Question

Adele tried to evaluate an expression. Here is her work:
4(6+12)÷32+3(4÷2)2
=
4(18)÷32+3(2)2 Step 1
=
4(18)÷9+3(4) Step 2
=
72÷9+3(4) Step 3
=
8+3(4) Step 4
=
8+12 Step 5
=
20 Step 6
Is Adele's work correct?

Answer 1

Let's evaluate the expression \( 4(6+12) \div 32 + 3(4 \div 2)2 \) step by step to check Adele's work.

1. **Original Expression**:
\[
4(6+12) \div 32 + 3(4 \div 2)2
\]

2. **Calculate inside the parentheses**:
\[
6 + 12 = 18
\]
\[
4 \div 2 = 2
\]
Now the expression becomes:
\[
4(18) \div 32 + 3(2)2
\]

3. **Update the expression**:
\[
4(18) \div 32 + 3(2)2
\]

4. **Calculate \(4(18)\) and \(3(2)2\)**:
\[
4(18) = 72
\]
\[
3(2)2 = 6 \cdot 2 = 12
\]
Now the expression is:
\[
72 \div 32 + 12
\]

5. **Perform the division**:
\[
72 \div 32 = 2.25
\]
Therefore, the expression now is:
\[
2.25 + 12
\]

6. **Final calculation**:
\[
2.25 + 12 = 14.25
\]

Now, let's summarize the findings in comparison with Adele's steps:

- Step 1: Correct
- Step 2: \( 32 \) should be \( 32 \) not \( 9\). Incorrect.

Thus, Adele made a mistake in Step 2 and incorrectly simplified the division.

The correct answer should be:
\[
2.25 + 12 = 14.25
\]

So, **Adele's final answer of 20 is incorrect.** The correct answer is \( 14.25 \).