we get,

‘R1 = 1 + (-10) + 0 = 1 – 10 + 0 = -9

‘R2 = (-4) + (-3) + (-2) = -4 – 3 – 2 = -9

‘R3 = (-6) + 4 + (-7) = -6 + 4 – 7 = -13 + 4 = -9

By adding the numbers in diagonals we get,

‘D1 = 1 + (-3) + (-7) = 1 – 3 – 7 = 1 – 10 = -9

‘D2 = 0 + (-3) + (-6) = 0 – 3 – 6 = -9

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

Q8. Verify a – (– b) = a + b for the following values of a and b.

(i) a = 21, b = 18

Answer: According to the question-

a = 21

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

Now, LHS = RHS

39 = 39

Hence, the value of a and b is verified.

(ii) a = 118, b = 125

Answer: According to the question-

a = 118

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

We get,

LHS = RHS

243 = 243

Hence, the value of a and b is verified.

(iii) a = 75, b = 84

Answer: According to the question-

a = 75

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

We get,

LHS = RHS

159 = 159

Hence, the value of a and b is verified.

(iv) a = 28, b = 11

Answer: According to the question-

a = 28

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

We get,

LHS = RHS

39 = 39

Hence, the value of a and b is verified.

Q9. Use the sign of >, < or = in the box to make the statements true.

(a) (-8) + (-4)  [ ]  (-8) – (-4)

Answer: According to question-

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

                                                   = -8 – 4

                                                    = -12

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

                                                 = -8 + 4

                                                 = -4

We get,

LHS < RHS

-12 < -4

Hence, (-8) + (-4) [<] (-8) – (-4)

(b) (-3) + 7 – (19)  [ ]  15 – 8 + (-9)

Answer: According to question-

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

We get,

LHS < RHS

-15 < -2

Hence, (-3) + 7 – (19) [<] 15 – 8 + (-9)

(c) 23 – 41 + 11 [ ]  23 – 41 – 11

Answer:

According to question

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

                                                          = 34 – 41

                                                              = – 7

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

                                                = 23 – 52

                                                = – 29

We get,

LHS > RHS

– 7 > -29

Hence, 23 – 41 + 11 [>] 23 – 41 – 11

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

Answer:

According to question:

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

We get,

LHS < RHS

0 < 20

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

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

Answer: According to question-

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

                                                  = – 231 + 130

                                                  = -101

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

                                                 = – 399 + 240

                                                  = – 159

We get,

LHS > RHS

-101 > -159

Hence, – 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.

(attach fig😊from question)

(i) He jumps 3 steps down and then jumps back 2 steps up. In how many jumps will he reach the water level?

Answer:

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

According to question:

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

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

Hence, Monkey took 11 jumps (i.e., 9th step) 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?

Answer:

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

According to question:

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

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

Hence, Monkey took 5 jumps to reach back the top step i.e., 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?

Answer:

According to the question,

Given, 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

Hence, Moves in part (i) represents monkey is going down 8 steps because of negative integer

Now,

Monkey moves in part (ii)

= 4 – 2 + … = 8

Then LHS = 4 – 2 + 4 – 2 + 4

                 = 12 – 4

                 = 8

RHS = 8

Hence, Moves in part (ii) represents monkey is going up 8 steps because of the positive integer.

About the Author: MakeToss

2 Comments

Leave a Reply

Your email address will not be published.

error: