The product of two rational numbers is `(-16)/(9)`. If one of the numbers is `(-4)/(3)` find the other .

Answer

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

### Step 1: Understand the problem
We know that the product of two rational numbers is given as \(-\frac{16}{9}\), and one of the numbers is \(-\frac{4}{3}\). We need to find the other number, which we will denote as \(x\).

### Step 2: Set up the equation
From the problem, we can set up the equation:
\[ -\frac{4}{3} \times x = -\frac{16}{9} \]

### Step 3: Isolate \(x\)
To find \(x\), we need to isolate it. We can do this by dividing both sides of the equation by \(-\frac{4}{3}\). Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of \(-\frac{4}{3}\) is \(-\frac{3}{4}\). Therefore, we can rewrite the equation as:
\[ x = -\frac{16}{9} \div -\frac{4}{3} = -\frac{16}{9} \times -\frac{3}{4} \]

### Step 4: Simplify the right side
Now, we can simplify the right side:
\[ x = \frac{16 \times 3}{9 \times 4} \]
Calculating the numerator and the denominator:
\[ x = \frac{48}{36} \]

### Step 5: Reduce the fraction
Now, we can simplify \(\frac{48}{36}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 12:
\[ x = \frac{48 \div 12}{36 \div 12} = \frac{4}{3} \]

### Conclusion
Thus, the other rational number is:
\[ x = \frac{4}{3} \]