`{:("Quantity A","Quantity B"),(0.125+(4)/(5)+(2)/(3)+1.2,0.8+0.bar6+(6)/(5)+(1)/(8)):}`

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 problem, we need to evaluate both Quantity A and Quantity B and compare their values. Let's break it down step by step.

### Step 1: Evaluate Quantity A
Quantity A is given as:
\[ 0.125 + \frac{4}{5} + \frac{2}{3} + 1.2 \]

#### Step 1.1: Convert each term to decimal
- \( 0.125 \) is already in decimal form.
- \( \frac{4}{5} = 0.8 \)
- \( \frac{2}{3} \approx 0.6667 \) (or \( 0.6\overline{6} \))
- \( 1.2 \) is already in decimal form.

#### Step 1.2: Add the decimal values
Now we can add these values together:
\[ 0.125 + 0.8 + 0.6667 + 1.2 \]

Calculating this step-by-step:
1. \( 0.125 + 0.8 = 0.925 \)
2. \( 0.925 + 0.6667 \approx 1.5917 \)
3. \( 1.5917 + 1.2 \approx 2.7917 \)

So, Quantity A is approximately:
\[ \text{Quantity A} \approx 2.7917 \]

### Step 2: Evaluate Quantity B
Quantity B is given as:
\[ 0.8 + 0.6\overline{6} + \frac{6}{5} + \frac{1}{8} \]

#### Step 2.1: Convert each term to decimal
- \( 0.8 \) is already in decimal form.
- \( 0.6\overline{6} \approx 0.6667 \)
- \( \frac{6}{5} = 1.2 \)
- \( \frac{1}{8} = 0.125 \)

#### Step 2.2: Add the decimal values
Now we can add these values together:
\[ 0.8 + 0.6667 + 1.2 + 0.125 \]

Calculating this step-by-step:
1. \( 0.8 + 0.6667 \approx 1.4667 \)
2. \( 1.4667 + 1.2 \approx 2.6667 \)
3. \( 2.6667 + 0.125 \approx 2.7917 \)

So, Quantity B is approximately:
\[ \text{Quantity B} \approx 2.7917 \]

### Step 3: Compare Quantity A and Quantity B
Now we compare the two quantities:
\[ \text{Quantity A} \approx 2.7917 \quad \text{and} \quad \text{Quantity B} \approx 2.7917 \]

Since both quantities are approximately equal, we conclude:
\[ \text{Quantity A} = \text{Quantity B} \]

### Final Answer
The correct option is that Quantity A is equal to Quantity B.

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