Find:
`3(1)/(6)-2(1)/(15)`

Answer

To solve the problem \( 3\frac{1}{6} - 2\frac{1}{15} \), we will follow these steps:

### Step 1: Convert the mixed fractions to improper fractions
1. For \( 3\frac{1}{6} \):
- Multiply the whole number (3) by the denominator (6): \( 3 \times 6 = 18 \)
- Add the numerator (1): \( 18 + 1 = 19 \)
- So, \( 3\frac{1}{6} = \frac{19}{6} \)

2. For \( 2\frac{1}{15} \):
- Multiply the whole number (2) by the denominator (15): \( 2 \times 15 = 30 \)
- Add the numerator (1): \( 30 + 1 = 31 \)
- So, \( 2\frac{1}{15} = \frac{31}{15} \)

### Step 2: Rewrite the expression
Now we can rewrite the expression as:
\[ \frac{19}{6} - \frac{31}{15} \]

### Step 3: Find the least common multiple (LCM) of the denominators
The denominators are 6 and 15. To find the LCM:
- The prime factorization of 6 is \( 2 \times 3 \)
- The prime factorization of 15 is \( 3 \times 5 \)
- The LCM is found by taking the highest power of each prime: \( 2^1 \times 3^1 \times 5^1 = 30 \)

### Step 4: Convert each fraction to have the same denominator
1. For \( \frac{19}{6} \):
- Multiply the numerator and denominator by 5:
\[ \frac{19 \times 5}{6 \times 5} = \frac{95}{30} \]

2. For \( \frac{31}{15} \):
- Multiply the numerator and denominator by 2:
\[ \frac{31 \times 2}{15 \times 2} = \frac{62}{30} \]

### Step 5: Subtract the fractions
Now we can subtract:
\[ \frac{95}{30} - \frac{62}{30} = \frac{95 - 62}{30} = \frac{33}{30} \]

### Step 6: Simplify the fraction
The fraction \( \frac{33}{30} \) can be simplified:
- Both the numerator and denominator can be divided by 3:
\[ \frac{33 \div 3}{30 \div 3} = \frac{11}{10} \]

### Final Answer
Thus, the final answer is:
\[ \frac{11}{10} \]