Replace # sign with the mathematical operators '+', '÷', '-' or '×' to get a balanced equation out of 186 # 31 # 36 # 30.
A. + - =
B. - = +
C - ÷ +
D. ÷ = -

Options

A. D
B. B
C. C
D. A

Answer

To solve the problem of replacing the # signs with mathematical operators to create a balanced equation from the expression \( 186 \# 31 \# 36 \# 30 \), we will evaluate each option step by step.

### Step-by-Step Solution:

1. **Identify the Expression**:
The expression we need to evaluate is:
\[ 186 \# 31 \# 36 \# 30 \]

2. **Evaluate Option A**:
Replace # with +, -, =:
\[ 186 + 31 - 36 = 30 \]
Calculate the left side:
\[ 186 + 31 = 217 \]
\[ 217 - 36 = 181 \]
Since \( 181 \neq 30 \), **Option A is incorrect**.

3. **Evaluate Option B**:
Replace # with -, =, +:
\[ 186 - 31 = 36 + 30 \]
Calculate both sides:
Left side:
\[ 186 - 31 = 155 \]
Right side:
\[ 36 + 30 = 66 \]
Since \( 155 \neq 66 \), **Option B is incorrect**.

4. **Evaluate Option C**:
Replace # with -, ÷, +:
\[ 186 - 31 \div 36 = 30 \]
First, perform the division:
\[ 31 \div 36 \approx 0.8611 \text{ (not an integer)} \]
Now calculate:
\[ 186 - 0.8611 \approx 185.1389 \]
Since \( 185.1389 \neq 30 \), **Option C is incorrect**.

5. **Evaluate Option D**:
Replace # with ÷, =, -:
\[ 186 \div 31 = 36 - 30 \]
Calculate both sides:
Left side:
\[ 186 \div 31 = 6 \]
Right side:
\[ 36 - 30 = 6 \]
Since \( 6 = 6 \), **Option D is correct**.

### Final Answer:
The correct option is **D: ÷ = -**.