Let's analyze and correct the given sequence of steps in detail:
Given Expression: [tex]\( 11 + (3 \times 9) \)[/tex]
1. Step 1:
- The expression is written as [tex]\( 11 + (9 \times 3) \)[/tex].
- This is correct; we can use the commutative property of multiplication to rewrite [tex]\( 3 \times 9 \)[/tex] as [tex]\( 9 \times 3 \)[/tex] without changing the value.
2. Step 2:
- The next step written is [tex]\( (11 + 9) \times 3 \)[/tex].
- Here is the error: the associative property is incorrectly applied. In proper mathematical operations, parentheses have priority, and multiplication should be performed before addition according to the order of operations (PEMDAS/BODMAS).
3. Correct Approach:
- Let's follow the correct order of operations: Parentheses → Exponents (if any) → Multiplication and Division → Addition and Subtraction.
- First, we perform the multiplication inside the parentheses:
[tex]\[
3 \times 9 = 27
\][/tex]
- Now we add this result to 11:
[tex]\[
11 + 27
\][/tex]
- Performing the addition:
[tex]\[
11 + 27 = 38
\][/tex]
4. Final Step:
- The correct solution after performing the correct order of operations is [tex]\( 38 \)[/tex].
Summary:
- The error in Step 2 was introducing parentheses and regrouping inappropriately, which is not allowed.
- Correct multiplication first gives [tex]\( 3 \times 9 = 27 \)[/tex], then addition [tex]\( 11 + 27 = 38 \)[/tex].
Therefore, the correct result for the given expression [tex]\( 11 + (3 \times 9) \)[/tex] is 38.
