Question

Be sure to show work.
Which expression is equivalent to 8+4/3 + 4 x 2^3?
A. 8+4/3 + 4 x 6
B. 8 + 4 /3 + 24
C. 4 + 4 x 8
D. 8 x 8
Is the answer C show work

Answer 1

Let's simplify the expression \( 8 + \frac{4}{3} + 4 \times 2^3 \) step by step.

1. **Evaluate the exponent**:
\[
2^3 = 8
\]
Now, we substitute this back into the expression:
\[
8 + \frac{4}{3} + 4 \times 8
\]

2. **Multiply**:
\[
4 \times 8 = 32
\]
Now the expression is:
\[
8 + \frac{4}{3} + 32
\]

3. **Add the whole numbers**:
\[
8 + 32 = 40
\]
So now we have:
\[
40 + \frac{4}{3}
\]

4. **Convert to a single fraction**:
\[
40 = \frac{120}{3}
\]
Thus, we can combine terms:
\[
\frac{120}{3} + \frac{4}{3} = \frac{120 + 4}{3} = \frac{124}{3}
\]

Now we need to evaluate each option given:

**Option A: \( 8 + \frac{4}{3} + 4 \times 6 \)**

Calculate \( 4 \times 6 = 24 \):
\[
8 + \frac{4}{3} + 24
\]
Combine:
\[
8 + 24 = 32 \quad \text{and convert to fraction: } 32 = \frac{96}{3}
\]
\[
32 + \frac{4}{3} = \frac{96}{3} + \frac{4}{3} = \frac{100}{3}
\]

**Option B: \( 8 + \frac{4}{3} + 24 \)**

Combine:
\[
8 + 24 = 32 \quad \text{and convert to fraction: } 32 = \frac{96}{3}
\]
This gives:
\[
32 + \frac{4}{3} = \frac{100}{3}
\]

**Option C: \( 4 + 4 \times 8 \)**

Calculate \( 4 \times 8 = 32 \):
\[
4 + 32 = 36
\]

**Option D: \( 8 \times 8 \)**

Calculate \( 8 \times 8 = 64 \).

None of the options simplify to \( \frac{124}{3} \) which is approximately \( 41.33 \).

So, the answer is not option C. The correct calculation shows that none of the options match our initial expression \( 8 + \frac{4}{3} + 4 \times 2^3 \) evaluating to \( \frac{124}{3} \).