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

Options

A. `8 2/5`
B. `7 2/5`
C. `8 1/5`
D. none of these

Answer

To find out what should be added to \(6 \frac{3}{5}\) to get 15, we can follow these steps:

### Step 1: Convert the mixed number to an improper fraction
The mixed number \(6 \frac{3}{5}\) can be converted to an improper fraction. To do this, multiply the whole number (6) by the denominator (5) and then add the numerator (3):

\[ 6 \frac{3}{5} = \frac{6 \times 5 + 3}{5} = \frac{30 + 3}{5} = \frac{33}{5} \]

### Step 2: Set up the equation
Let \(x\) be the number that we need to add to \(6 \frac{3}{5}\) to get 15. We can write the equation as:

\[ \frac{33}{5} + x = 15 \]

### Step 3: Isolate \(x\)
To find \(x\), we need to isolate it on one side of the equation. We can do this by subtracting \(\frac{33}{5}\) from both sides:

\[ x = 15 - \frac{33}{5} \]

### Step 4: Convert 15 to a fraction
To subtract \(\frac{33}{5}\) from 15, we should express 15 as a fraction with the same denominator (5):

\[ 15 = \frac{15 \times 5}{5} = \frac{75}{5} \]

### Step 5: Perform the subtraction
Now we can subtract the fractions:

\[ x = \frac{75}{5} - \frac{33}{5} = \frac{75 - 33}{5} = \frac{42}{5} \]

### Step 6: Convert back to a mixed number (if necessary)
The improper fraction \(\frac{42}{5}\) can be converted back to a mixed number:

\[ \frac{42}{5} = 8 \frac{2}{5} \]

### Conclusion
Thus, the number that should be added to \(6 \frac{3}{5}\) to get 15 is \(8 \frac{2}{5}\).

---