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What should be calculated first when finding the value of the following expression?

[tex]\[ [(-3) \cdot (-8) + 6] - (-6 \div (-2)) \][/tex]

A. \(-6 - (-6)\)

B. \(-6 \div (-2)\)

C. \((-3) \cdot (-8)\)

D. [tex]\(-8 + 6\)[/tex]


Sagot :

To determine what should be calculated first in the given mathematical expression,
[tex]\[ [(-3) \cdot (-8) + 6] - (-6 \div (-2)), \][/tex]
we must follow the order of operations, also known as PEMDAS/BODMAS (Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

1. Parentheses/Brackets:
Evaluate the expressions within the brackets first. The outer brackets contain two sub-expressions:
[tex]\[(-3) \cdot (-8) + 6\][/tex]
and
[tex]\[-(-6 \div (-2))\][/tex]

2. Inside the Brackets:
We need to focus on the operations within each of these sub-expressions separately before combining them.

3. Sub-expression Evaluation:
- Within the first sub-expression \((-3) \cdot (-8) + 6\), the multiplication \((-3) \cdot (-8)\) must be performed first.
- Within the second sub-expression \(-(-6 \div (-2))\), the division \(-6 \div (-2)\) must be performed first.

Now, we look at the options provided to determine which specific part of the expression should be calculated first:

A. \(-6 - (-6)\) - This does not appear directly within our expression and does not represent an initial step.
B. \(-6 \div (-2)\) - This division operation occurs within the sub-expression \(-(-6 \div (-2))\).
C. \((-3) \cdot (-8)\) - This multiplication operation occurs within the sub-expression \((-3) \cdot (-8) + 6\).
D. \(-8 + 6\) - This addition/subtraction operation is not directly within our expression initially in this form.

Thus, the correct first operation as per the order of operations from the given choices is:

B. [tex]\(-6 \div (-2)\)[/tex]