We can write 4 x (- 8) as
4 x (- 8) = (- 8) + (- 8) + (- 8) + (- 8)
It can be represented on the number line as under:

We have, 8 x (- 2) = (- 2) + (- 2) + (- 2) + (-2) + (-2) + (-2) + (-2) + (-2)
It can be represented on the number line as under:

We have, 3 x (-7) = (-7) + (-7) + (-7)
It can be represented on the number line as under:

We have,
10 x (-1) = (-1) + (-1) + (-1) + (-1) + (-1) + (-1) + (-1) + (-1) + (-1) + (-1)
It can be represented on the number line as under:
.

(i) 49
(ii) 28

23rd January

As per the given information,
Profit on Monday = Rs 47
Loss on Tuesday = Rs 12
Loss on Wednesday = Rs 8
\(\therefore\) Net profit = Total profit - Total loss
Now, total profit = 47
and total loss =12 + 8 = 20
\(\therefore\) Net profit = 47 - 20 = Rs 27

As per the given information, we can draw the given diagram.

Let O be the point of the level of the sea.
Difference between these two points A and B = Height between sea level and point A + Height between point B and sea level.
= AO + OB = 1800 + 700
= 2500 m

For two integers, which are greater than -4, but their difference is smaller than -2.
So, first integer = - 3 and second integer = -1
Their difference = - 3 -1 = - 4
Hence, - 4 is smaller than -2.

For a pair of integers whose product is -36 and whose difference = 15.
So, first integer = -3 and second integer = 12
Their product = (-3) \(\times\) 12 = -(3 \(\times\) 12)= -36
and the difference between these two integer is 15.

(i) We know that, 3 \(\div\) 1= 3, so 3 \(\div\) (- 1)= - 3
On comparing with a \(\div\) b = - 3, we get a = 3 and b = -1
Hence, the required pair of integers is (3, -1).
(ii) We know that, 12 \(\div\) 4 = 3, so 12 \(\div\)(- 4) = - 3
On comparing with a \(\div\) b = - 3, we get a = 12 and b = -4
Hence, the required pair of integers is (12, - 4).
(iii) We know that, 9 \(\div\) 3 = 3, so 9 \(\div\) (- 3) = - 3
On comparing with a \(\div\) b = - 3, we get a = 9 and b = -3
Hence, the required pair of integers is (9, - 3).
(iv) We know that,12 \(\div\) 4 = 3, so (-12) \(\div\) 4 = -3
On comparing with a \(\div\) b = - 3, we get a = -12 and b=4
Hence, the required pair of integers is (-12, 4).
(v) We know that, 15 \(\div\) 5 = 3, so 15 + (- 5) = -3
On comparing with a \(\div\) b = - 3, we get a = 15 and b = -5
Hence, the required pair of integers is (15, - 5).

Given, total number of questions = 10
Marks for a correct answer = 5
Marks for an incorrect answer = (- 2)
Marks for not attempted the question = 0
(i) Mohan's score = (Correct questions \(\times\) Marks) + (Incorrect questions \(\times\) Marks)
= 4 \(\times\) (5) + 6 \(\times\) (- 2)
= 20 + (-12) = 20 -12 = 8
(ii) Reshmas score = 5 \(\times\) 5 + 5 \(\times\) (- 2)
=25 + (-10) = 15
(iii) Heena's score = 2 \(\times\) 5 + 5 \(\times\) (- 2) + 3 \(\times\) 0
=10 + (-10) + 0 = 0

Let the number of steps moved down to be represented by negative integers and number of steps moved up to be represented by positive integers. Given that, the total number of steps to be moved down to reach water level= 9
(i) Number of steps moved down in one jump = - 3
and number of steps moved up in one jump = 2

From the above figure, monkey will reach the water level in 11 jumps.
Alternate Method:
The monkey is sitting on the topmost step i.e. the first step. While going down, the monkey jumps 3 steps down and then jumps back 2 steps up. To reach the water level, he has to jump as follows:
-3 + 2 -3 + 2 -3 + 2 -3 + 2 -3 + 2 -3 = -8
Hence, he takes 11 jumps to reach the water level.
ii) In one jump number of steps moved up = 4
In one jump, number of steps moved down = - 2

Distance covered in single jump = 4 - 2 =2
Now, total number of steps for top = 9
From the above figure, he will reach back the top step in 5 jumps.
Alternate Method
Afterdrinkingwaters,he has to jump as followsto go back:
4 -2 + 4 - 2 + 4 = 8
Hence, he takes 5 jumps to reach back the top
(iii) (a) We have,
-3 + 2 -3 + 2 - 3 + 2 - 3 + 2 - 3 + 2 -3 = -8
(b) 4 - 2 + 4 - 2 + 4 = 8
According to the question, the sum 8 in part (b) represents going up 8 steps.