The value of 30 + 180 ÷ 30 × 6 − 15 − 16 − 60 ÷ 3 − 15 is:

The correct option is 0.

To evaluate the given mathematical expression, we must follow the standard order of operations, commonly known as BODMAS or PEMDAS:

1. Brackets / Parentheses
2. Orders / Exponents
3. Division and Multiplication (from left to right)
4. Addition and Subtraction (from left to right)

The given expression is:

$30+180÷30\times 6-15-16-60÷3-15$

Step 1: Perform Division

First, we perform all division operations in the order they appear from left to right.

The first division is $180÷30=6$.

The second division is $60÷3=20$.

Substituting these values back into the expression gives:

$30+6\times 6-15-16-20-15$

Step 2: Perform Multiplication

Next, perform the multiplication operation:

$6\times 6=36$

Substituting this back into the expression gives:

$30+36-15-16-20-15$

Step 3: Perform Addition and Subtraction (Left to Right)

Now, perform addition and subtraction sequentially from left to right:

Add the first two numbers:
$30+36=66$

Subtract 15:
$66-15=51$

Subtract 16:
$51-16=35$

Subtract 20:
$35-20=15$

Subtract 15:
$15-15=0$

Thus, the final value of the expression is 0.