Work out the following :
`2""1/3+5/6`

Answer

To solve the problem \(2 \frac{1}{3} + \frac{5}{6}\), we will follow these steps:

### Step 1: Convert the mixed fraction to an improper fraction
A mixed fraction consists of a whole number and a proper fraction. To convert \(2 \frac{1}{3}\) into an improper fraction, we use the formula:
\[ \text{Improper Fraction} = \left(\text{Whole Number} \times \text{Denominator}\right) + \text{Numerator} \div \text{Denominator} \]
For \(2 \frac{1}{3}\):
\[ = \left(2 \times 3 + 1\right) \div 3 = \frac{6 + 1}{3} = \frac{7}{3} \]

### Step 2: Write the expression with the improper fraction
Now we can rewrite the original expression:
\[ \frac{7}{3} + \frac{5}{6} \]

### Step 3: Find the least common multiple (LCM) of the denominators
The denominators are 3 and 6. The LCM of 3 and 6 is 6.

### Step 4: Convert each fraction to have the same denominator
We need to convert \(\frac{7}{3}\) to have a denominator of 6:
\[ \frac{7}{3} = \frac{7 \times 2}{3 \times 2} = \frac{14}{6} \]
Now we can rewrite the expression:
\[ \frac{14}{6} + \frac{5}{6} \]

### Step 5: Add the fractions
Since the denominators are the same, we can add the numerators:
\[ \frac{14 + 5}{6} = \frac{19}{6} \]

### Step 6: Write the final answer
The final answer is:
\[ \frac{19}{6} \]