Solving the Arithmetic Equation for Missing Number

This solution explains how to find the value that replaces the question mark '?' in the given mathematical expression: (23 × 56 ÷ 7 + 12) - ? = 200. We will follow the standard order of operations (often remembered by acronyms like BODMAS or PEMDAS) to simplify the expression and solve for the unknown value.

Step-by-Step Calculation Breakdown

To find the missing number, we first simplify the expression within the parentheses:

1. Simplify Parentheses Content

The expression inside the parentheses is (23 × 56 ÷ 7 + 12). We follow the order of operations (Multiplication and Division before Addition):

• First, perform the multiplication:

  23 \times 56 = 1288

• Next, perform the division:

  1288 \div 7 = 184

• Finally, perform the addition within the parentheses:

  184 + 12 = 196

So, the expression simplifies to 196.

2. Solve the Simplified Equation

Now, substitute the simplified value back into the original equation:

196 - ? = 200

To find the value of '?', we need to isolate it. We can rearrange the equation:

• Subtract 196 from both sides of the equation:

  - ? = 200 - 196

  - ? = 4

• Multiply both sides by -1 to solve for '?':

  ? = -4

Final Answer Explanation

By following the order of operations and algebraic manipulation, we determine that the number replacing the question mark '?' is -4. This value satisfies the original equation: (23 × 56 ÷ 7 + 12) - (-4) = 196 + 4 = 200.