The product of two numbers is `(-16)/(35)`. If one of the numbers is `(-15)/(14)`, the other is

Options

A. `(-2)/(5)`
B. `(8)/(15)`
C. `(32)/(75)`
D. `(-8)/(3)`

Answer

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

### Step 1: Set up the equation
Let the second number be \( x \). According to the problem, we have:
\[ \text{First number} \times \text{Second number} = \text{Product} \]
This can be expressed as:
\[ \left(-\frac{15}{14}\right) \times x = -\frac{16}{35} \]

### Step 2: Isolate \( x \)
To find \( x \), we need to isolate it on one side of the equation. We can do this by dividing both sides by \(-\frac{15}{14}\):
\[ x = \frac{-\frac{16}{35}}{-\frac{15}{14}} \]

### Step 3: Simplify the right side
When dividing fractions, we multiply by the reciprocal of the divisor:
\[ x = -\frac{16}{35} \times -\frac{14}{15} \]
The negatives cancel out:
\[ x = \frac{16 \times 14}{35 \times 15} \]

### Step 4: Calculate the numerator and denominator
Now, calculate the numerator and denominator:
\[ x = \frac{224}{525} \]
Here, \( 16 \times 14 = 224 \) and \( 35 \times 15 = 525 \).

### Step 5: Simplify the fraction
Now we need to check if \( \frac{224}{525} \) can be simplified. The greatest common divisor (GCD) of 224 and 525 is 1, so it cannot be simplified further.

### Final Answer
Thus, the other number is:
\[ \frac{224}{525} \]