Find: `((6)/(11) xx (77)/(48)) - (19)/(11)`

Answer

To solve the expression \(\left(\frac{6}{11} \times \frac{77}{48}\right) - \frac{19}{11}\), we will follow these steps:

### Step 1: Simplify the multiplication inside the parentheses
We start with the multiplication of the fractions:
\[ \frac{6}{11} \times \frac{77}{48} \]
We can rewrite \(77\) as \(7 \times 11\) and \(48\) as \(6 \times 8\):
\[ \frac{6}{11} \times \frac{7 \times 11}{6 \times 8} \]

### Step 2: Cancel common factors
Now, we can cancel the common factors:
- The \(6\) in the numerator and denominator cancels out.
- The \(11\) in the numerator and denominator cancels out.

This leaves us with:
\[ \frac{7}{8} \]

### Step 3: Rewrite the expression
Now we rewrite the expression:
\[ \frac{7}{8} - \frac{19}{11} \]

### Step 4: Find the LCM of the denominators
To subtract these fractions, we need a common denominator. The denominators are \(8\) and \(11\). The least common multiple (LCM) of \(8\) and \(11\) is:
\[ \text{LCM}(8, 11) = 88 \]

### Step 5: Convert each fraction to have the common denominator
Now we convert each fraction:
- For \(\frac{7}{8}\):
\[ \frac{7}{8} = \frac{7 \times 11}{8 \times 11} = \frac{77}{88} \]
- For \(\frac{19}{11}\):
\[ \frac{19}{11} = \frac{19 \times 8}{11 \times 8} = \frac{152}{88} \]

### Step 6: Subtract the fractions
Now we can subtract the two fractions:
\[ \frac{77}{88} - \frac{152}{88} = \frac{77 - 152}{88} = \frac{-75}{88} \]

### Final Answer
Thus, the final answer is:
\[ \frac{-75}{88} \]

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