Find the approximate value that should replace the question mark (?) in the equation below.

$(15.02\times 12)÷11.99+{24.78}^2=?$

The correct answer is 640.

To find the approximate value of the given expression, we round each decimal number to its nearest whole integer to simplify the calculations.

The original equation is:

$(15.02\times 12)÷11.99+{24.78}^2=?$

Step 1: Round the decimal numbers to the nearest whole numbers.
- 15.02 is rounded to 15.
- 11.99 is rounded to 12.
- 24.78 is rounded to 25.

Substituting these approximate values into the equation gives:

$(15\times 12)÷12+{25}^2=?$

Step 2: Simplify using the order of operations (BODMAS/PEMDAS).
First, evaluate the operations inside the parentheses and the division. Notice that multiplying by 12 and then dividing by 12 cancel each other out:

$(15\times 12)÷12=180÷12=15$

Next, evaluate the exponent term:

${25}^2=25\times 25=625$

Step 3: Add the simplified terms together.

$?=15+625=640$

Thus, the approximate value that should replace the question mark (?) is 640.