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(i) Is 10 × (6 – (–2)] = 10 × 6 – 10 × (–2)?

L.H.S =  R.H.S =  L.H.S = R.H.S

10.(iii) 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.

(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?

If we represent the down steps by negative and up steps by positive then: Moves in (i): Also, Moves in part (ii): Therefore, the sum +8 represents going up by eight steps.

10.(ii) 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.

(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 number of steps moved down be represented by positive integers and the number of steps moved up by negative integers. Given, Monkey is at the step = 9 Now, The step after: 1st jump  = 2nd jump  = 3rd jump  = 4th jump  = 5th jump  = Therefore, after 5 jumps, the monkey will reach back at the top.

10.(i)  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 number of steps moved down be represented by positive integers and the number of steps moved up by negative integers. Given, Monkey is at the step = 1 Now, The step after: 1st jump  = 2nd jump  = 3rd jump  = 4th jump  = 5th jump  = 6th jump = 7th jump  = 8th jump  = 9th jump  = 10th jump = 11th jump = Therefore, after 11 jumps, the monkey reaches the water level which is at...

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

(Note: On a number line, the number on the right is greater than a number towards its left.) (a) (– 8) + (– 4)           (–8) – (– 4) L.H.S =  R.H.S =  Clearly,  (b) (– 3) + 7 – (19)            15 – 8 + (– 9) L.H.S =  R.H.S =  Clearly,  (c) 23 – 41 + 11         23 – 41 – 11 L.H.S =  R.H.S =  Clearly,  (d) 39 + (– 24) – (15)        36 + (– 52) – (– 36) L.H.S =  R.H.S =  Clearly,  (e) – 231 +...

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)    $a = 28, b = 11$

(i)      L.H.S =  R.H.S =   L.H.S = R.H.S Hence verified. (ii)      L.H.S =  R.H.S =   L.H.S = R.H.S Hence verified. (iii)      L.H.S =  R.H.S =   L.H.S = R.H.S Hence verified. (iv)     L.H.S =  R.H.S =   L.H.S = R.H.S Hence verified.

7. In a magic square each row, column and diagonal have the same sum. Check if the following is a magic square.

(ii)

 1 -10 0 -4 -3 -2 -6 4 -7

Taking Rows- Taking Columns- Taking Diagonals- As the sum of all the rows, columns and diagonals are equal, this is a magic square.

7. In a magic square each row, column and diagonal have the same sum. Check if the following is a magic square.

(i)

 5 -1 -4 -5 -2 7 0 3 -3

Taking Rows- Taking Columns- Taking Diagonals- As the sum of one of the diagonals is not equal to 0, it is not a magic square.

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?

We will represent the distance travelled towards west with negative integer. Distance travelled towards east = Distance travelled towards west = Distance travelled from A =  As the distance is negative, so final position of Rita from A is towards the west direction.

5.  Mohan deposits Rs 2,000 in his bank account and withdraws Rs 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.

Given, The amount deposited in bank account = Amount withdrawn from bank account = Balance in account = Amount deposited in bank account + Amount withdrawn from the bank account Therefore,balance in Mohan’s account after the withdrawal is

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?

The plane is flying at the height of 5000 m above the sea level Distance of the plane from sea level =  Also, the submarine floating 1200 m below the sea level Distance of the submarine from sea level =  Distance between them =

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?

The temperature of Srinagar on Monday =  According to question, The temperature of Tuesday =   The temperature of Srinagar on Tuesday =  Again, according to question The temperature of Wednesday=  The temperature of Srinagar on Wednesday =

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?

Given, Jack’s scores in five successive rounds are  Therefore, his total score =  His total score at the end was

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 the temperature of Srinagar and Shimla taken together is less than the temperature at Shimla? Is it also less than the temperature at Srinagar?

(a) The temperature of the places in degree celsius (°C) marked on it   are : Places Temperature Lahulspiti Srinagar Shimla Ooty Bangalore (b) The hottest temperature is  and coldest is  The temperature difference between them =  (c) The temperatures at Lahulspiti is  and Srinagar is  The temperature difference between Lahulspiti and Srinagar is ...
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