The product of two numbers is `(16)/(3).` If one of the numbers is `(26)/(3).` Find the other number.

Options

A. `(1)/(13)`
B. `(8)/(13)`
C. `(9)/(13)`
D. `(16)/(9)`

Answer

To find the other number when the product of two numbers is \( \frac{16}{3} \) and one of the numbers is \( \frac{26}{3} \), we can follow these steps:

### Step 1: Set up the equation
Let the two numbers be \( x \) and \( y \). We know:
\[ x \cdot y = \frac{16}{3} \]
Given that one of the numbers \( x = \frac{26}{3} \), we can substitute this into the equation:
\[ \frac{26}{3} \cdot y = \frac{16}{3} \]

### Step 2: Isolate \( y \)
To find \( y \), we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by \( \frac{26}{3} \):
\[ y = \frac{\frac{16}{3}}{\frac{26}{3}} \]

### Step 3: Simplify the division
Dividing by a fraction is the same as multiplying by its reciprocal. Thus, we can rewrite the equation:
\[ y = \frac{16}{3} \cdot \frac{3}{26} \]

### Step 4: Cancel out common terms
Now, we can cancel the \( 3 \) in the numerator and denominator:
\[ y = \frac{16}{1} \cdot \frac{1}{26} \]
This simplifies to:
\[ y = \frac{16}{26} \]

### Step 5: Simplify the fraction
Next, we can simplify \( \frac{16}{26} \) by finding the greatest common divisor (GCD) of 16 and 26, which is 2:
\[ y = \frac{16 \div 2}{26 \div 2} = \frac{8}{13} \]

### Conclusion
Thus, the other number \( y \) is:
\[ y = \frac{8}{13} \]

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