Question Mark Value Calculation

The problem asks us to determine the numerical value that should replace the question mark ('?') in the given mathematical expression:

$$ 420 \div 28 \times 288 \div 32 = ? $$

To solve this accurately, we must adhere to the standard order of operations, commonly known as BODMAS or PEMDAS. This rule dictates the sequence in which mathematical operations should be performed: Brackets, Orders (powers and roots), Division and Multiplication (from left to right), and Addition and Subtraction (from left to right).

Step-by-Step Calculation Process

In this expression, we only have division and multiplication operations. According to the order of operations, we perform these from left to right.

1. First Step: Leftmost Division

   We start by performing the division that appears first from the left:

   $$ 420 \div 28 $$

   Calculating this division:

   $$ \frac{420}{28} = 15 $$

   After this step, the expression simplifies to:

   $$ 15 \times 288 \div 32 $$

2. Second Step: Multiplication

   Next, we proceed with the multiplication operation, moving from left to right:

   $$ 15 \times 288 $$

   Performing the multiplication:

   $$ 15 \times 288 = 4320 $$

   The expression is now reduced to a single division:

   $$ 4320 \div 32 $$

3. Third Step: Final Division

   Finally, we perform the last operation, which is division:

   $$ 4320 \div 32 $$

   Calculating the final result:

   $$ \frac{4320}{32} = 135 $$

Result Summary

By following the order of operations systematically, we find that the value which should come in place of the question mark is 135.