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

Answer 1

To determine which expression is equivalent to \( 8 + \frac{4}{3} + 4 \times 2^3 \), let's simplify the given expression step by step.

1. **Calculate \( 2^3 \)**:
\[
2^3 = 2 \times 2 \times 2 = 8
\]

2. **Substitute this value back into the expression**:
\[
8 + \frac{4}{3} + 4 \times 8
\]

3. **Calculate \( 4 \times 8 \)**:
\[
4 \times 8 = 32
\]

4. **Now substitute this back in**:
\[
8 + \frac{4}{3} + 32
\]

5. **Combine the constants** \( 8 + 32 \):
\[
8 + 32 = 40
\]

6. **Now add \( \frac{4}{3} \) to \( 40 \)**:
We convert \( 40 \) to a fraction:
\[
40 = \frac{120}{3}
\]
This gives us:
\[
\frac{120}{3} + \frac{4}{3} = \frac{120 + 4}{3} = \frac{124}{3}
\]

Now we need to check which of the provided options also simplifies to \( \frac{124}{3} \):

### Evaluate Each Option

**A.** \( 8 + \frac{4}{3} + 4 \times 6 \)
- Calculate \( 4 \times 6 \):
\[
4 \times 6 = 24
\]
- The expression becomes:
\[
8 + \frac{4}{3} + 24 = 32 + \frac{4}{3}
\]
Converting \( 32 \):
\[
32 = \frac{96}{3}
\]
So:
\[
\frac{96}{3} + \frac{4}{3} = \frac{100}{3} \quad \text{(not equal to \( \frac{124}{3} \))}
\]

**B.** \( 8 + \frac{4}{3} + 24 \)
- Combine \( 8 + 24 \):
\[
8 + 24 = 32
\]
- The expression becomes:
\[
32 + \frac{4}{3} = \frac{96}{3} + \frac{4}{3} = \frac{100}{3} \quad \text{(not equal to \( \frac{124}{3} \))}
\]

**C.** \( 4 + 4 \times 8 \)
- Calculate \( 4 \times 8 \):
\[
4 \times 8 = 32
\]
- Then we have:
\[
4 + 32 = 36 \quad \text{(not equal to \( \frac{124}{3} \))}
\]

**D.** \( 8 \times 8 \)
- Calculate:
\[
8 \times 8 = 64 \quad \text{(not equal to \( \frac{124}{3} \))}
\]

After evaluating all the options, none of them are equivalent to the original expression \( 8 + \frac{4}{3} + 4 \times 2^3 = \frac{124}{3} \).

Thus, the answer is that **none of the provided options** are equivalent.