What should be added to `7 4/15`— to get `8 2/5`— ?

Answer

To solve the problem of what should be added to \( 7 \frac{4}{15} \) to get \( 8 \frac{2}{5} \), we can follow these steps:

### Step 1: Convert the mixed numbers to improper fractions.
- For \( 7 \frac{4}{15} \):
\[ 7 \frac{4}{15} = \frac{(7 \times 15) + 4}{15} = \frac{105 + 4}{15} = \frac{109}{15} \]

- For \( 8 \frac{2}{5} \):
\[ 8 \frac{2}{5} = \frac{(8 \times 5) + 2}{5} = \frac{40 + 2}{5} = \frac{42}{5} \]

### Step 2: Set up the equation.
We need to find \( x \) such that:
\[ \frac{109}{15} + x = \frac{42}{5} \]

### Step 3: Isolate \( x \).
To find \( x \), we can rearrange the equation:
\[ x = \frac{42}{5} - \frac{109}{15} \]

### Step 4: Find a common denominator.
The least common multiple of 5 and 15 is 15. We can convert \( \frac{42}{5} \) to have a denominator of 15:
\[ \frac{42}{5} = \frac{42 \times 3}{5 \times 3} = \frac{126}{15} \]

### Step 5: Subtract the fractions.
Now we can perform the subtraction:
\[ x = \frac{126}{15} - \frac{109}{15} = \frac{126 - 109}{15} = \frac{17}{15} \]

### Step 6: Convert the result back to a mixed number.
To convert \( \frac{17}{15} \) to a mixed number:
\[ \frac{17}{15} = 1 \frac{2}{15} \]

### Final Answer:
Thus, the value that should be added to \( 7 \frac{4}{15} \) to get \( 8 \frac{2}{5} \) is:
\[ 1 \frac{2}{15} \]

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