What should be added to `6(7)/(15)` to get `8(1)/(5)?`

Answer

To solve the problem of what should be added to \( 6\frac{7}{15} \) to get \( 8\frac{1}{5} \), we can follow these steps:

### Step 1: Convert the mixed numbers to improper fractions
1. Convert \( 6\frac{7}{15} \) to an improper fraction:
- Multiply the whole number (6) by the denominator (15): \( 6 \times 15 = 90 \)
- Add the numerator (7): \( 90 + 7 = 97 \)
- So, \( 6\frac{7}{15} = \frac{97}{15} \)

2. Convert \( 8\frac{1}{5} \) to an improper fraction:
- Multiply the whole number (8) by the denominator (5): \( 8 \times 5 = 40 \)
- Add the numerator (1): \( 40 + 1 = 41 \)
- So, \( 8\frac{1}{5} = \frac{41}{5} \)

### Step 2: Set up the equation
We need to find \( x \) such that:
\[ \frac{97}{15} + x = \frac{41}{5} \]

### Step 3: Isolate \( x \)
To find \( x \), we can rearrange the equation:
\[ x = \frac{41}{5} - \frac{97}{15} \]

### Step 4: Find a common denominator
The least common multiple (LCM) of 5 and 15 is 15. We will convert \( \frac{41}{5} \) to have a denominator of 15:
- Multiply the numerator and denominator of \( \frac{41}{5} \) by 3:
\[ \frac{41 \times 3}{5 \times 3} = \frac{123}{15} \]

### Step 5: Subtract the fractions
Now we can subtract the two fractions:
\[ x = \frac{123}{15} - \frac{97}{15} = \frac{123 - 97}{15} = \frac{26}{15} \]

### Step 6: Simplify if necessary
The fraction \( \frac{26}{15} \) is already in its simplest form.

### Conclusion
The value that should be added to \( 6\frac{7}{15} \) to get \( 8\frac{1}{5} \) is:
\[ \frac{26}{15} \]