Question

Dakota tried to evaluate an expression. Here is her work:
8(18÷6)–(52–3)+4
=
83–(10–3)+4 Step 1
=
83–7+4 Step 2
=
24–7+4 Step 3
=
24–11 Step 4
=
13 Step 5
Is Dakota's work correct?




Questions

Answer 1

Let's break down the expression step by step to check the calculations made by Dakota:

The original expression is:
\[ 8(18÷6)–(52–3)+4 \]

### Step-by-step Evaluation:
1. **Calculate \( 18 ÷ 6 \)**:
\[
18 ÷ 6 = 3
\]

2. **Substitute back into the expression**:
\[
8(3) - (52 - 3) + 4
\]

3. **Calculate \( 8(3) \)**:
\[
8 \cdot 3 = 24
\]

4. **Calculate \( 52 - 3 \)**:
\[
52 - 3 = 49
\]

5. **Now substitute these values back into the expression**:
\[
24 - 49 + 4
\]

6. **Now evaluate from left to right**:
- Calculate \( 24 - 49 \):
\[
24 - 49 = -25
\]
- Then add \( 4 \):
\[
-25 + 4 = -21
\]

### Final Result:
Thus, the correct evaluation of the expression \( 8(18÷6)–(52–3)+4 \) is \( -21 \).

### Comparison with Dakota's Work:
Now let's compare this with Dakota's calculations:
- Dakota wrote \( 83 \) which seems to be a mistake, as it should be \( 24 \).
- She also stated \( 10 - 3 = 7 \) which was correct but the preceding computation was not.
- Continuing from there, her result of \( 13 \) is incorrect.

### Conclusion:
Dakota's work is not correct, and the correct answer is \( -21 \).