Solve the following addition problems using properties of addition. Check if both sides of the equation are equal.

The sum is $\boxed{\text{556204}}$.

b)

The sum is $\boxed{\text{549237}}$.

c)

The sum is $\boxed{\text{442840}}$.

d)

The sum is $\boxed{\text{997543}}$.

2. Use properties of addition to determine, if both sides are equal or not. Put '=' or '$\neq$'

a)

This demonstrates the commutative property of addition.
The sides are $\boxed{=}$.

b)

This demonstrates the associative property of addition.
The sides are $\boxed{=}$.

c)

This demonstrates the additive identity property.
The sides are $\boxed{=}$.

d)

This demonstrates the additive identity property.
The sides are $\boxed{=}$.

e)

The sides are $\boxed{\neq}$.

3. Find the value of the following:

a) 1000 more than 113972

The value is $\boxed{\text{114972}}$.

b) 10000 more than 590074

The value is $\boxed{\text{600074}}$.

c) 2000 more than 888888

The value is $\boxed{\text{890888}}$.

d) 30000 more than 99999

The value is $\boxed{\text{129999}}$.

4. Roger wants to buy a car. He has a budget of rupees thirty nine lakhs. There are two options as shown below. Which option is within his budget?

Roger's budget is thirty nine lakhs, which is $\text{₹ } 39,00,000$.

Option A:

Option A is over budget.

Option B:

Option B is exactly within budget.

Roger's budget is $\text{₹ } 39,00,000$.
Option A total cost: $\text{₹ } 39,12,172$.
Option B total cost: $\text{₹ } 39,00,000$.

Therefore, $\boxed{\text{Option B}}$ is within his budget.

5. Nancy booked a two bedroom flat for rupees forty five lakh. There is an increase of rupees two lakh and forty thousand. What is the new price after increase? Is it more than $\text{₹ } 50,00,000$?

Initial price = $\text{₹ } 45,00,000$
Increase = $\text{₹ } 2,40,000$

The new price after the increase is $\boxed{\text{₹ } 47,40,000}$.

The new price is not more than $\text{₹ } 50,00,000$.

So, the new price is $\text{₹ } 47,40,000$, and it is $\boxed{\text{not more than } \text{₹ } 50,00,000}$.