Question

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 find the expression equivalent to \( 8 + \frac{4}{3} + 4 \times 2^3 \), we need to simplify it step by step.

1. First, calculate \( 2^3 \):
\[
2^3 = 8
\]

2. Now substitute this value into the original expression:
\[
8 + \frac{4}{3} + 4 \times 8
\]

3. Next, calculate \( 4 \times 8 \):
\[
4 \times 8 = 32
\]

4. Now rewrite the expression:
\[
8 + \frac{4}{3} + 32
\]

5. Combine the whole numbers:
\[
8 + 32 = 40
\]

6. Thus, the entire expression becomes:
\[
40 + \frac{4}{3}
\]

7. We can also express it as:
\[
40 + \frac{4}{3} = \frac{120}{3} + \frac{4}{3} = \frac{124}{3}
\]

Now let's analyze each of the options:

A. \( 8 + \frac{4}{3} + 4 \times 6 \)
- This simplifies to \( 8 + \frac{4}{3} + 24 \).
- Equivalent to \( 8 + \frac{4}{3} + 24\) is not equal to \(40 + \frac{4}{3} = 40 + \frac{4}{3} \).

B. \( 8 + \frac{4}{3} + 24 \)
- This is equal to \( 8 + \frac{4}{3} + 24 = 32 + \frac{4}{3} \), which is not equal to our expression.

C. \( 4 + 4 \times 8 \)
- This simplifies to \( 4 + 32 = 36\), which is not equal to our expression.

D. \( 8 \times 8 \)
- This equals \( 64\), which is also not equal to our expression.

None of the options given are equivalent to the original expression. The correct answer based on the calculations stands at \( 40 + \frac{4}{3} \). However, among the options presented, **none of the expressions equal the original expression correctly.**