To determine which operation should be performed first in the given expression [tex]\(2 - 7 \div 4 \times (3 + 9)\)[/tex], we need to follow the order of operations, often remembered by the acronym PEMDAS/BODMAS. This acronym stands for Parentheses/Brackets, Exponents/Orders (i.e., powers and roots, etc.), Multiplication and Division (left to right), Addition and Subtraction (left to right).
Let’s analyze the expression step by step:
1. Parentheses/Brackets: The first operation inside the parentheses is [tex]\(3 + 9\)[/tex]. Addition within the parentheses should be performed first:
[tex]\[
3 + 9 = 12
\][/tex]
So the expression now simplifies to:
[tex]\[
2 - 7 \div 4 \times 12
\][/tex]
2. Division and Multiplication: According to the order of operations, we solve division and multiplication from left to right.
The first operation is [tex]\(7 \div 4\)[/tex].
Given the analysis so far, the first operation based on the order of operations is addition (i.e., [tex]\(3 + 9\)[/tex] inside the parentheses).
So, the correct answer is:
- addition
