The product of two numbers is `(-1)/(6)` . If one of them is `(-5)/(8)` the other number is

Options

A. `(-4)/(15)`
B. `(4)/(15)`
C. `(15)/(4)`
D. `(-15)/(4)`

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.**
We know that the product of two numbers is given by the equation:
\[ \text{First number} \times \text{Second number} = \text{Product} \]
In this case, we have:
\[ \left(-\frac{5}{8}\right) \times x = -\frac{1}{6} \]
where \( x \) is the second number we want to find.

**Step 2: Isolate \( x \).**
To find \( x \), we can rearrange the equation by dividing both sides by \(-\frac{5}{8}\):
\[ x = \frac{-\frac{1}{6}}{-\frac{5}{8}} \]
When we divide by a negative number, the negatives cancel out.

**Step 3: Simplify the right side.**
Dividing by a fraction is the same as multiplying by its reciprocal:
\[ x = \frac{-\frac{1}{6}}{-\frac{5}{8}} = \frac{1}{6} \times \frac{8}{5} \]

**Step 4: Perform the multiplication.**
Now we multiply the fractions:
\[ x = \frac{1 \times 8}{6 \times 5} = \frac{8}{30} \]

**Step 5: Simplify the fraction.**
Now we can simplify \(\frac{8}{30}\):
\[ x = \frac{4}{15} \]

So, the other number is:
\[ \boxed{\frac{4}{15}} \]