`8(1)/(3)+ 10(5)/( 6) =?`

Options

A. `(5)/( 6)`
B. `(2)/(3)`
C. `(10)/( 13)`
D. `(11)/(13)`

Answer

To solve the problem \(8 \frac{1}{3} + 10 \frac{5}{6}\), we will follow these steps:

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

- For \(8 \frac{1}{3}\):
\[ 8 \frac{1}{3} = \frac{8 \times 3 + 1}{3} = \frac{24 + 1}{3} = \frac{25}{3} \]

- For \(10 \frac{5}{6}\):
\[ 10 \frac{5}{6} = \frac{10 \times 6 + 5}{6} = \frac{60 + 5}{6} = \frac{65}{6} \]

### Step 2: Find the Least Common Multiple (LCM)
Next, we need to find the LCM of the denominators \(3\) and \(6\).

The LCM of \(3\) and \(6\) is \(6\).

### Step 3: Convert Fractions to Have the Same Denominator
Now, we will convert both fractions to have the same denominator of \(6\).

- For \(\frac{25}{3}\):
\[ \frac{25}{3} = \frac{25 \times 2}{3 \times 2} = \frac{50}{6} \]

- The second fraction \(\frac{65}{6}\) already has the denominator \(6\).

### Step 4: Add the Fractions
Now we can add the two fractions:
\[ \frac{50}{6} + \frac{65}{6} = \frac{50 + 65}{6} = \frac{115}{6} \]

### Step 5: Convert the Improper Fraction to a Mixed Number
Finally, we convert \(\frac{115}{6}\) back to a mixed number.

- Divide \(115\) by \(6\):
\[ 115 \div 6 = 19 \quad \text{(whole number)} \]
The remainder is:
\[ 115 - (19 \times 6) = 115 - 114 = 1 \]
So, we can write:
\[ \frac{115}{6} = 19 \frac{1}{6} \]

### Final Answer
Thus, the final answer is:
\[ 8 \frac{1}{3} + 10 \frac{5}{6} = 19 \frac{1}{6} \]