Question

Which expression is equivalent to 8 + 4/3 + 4 • 2 + 3 A 8 + 4/3 + 4 • 6 B 8 + 4/3 + 24 C 4 + 4 • 8 D 8 • 8

Answer 1

Let's simplify the expression given:

8 + 4/3 + 4 • 2 + 3

First, we calculate each part step by step:

1. **Multiply**: \(4 \cdot 2 = 8\)
2. **Then substitute back**:
\(8 + \frac{4}{3} + 8 + 3\)

Now we can combine the constants (8 + 8 + 3):

1. \(8 + 8 = 16\)
2. Then add 3:
\(16 + 3 = 19\)

Now we have:

\[ 19 + \frac{4}{3} \]

Next, let's convert 19 into a fraction with a denominator of 3 for better addition:

\[
19 = \frac{57}{3}
\]

So now, we can add \(\frac{4}{3}\):

\[
\frac{57}{3} + \frac{4}{3} = \frac{57 + 4}{3} = \frac{61}{3}
\]

Now, let's look at all the provided options to find an equivalent expression:

A. \(8 + \frac{4}{3} + 4 \cdot 6\)
- Calculate \(4 \cdot 6 = 24\)
- New expression: \(8 + \frac{4}{3} + 24 = 32 + \frac{4}{3} = \frac{96 + 4}{3} = \frac{100}{3}\) (not equivalent)

B. \(8 + \frac{4}{3} + 24\)
- New expression: \(32 + \frac{4}{3} = \frac{100}{3}\) (not equivalent)

C. \(4 + 4 \cdot 8\)
- Calculate \(4 \cdot 8 = 32\)
- New expression: \(4 + 32 = 36\) (not equivalent)

D. \(8 \cdot 8\)
- Calculate \(8 \cdot 8 = 64\) (not equivalent)

None of these expressions are equivalent to \(19 + \frac{4}{3} = \frac{61}{3}\). Therefore, none of the given options match the original expression.