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
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
Answers
GPT-4o mini
To determine which expression is equivalent to \(8 + \frac{4}{3} + 4 \times 2^3\), we will follow the order of operations (PEMDAS/BODMAS), which means we will first evaluate exponents, then multiplication and division from left to right, and finally addition and subtraction.
1. **Calculate \(2^3\)**:
\[
2^3 = 8
\]
2. **Calculate \(4 \times 2^3\)**:
\[
4 \times 8 = 32
\]
3. **Substitute this back into the expression**:
\[
8 + \frac{4}{3} + 32
\]
4. **Combine the constants \(8\) and \(32\)**:
\[
8 + 32 = 40
\]
5. **Now rewrite the expression**:
\[
40 + \frac{4}{3}
\]
Next, let's evaluate the provided answer choices to see which one matches \(40 + \frac{4}{3}\).
**A.** \(8 + \frac{4}{3} + 4 \times 6\)
Calculate \(4 \times 6\):
\[
4 \times 6 = 24
\]
So, \(8 + \frac{4}{3} + 24\) gives:
\[
8 + 24 + \frac{4}{3} = 32 + \frac{4}{3}
\]
**(not equivalent)**
**B.** \(8 + \frac{4}{3} + 24\)
We already calculated that:
\[
8 + 24 + \frac{4}{3} = 32 + \frac{4}{3}
\]
**(not equivalent)**
**C.** \(4 + 4 \times 8\)
Calculate \(4 \times 8\):
\[
4 \times 8 = 32
\]
So, \(4 + 32\) gives:
\[
36
\]
**(not equivalent)**
**D.** \(8 \times 8\)
Calculate \(8 \times 8\):
\[
8 \times 8 = 64
\]
**(not equivalent)**
After evaluating all the expressions, we can see that there is no expression in the choices that matches \(40 + \frac{4}{3}\).
The correct evaluation of the original expression is \(40 + \frac{4}{3}\), and none of the answer choices are equivalent to this. If you see a similar question or if there are any potential errors in the answer choices, please check and provide more context or different options if needed.
1. **Calculate \(2^3\)**:
\[
2^3 = 8
\]
2. **Calculate \(4 \times 2^3\)**:
\[
4 \times 8 = 32
\]
3. **Substitute this back into the expression**:
\[
8 + \frac{4}{3} + 32
\]
4. **Combine the constants \(8\) and \(32\)**:
\[
8 + 32 = 40
\]
5. **Now rewrite the expression**:
\[
40 + \frac{4}{3}
\]
Next, let's evaluate the provided answer choices to see which one matches \(40 + \frac{4}{3}\).
**A.** \(8 + \frac{4}{3} + 4 \times 6\)
Calculate \(4 \times 6\):
\[
4 \times 6 = 24
\]
So, \(8 + \frac{4}{3} + 24\) gives:
\[
8 + 24 + \frac{4}{3} = 32 + \frac{4}{3}
\]
**(not equivalent)**
**B.** \(8 + \frac{4}{3} + 24\)
We already calculated that:
\[
8 + 24 + \frac{4}{3} = 32 + \frac{4}{3}
\]
**(not equivalent)**
**C.** \(4 + 4 \times 8\)
Calculate \(4 \times 8\):
\[
4 \times 8 = 32
\]
So, \(4 + 32\) gives:
\[
36
\]
**(not equivalent)**
**D.** \(8 \times 8\)
Calculate \(8 \times 8\):
\[
8 \times 8 = 64
\]
**(not equivalent)**
After evaluating all the expressions, we can see that there is no expression in the choices that matches \(40 + \frac{4}{3}\).
The correct evaluation of the original expression is \(40 + \frac{4}{3}\), and none of the answer choices are equivalent to this. If you see a similar question or if there are any potential errors in the answer choices, please check and provide more context or different options if needed.