The product of two fractions is 8`7/25` .If one of them is 3`1/15` , find the other.

Answer

To find the other fraction when the product of two fractions is given, we can follow these steps:

### Step 1: Set Up the Equation
Let the other fraction be \( x \). According to the problem, we have:
\[ x \times 3 \frac{1}{15} = 8 \frac{7}{25} \]

### Step 2: Convert Mixed Numbers to Improper Fractions
First, we need to convert the mixed numbers into improper fractions.

For \( 3 \frac{1}{15} \):
\[ 3 \frac{1}{15} = \frac{(3 \times 15) + 1}{15} = \frac{45 + 1}{15} = \frac{46}{15} \]

For \( 8 \frac{7}{25} \):
\[ 8 \frac{7}{25} = \frac{(8 \times 25) + 7}{25} = \frac{200 + 7}{25} = \frac{207}{25} \]

### Step 3: Rewrite the Equation
Now we can rewrite the equation with the improper fractions:
\[ x \times \frac{46}{15} = \frac{207}{25} \]

### Step 4: Solve for \( x \)
To find \( x \), we can isolate it by multiplying both sides by the reciprocal of \( \frac{46}{15} \):
\[ x = \frac{207}{25} \times \frac{15}{46} \]

### Step 5: Simplify the Expression
Now we can simplify this expression. First, we can cancel out common factors.

1. The number 15 can be divided by 5:
\[ 15 \div 5 = 3 \quad \text{and} \quad 25 \div 5 = 5 \]
So we have:
\[ x = \frac{207}{5} \times \frac{3}{46} \]

2. Next, we can simplify \( \frac{207}{46} \):
- The greatest common divisor (GCD) of 207 and 46 is 23.
- Dividing both by 23:
\[ 207 \div 23 = 9 \quad \text{and} \quad 46 \div 23 = 2 \]
So we have:
\[ x = \frac{9}{2} \times 3 = \frac{27}{2} \]

### Step 6: Convert to Mixed Number
Now, we convert \( \frac{27}{2} \) into a mixed number:
\[ 27 \div 2 = 13 \quad \text{with a remainder of } 1 \]
Thus, we can write:
\[ \frac{27}{2} = 13 \frac{1}{2} \]

### Final Answer
The other fraction is:
\[ \boxed{13 \frac{1}{2}} \]