Evaluate the difference:
`8(9)/(11)-5(5)/(12)`

Answer

To evaluate the difference \( \frac{8 \times 9}{11} - \frac{5 \times 5}{12} \), we can follow these steps:

### Step 1: Calculate the individual fractions
First, calculate the values of the fractions:
- For the first fraction:
\[ \frac{8 \times 9}{11} = \frac{72}{11} \]
- For the second fraction:
\[ \frac{5 \times 5}{12} = \frac{25}{12} \]

### Step 2: Set up the expression
Now, we can write the expression as:
\[ \frac{72}{11} - \frac{25}{12} \]

### Step 3: Find the least common multiple (LCM)
To subtract these fractions, we need a common denominator. The denominators are 11 and 12. The LCM of 11 and 12 is 132.

### Step 4: Convert the fractions to have a common denominator
Now we convert each fraction to have the common denominator of 132:
- For \( \frac{72}{11} \):
\[ \frac{72}{11} = \frac{72 \times 12}{11 \times 12} = \frac{864}{132} \]
- For \( \frac{25}{12} \):
\[ \frac{25}{12} = \frac{25 \times 11}{12 \times 11} = \frac{275}{132} \]

### Step 5: Subtract the fractions
Now we can subtract the two fractions:
\[ \frac{864}{132} - \frac{275}{132} = \frac{864 - 275}{132} = \frac{589}{132} \]

### Step 6: Simplify the result
Now, we check if \( \frac{589}{132} \) can be simplified. Since 589 and 132 do not have any common factors, this fraction is in its simplest form.

### Final Answer
Thus, the final answer is:
\[ \frac{589}{132} \]

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