`{:("Quantity A","Quantity B"),(((4)/(3)+(-2))/(-2),(-(4)/(3)+2)/(2)):}`

Options

A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the infromation given.

Answer

To solve the given problem, we need to evaluate both Quantity A and Quantity B and compare them.

**Step 1: Evaluate Quantity A**

Quantity A is given as:

\[ \text{Quantity A} = \frac{4}{3} + \frac{-2}{-2} \]

First, simplify \(\frac{-2}{-2}\):

\[ \frac{-2}{-2} = 1 \]

Now substitute this back into Quantity A:

\[ \text{Quantity A} = \frac{4}{3} + 1 \]

To add these fractions, convert 1 into a fraction with a common denominator:

\[ 1 = \frac{3}{3} \]

Now we can add:

\[ \text{Quantity A} = \frac{4}{3} + \frac{3}{3} = \frac{4 + 3}{3} = \frac{7}{3} \]

**Step 2: Evaluate Quantity B**

Quantity B is given as:

\[ \text{Quantity B} = \frac{-\left(\frac{4}{3}\right) + 2}{2} \]

First, simplify \(-\left(\frac{4}{3}\right) + 2\):

Convert 2 into a fraction:

\[ 2 = \frac{6}{3} \]

Now substitute this back into Quantity B:

\[ \text{Quantity B} = \frac{-\frac{4}{3} + \frac{6}{3}}{2} \]

Combine the fractions in the numerator:

\[ -\frac{4}{3} + \frac{6}{3} = \frac{-4 + 6}{3} = \frac{2}{3} \]

Now substitute this back into Quantity B:

\[ \text{Quantity B} = \frac{\frac{2}{3}}{2} \]

This can be simplified as follows:

\[ \text{Quantity B} = \frac{2}{3} \times \frac{1}{2} = \frac{2}{6} = \frac{1}{3} \]

**Step 3: Compare Quantity A and Quantity B**

Now we have:

\[ \text{Quantity A} = \frac{7}{3} \]
\[ \text{Quantity B} = \frac{1}{3} \]

Clearly, \(\frac{7}{3} > \frac{1}{3}\).

Thus, we conclude that:

\[ \text{Quantity A} > \text{Quantity B} \]

**Final Answer:** Quantity A is greater than Quantity B.

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