We have, (-31) \(\div\) [ (-30) + (-1) ]
= (-31) \(\div\) (-31) = 31/31 = 1

We know that the product of any integer and (-1) is the additive inverse of the integer.
(-1) \(\times\) (-37) = 37

Ramu went wrong in solving - (- 3) and took it as -3.

+ 5/2

10 + (-4) = 10 - 4 = +6 or 6  [\(\because\) difference = 6, higher integer sign is' +']

We know that, if the number of negative integers in a product is even, then the product is a positive integer; if the number of negative integers in a product is odd, then the product is a negative integer.
∴ The product (-9) x (-5) x (-6) x (-3) is positive because an even number of negative integers are multiplied.
The product (-9) x (-5) x 6 x (-3) is negative because an odd number of negative integers are multiplied.
(ii) (a) Positive [ ∵ Product of 8 negative integers is positive]
(b) Negative [ ∵ Product of 5 negative integers is negative]
(c) Positive [ ∵ 12 is even and product of even number of negative
(d) Positive [ ∵ 2m is an even number]

Distance towards East denoted (+ve) sign and Distance towards West denoted (-ve) sign.
Since first Ridhaan goes toward East 25 km
So distance covered by him = + 25 km
Again, he goes towards West.
So, distance covered by him on same road
= -35 km.
So,position of Ridhaan from A= + 25 - 35
= -10 km.
(b) Value: Addition of Integers.
(c) Value: A rolling stone can gather no moss.

True,
Case I Going 500 m towards East first and then 200 m back.

As per the figure shown above final position will be 300 m in East.
Case II Going 200 m towards West first and then going 500 m back.
In the given case also, final position will be 300 m in the East.

Hence, given statement is true.

From the given figure, it is clear that the directions East and West are opposite to each other.
According to the question,

If moving towards East is a positive integer, then moving towards West is represented by a negative integer.
Now, distance moved towards West = - 30 km 
and distance moved towards East = 20 km
\(\therefore\) Rita's final position from A = 20 + (- 30) = 20 - 30
= -10 km (i.e. West)

Number line with all numbers is shown below:

From the above number line, the temperature of the indicated places are as follow:

125

As per the given information in the question, Already available saving amount is Rs 500.
On 4/9 with cheque number 384102 withdraw Rs 120, also with cheque number 275146 on 12/9 deposited amount was Rs 200.
In the same way on 22/9 with cheque number 384103, Rs 240 paid to LIC of India, also.
On 29/9 with cheque number 801351, deposited amount was Rs 150.
Thus, net amount available in bank account will be = Already saved amount + Deposited amount - Debited amount (amount which are paid)
= 500 + 200 + 150 -120 - 240
= 850 + (-360) = Rs 490.

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

Balance = 2000 - 1000 = Rs.1000.