Evaluate the difference:
`6(7)/(15)-5(5)/(12)`

Answer

To evaluate the difference \( 6\frac{7}{15} - 5\frac{5}{12} \), we will follow these steps:

### Step 1: Convert the mixed fractions to improper fractions.

**For \( 6\frac{7}{15} \):**
- Multiply the whole number (6) by the denominator (15) and add the numerator (7).
- Calculation: \( 6 \times 15 + 7 = 90 + 7 = 97 \)
- So, \( 6\frac{7}{15} = \frac{97}{15} \).

**For \( 5\frac{5}{12} \):**
- Multiply the whole number (5) by the denominator (12) and add the numerator (5).
- Calculation: \( 5 \times 12 + 5 = 60 + 5 = 65 \)
- So, \( 5\frac{5}{12} = \frac{65}{12} \).

### Step 2: Subtract the two improper fractions.

Now we have:
\[ \frac{97}{15} - \frac{65}{12} \]

### Step 3: Find a common denominator.

The denominators are 15 and 12. The least common multiple (LCM) of 15 and 12 is 60.

**Convert \( \frac{97}{15} \) to have a denominator of 60:**
- Multiply both the numerator and denominator by 4:
\[ \frac{97 \times 4}{15 \times 4} = \frac{388}{60} \]

**Convert \( \frac{65}{12} \) to have a denominator of 60:**
- Multiply both the numerator and denominator by 5:
\[ \frac{65 \times 5}{12 \times 5} = \frac{325}{60} \]

### Step 4: Subtract the fractions.

Now we can subtract:
\[ \frac{388}{60} - \frac{325}{60} = \frac{388 - 325}{60} = \frac{63}{60} \]

### Step 5: Simplify the result.

The fraction \( \frac{63}{60} \) can be simplified. We can convert it to a mixed number:
- Divide 63 by 60:
- The quotient is 1 (whole number part).
- The remainder is \( 63 - 60 = 3 \).
- So, \( \frac{63}{60} = 1\frac{3}{60} \).

### Step 6: Simplify \( \frac{3}{60} \).

The fraction \( \frac{3}{60} \) can be simplified:
- Divide both the numerator and denominator by 3:
\[ \frac{3 \div 3}{60 \div 3} = \frac{1}{20} \]

### Final Answer:

Thus, the final answer is:
\[ 1\frac{1}{20} \]