Work out the following :
`3""5/6-2""7/15`

Answer

To solve the problem \( 3\frac{5}{6} - 2\frac{7}{15} \), we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
First, we need to convert the mixed numbers into improper fractions.

1. For \( 3\frac{5}{6} \):
- Multiply the whole number (3) by the denominator (6):
\[ 3 \times 6 = 18 \]
- Add the numerator (5):
\[ 18 + 5 = 23 \]
- So, \( 3\frac{5}{6} \) becomes:
\[ \frac{23}{6} \]

2. For \( 2\frac{7}{15} \):
- Multiply the whole number (2) by the denominator (15):
\[ 2 \times 15 = 30 \]
- Add the numerator (7):
\[ 30 + 7 = 37 \]
- So, \( 2\frac{7}{15} \) becomes:
\[ \frac{37}{15} \]

### Step 2: Subtract the Improper Fractions
Now we need to subtract the two improper fractions:
\[ \frac{23}{6} - \frac{37}{15} \]

### Step 3: Find a Common Denominator
To subtract these fractions, we need a common denominator. The least common multiple (LCM) of 6 and 15 is 30.

### Step 4: Convert Each Fraction to Have the Common Denominator
1. Convert \( \frac{23}{6} \) to have a denominator of 30:
- Multiply the numerator and denominator by 5:
\[ \frac{23 \times 5}{6 \times 5} = \frac{115}{30} \]

2. Convert \( \frac{37}{15} \) to have a denominator of 30:
- Multiply the numerator and denominator by 2:
\[ \frac{37 \times 2}{15 \times 2} = \frac{74}{30} \]

### Step 5: Subtract the Converted Fractions
Now we can subtract:
\[ \frac{115}{30} - \frac{74}{30} = \frac{115 - 74}{30} = \frac{41}{30} \]

### Step 6: Convert the Result Back to a Mixed Number
To convert \( \frac{41}{30} \) back to a mixed number:
- Divide 41 by 30:
- 30 goes into 41 one time (1).
- The remainder is \( 41 - 30 = 11 \).

Thus, \( \frac{41}{30} \) can be written as:
\[ 1\frac{11}{30} \]

### Final Answer
The final answer is:
\[ 1\frac{11}{30} \]

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