The product of two numbers is `15 5/6` If one of the numbers is` 6 1/3` , find the other.

Answer

To find the other number when the product of two numbers is \( 15 \frac{5}{6} \) and one of the numbers is \( 6 \frac{1}{3} \), we can follow these steps:

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

For \( 15 \frac{5}{6} \):
\[ 15 \frac{5}{6} = \frac{15 \times 6 + 5}{6} = \frac{90 + 5}{6} = \frac{95}{6} \]

For \( 6 \frac{1}{3} \):
\[ 6 \frac{1}{3} = \frac{6 \times 3 + 1}{3} = \frac{18 + 1}{3} = \frac{19}{3} \]

### Step 2: Set Up the Equation
Let the other number be \( x \). According to the problem, the product of the two numbers is:
\[ \frac{19}{3} \times x = \frac{95}{6} \]

### Step 3: Solve for \( x \)
To find \( x \), we can rearrange the equation:
\[ x = \frac{95}{6} \div \frac{19}{3} \]

Dividing by a fraction is the same as multiplying by its reciprocal:
\[ x = \frac{95}{6} \times \frac{3}{19} \]

### Step 4: Simplify the Expression
Now we can simplify:
\[ x = \frac{95 \times 3}{6 \times 19} \]

Calculating the numerator:
\[ 95 \times 3 = 285 \]

Calculating the denominator:
\[ 6 \times 19 = 114 \]

So we have:
\[ x = \frac{285}{114} \]

### Step 5: Simplify the Fraction
Now we simplify \( \frac{285}{114} \):
Both 285 and 114 can be divided by 3:
\[ \frac{285 \div 3}{114 \div 3} = \frac{95}{38} \]

### Step 6: Convert to Mixed Number
To convert \( \frac{95}{38} \) to a mixed number:
\[ 95 \div 38 = 2 \quad \text{(with a remainder of 19)} \]
So,
\[ \frac{95}{38} = 2 \frac{19}{38} \]

### Final Answer
Therefore, the other number is:
\[ 2 \frac{19}{38} \]

---