This question asks us to find the missing number represented by the question mark '?' in the given mathematical equation. The equation involves division, addition, and multiplication, and we need to determine the value that satisfies the equation.

Understanding the Equation

The equation provided is:

? ÷ 13 + 23 × 12 = 290

To solve this, we must follow the standard order of operations, often remembered by the acronym BODMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction) or PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). According to this rule, multiplication and division are performed before addition.

Applying the Order of Operations

First, we perform the multiplication operation:

23 × 12

Calculation:

$$ 23 \times 12 = 276 $$

Now, substitute this result back into the original equation:

? ÷ 13 + 276 = 290

Isolating the Division Term

Next, we need to isolate the term containing the question mark ('? ÷ 13'). To do this, we subtract 276 from both sides of the equation:

? ÷ 13 = 290 - 276

Calculation:

$$ 290 - 276 = 14 $$

So, the equation becomes:

? ÷ 13 = 14

Solving for the Missing Number

Finally, to find the value of '?', we perform the division operation. We need to multiply 14 by 13:

? = 14 × 13

Calculation:

$$ 14 \times 13 = 182 $$

Therefore, the missing number in the equation is 182.

Verification

Let's check if 182 satisfies the original equation:

$$ 182 \div 13 + 23 \times 12 $$

Perform division:

$$ 182 \div 13 = 14 $$

Perform multiplication:

$$ 23 \times 12 = 276 $$

Perform addition:

$$ 14 + 276 = 290 $$

The result matches the right side of the equation (290), confirming our answer.

Summary of Steps

The value that should come in place of the question mark is 182.