The product of two numbers is `(-1)/(4)`. If one of them is `(-3)/(10)`, then the other is

Options

A. `(5)/(6)`
B. `(-5)/(6) `
C. `(4)/(3)`
D. `(-8)/(5)`

Answer

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

### Step-by-Step Solution:

1. **Identify the given information**:
We know that the product of two numbers is \(-\frac{1}{4}\) and one of the numbers is \(-\frac{3}{10}\).

2. **Let the unknown number be \(x\)**:
We can denote the unknown number as \(x\).

3. **Set up the equation**:
According to the problem, we can write the equation:
\[ -\frac{3}{10} \times x = -\frac{1}{4} \]

4. **Isolate \(x\)**:
To find \(x\), we need to isolate it. We can do this by dividing both sides of the equation by \(-\frac{3}{10}\):
\[ x = \frac{-\frac{1}{4}}{-\frac{3}{10}} \]

5. **Simplify the right-hand side**:
Dividing by a fraction is the same as multiplying by its reciprocal. Therefore, we can rewrite the equation as:
\[ x = -\frac{1}{4} \times -\frac{10}{3} \]

6. **Calculate the product**:
Now, we multiply the fractions:
\[ x = \frac{1 \times 10}{4 \times 3} = \frac{10}{12} \]

7. **Simplify the fraction**:
We can simplify \(\frac{10}{12}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 2:
\[ x = \frac{5}{6} \]

8. **Conclusion**:
Therefore, the other number is:
\[ x = \frac{5}{6} \]