The product of two numbers is `15 5/6` If one of the numbers is `6 2/3`, 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 \( 6 \frac{2}{3} \), we can follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
First, we need to convert both 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 \( 6 \frac{2}{3} \):
\[ 6 \frac{2}{3} = \frac{6 \times 3 + 2}{3} = \frac{18 + 2}{3} = \frac{20}{3} \]

### Step 2: Set Up the Equation
Let the other number be \( x \). According to the problem, we have:
\[ \frac{95}{6} = x \times \frac{20}{3} \]

### Step 3: Solve for \( x \)
To find \( x \), we can rearrange the equation:
\[ x = \frac{\frac{95}{6}}{\frac{20}{3}} \]

### Step 4: Dividing Fractions
Dividing by a fraction is the same as multiplying by its reciprocal:
\[ x = \frac{95}{6} \times \frac{3}{20} \]

### Step 5: Simplify the Expression
Now, we can simplify the multiplication:
\[ x = \frac{95 \times 3}{6 \times 20} \]
Calculating the numerator and the denominator:
\[ x = \frac{285}{120} \]

### Step 6: Simplify the Fraction
Now we need to simplify \( \frac{285}{120} \). We can find the greatest common divisor (GCD) of 285 and 120, which is 15:
\[ x = \frac{285 \div 15}{120 \div 15} = \frac{19}{8} \]

### Step 7: Convert Improper Fraction to Mixed Number
Finally, we convert \( \frac{19}{8} \) back to a mixed number:
\[ 19 \div 8 = 2 \quad \text{(with a remainder of 3)} \]
So, \( \frac{19}{8} = 2 \frac{3}{8} \).

Thus, the other number is \( 2 \frac{3}{8} \).

---