What should be added to `9(2)/(3)` to get 19?

Answer

To solve the question "What should be added to \( 9 \frac{2}{3} \) to get 19?", we can follow these steps:

### Step 1: Convert the mixed number to an improper fraction
The mixed number \( 9 \frac{2}{3} \) can be converted to an improper fraction.

To convert:
\[ 9 \frac{2}{3} = 9 + \frac{2}{3} = \frac{9 \times 3 + 2}{3} = \frac{27 + 2}{3} = \frac{29}{3} \]

### Step 2: Set up the equation
Let \( x \) be the number that we need to add to \( 9 \frac{2}{3} \) to get 19. Therefore, we can set up the equation:
\[ x + 9 \frac{2}{3} = 19 \]
Substituting the improper fraction:
\[ x + \frac{29}{3} = 19 \]

### Step 3: Isolate \( x \)
To find \( x \), we need to isolate it on one side of the equation. We can do this by subtracting \( \frac{29}{3} \) from both sides:
\[ x = 19 - \frac{29}{3} \]

### Step 4: Convert 19 to a fraction
To subtract \( \frac{29}{3} \) from 19, we need to express 19 as a fraction with a denominator of 3:
\[ 19 = \frac{19 \times 3}{3} = \frac{57}{3} \]

### Step 5: Perform the subtraction
Now we can perform the subtraction:
\[ x = \frac{57}{3} - \frac{29}{3} = \frac{57 - 29}{3} = \frac{28}{3} \]

### Step 6: Conclusion
Thus, the number that should be added to \( 9 \frac{2}{3} \) to get 19 is:
\[ x = \frac{28}{3} \]