The product of two rational numbers is `(-28)/(81)`. If one of the numbers is `(14)/(27)` then the other one is

Options

A. `(-2)/(3)`
B. `(2)/(3)`
C. `(3)/(2)`
D. `(-3)/(2)`

Answer

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

### Step-by-Step Solution:

1. **Identify the Given Information**:
We know that the product of two rational numbers is \(-\frac{28}{81}\). One of the numbers is \(\frac{14}{27}\). We need to find the other number, which we will denote as \(x\).

2. **Set Up the Equation**:
Since the product of the two numbers is given, we can set up the equation:
\[ \frac{14}{27} \times x = -\frac{28}{81} \]

3. **Isolate \(x\)**:
To find \(x\), we need to isolate it. We can do this by dividing both sides of the equation by \(\frac{14}{27}\):
\[ x = -\frac{28}{81} \div \frac{14}{27} \]

4. **Convert Division to Multiplication**:
Dividing by a fraction is the same as multiplying by its reciprocal. Therefore, we can rewrite the equation as:
\[ x = -\frac{28}{81} \times \frac{27}{14} \]

5. **Multiply the Fractions**:
Now we multiply the fractions:
\[ x = -\frac{28 \times 27}{81 \times 14} \]

6. **Simplify the Expression**:
We can simplify the expression by canceling common factors:
- The number \(27\) in the numerator and \(81\) in the denominator can be simplified:
\[ 27 = 3 \times 9 \quad \text{and} \quad 81 = 9 \times 9 \quad \Rightarrow \quad \frac{27}{81} = \frac{1}{3} \]
- The number \(28\) and \(14\) can also be simplified:
\[ 28 = 2 \times 14 \quad \Rightarrow \quad \frac{28}{14} = 2 \]

So, substituting these simplifications back into the equation gives us:
\[ x = -\frac{2 \times 1}{3} = -\frac{2}{3} \]

7. **Final Answer**:
Therefore, the other rational number is:
\[ x = -\frac{2}{3} \]