The product of two numbers is `(-28)/(27)`. If one of the numbers is `(-4)/(9)`, find the other.

Options

A. `(7)/(3)`
B. `(7)/(5)`
C. `(8)/(3)`
D. `(11)/(3)`

Answer

To solve the problem, we need to find the other number when the product of two numbers is given. Let's break down the steps:

### Step 1: Understand the Problem
We know that the product of two numbers is given as:
\[ \text{Product} = \frac{-28}{27} \]
One of the numbers is:
\[ \text{Number 1} = \frac{-4}{9} \]
We need to find the other number, which we will denote as \( x \).

### Step 2: Set Up the Equation
From the information given, we can set up the equation:
\[ \frac{-4}{9} \times x = \frac{-28}{27} \]

### Step 3: Solve for \( x \)
To find \( x \), we can rearrange the equation. We will isolate \( x \) by dividing both sides by \( \frac{-4}{9} \):
\[ x = \frac{-28}{27} \div \frac{-4}{9} \]
Dividing by a fraction is the same as multiplying by its reciprocal:
\[ x = \frac{-28}{27} \times \frac{9}{-4} \]

### Step 4: Simplify the Expression
Now, we can simplify:
1. The negatives cancel out:
\[ x = \frac{28 \times 9}{27 \times 4} \]
2. Calculate \( 28 \div 4 = 7 \) and \( 27 \div 9 = 3 \):
\[ x = \frac{7 \times 9}{3} = \frac{63}{3} \]
3. Finally, simplify \( \frac{63}{3} \):
\[ x = 21 \]

### Final Answer
The other number is:
\[ \boxed{21} \]

---