The product of two numbers is `3 (1)/(3)`. If one number is `3 (3)/(5)`, find the other.

Answer

To find the other number when the product of two numbers is \(3 \frac{1}{3}\) and one of the numbers is \(3 \frac{3}{5}\), we can follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
First, we need to convert the mixed numbers into improper fractions.

1. For \(3 \frac{1}{3}\):
\[ 3 \frac{1}{3} = 3 + \frac{1}{3} = \frac{3 \times 3 + 1}{3} = \frac{9 + 1}{3} = \frac{10}{3} \]

2. For \(3 \frac{3}{5}\):
\[ 3 \frac{3}{5} = 3 + \frac{3}{5} = \frac{3 \times 5 + 3}{5} = \frac{15 + 3}{5} = \frac{18}{5} \]

### Step 2: Set Up the Equation
Let the other number be \(x\). According to the problem, the product of the two numbers is:
\[ x \times \frac{18}{5} = \frac{10}{3} \]

### Step 3: Solve for \(x\)
To find \(x\), we can rearrange the equation:
\[ x = \frac{10}{3} \div \frac{18}{5} \]
Dividing by a fraction is the same as multiplying by its reciprocal:
\[ x = \frac{10}{3} \times \frac{5}{18} \]

### Step 4: Multiply the Fractions
Now, we multiply the fractions:
\[ x = \frac{10 \times 5}{3 \times 18} = \frac{50}{54} \]

### Step 5: Simplify the Fraction
Now, we simplify \(\frac{50}{54}\):
\[ \frac{50}{54} = \frac{25}{27} \quad \text{(dividing both numerator and denominator by 2)} \]

### Final Answer
Thus, the other number is:
\[ \boxed{\frac{25}{27}} \]