By how much does `(6)/(7//8)` exceed `(6//7)/(8)?`

Options

A. `6(1)/(8)`
B. `6(3)/(4)`
C. `7(3)/(4)`
D. `7(5)/(6)`

Answer

To solve the problem of how much `(6)/(7/8)` exceeds `(6/7)/(8)`, we can follow these steps:

### Step 1: Simplify the expressions
We start by simplifying both expressions.

1. **For the first expression**:
\[ \frac{6}{\frac{7}{8}} = 6 \times \frac{8}{7} = \frac{48}{7} \]

2. **For the second expression**:
\[ \frac{\frac{6}{7}}{8} = \frac{6}{7} \times \frac{1}{8} = \frac{6}{56} = \frac{3}{28} \]

### Step 2: Find the difference
Now, we need to find how much the first expression exceeds the second expression:
\[ \frac{48}{7} - \frac{3}{28} \]

### Step 3: Find a common denominator
To subtract these fractions, we need a common denominator. The least common multiple (LCM) of 7 and 28 is 28.

1. Convert \(\frac{48}{7}\) to have a denominator of 28:
\[ \frac{48}{7} = \frac{48 \times 4}{7 \times 4} = \frac{192}{28} \]

### Step 4: Perform the subtraction
Now we can subtract the two fractions:
\[ \frac{192}{28} - \frac{3}{28} = \frac{192 - 3}{28} = \frac{189}{28} \]

### Step 5: Simplify the result
Now we simplify \(\frac{189}{28}\):
- Divide both the numerator and denominator by their greatest common divisor (GCD), which is 7:
\[ \frac{189 \div 7}{28 \div 7} = \frac{27}{4} \]

### Final Answer
Thus, the amount by which \(\frac{6}{\frac{7}{8}}\) exceeds \(\frac{\frac{6}{7}}{8}\) is:
\[ \frac{27}{4} \]

---