What should be added to `15 2/3`to get `17 5/6`?

Options

A. `4 1/6`
B. `1 1/6`
C. `3 1/3`
D. `2 1/6`

Answer

To solve the question "What should be added to `15 2/3` to get `17 5/6`?", we can follow these steps:

### Step 1: Convert the mixed numbers to improper fractions.
- For `15 2/3`, we convert it as follows:
\[ 15 \times 3 + 2 = 45 + 2 = 47 \quad \text{(so, } 15 \frac{2}{3} = \frac{47}{3}\text{)} \]
- For `17 5/6`, we convert it similarly:
\[ 17 \times 6 + 5 = 102 + 5 = 107 \quad \text{(so, } 17 \frac{5}{6} = \frac{107}{6}\text{)} \]

### Step 2: Set up the equation.
We need to find the value of \( x \) such that:
\[ \frac{47}{3} + x = \frac{107}{6} \]

### Step 3: Isolate \( x \).
To find \( x \), we rearrange the equation:
\[ x = \frac{107}{6} - \frac{47}{3} \]

### Step 4: Find a common denominator.
The denominators are 6 and 3. The least common multiple (LCM) of 6 and 3 is 6. We need to convert \( \frac{47}{3} \) to have a denominator of 6:
\[ \frac{47}{3} = \frac{47 \times 2}{3 \times 2} = \frac{94}{6} \]

### Step 5: Subtract the fractions.
Now we can subtract:
\[ x = \frac{107}{6} - \frac{94}{6} = \frac{107 - 94}{6} = \frac{13}{6} \]

### Step 6: Convert the result back to a mixed number.
To convert \( \frac{13}{6} \) back to a mixed number:
- Divide 13 by 6, which gives 2 with a remainder of 1.
- Thus, \( \frac{13}{6} = 2 \frac{1}{6} \).

### Final Answer:
So, the value that should be added to `15 2/3` to get `17 5/6` is:
\[ 2 \frac{1}{6} \]

---