`(4)/(9) divide ?= (-8)/(15)`

Options

A. `(-32)/(45)`
B. `(-8)/(5)`
C. `(-9)/(10)`
D. `(-5)/(6)`

Answer

To solve the equation \( \frac{4}{9} \div ? = \frac{-8}{15} \), we can follow these steps:

### Step 1: Set up the equation
Let \( x \) be the unknown value (the question mark). We can rewrite the equation as:
\[ \frac{4}{9} \div x = \frac{-8}{15} \]

### Step 2: Convert the division into multiplication
When we divide by \( x \), we can multiply by its reciprocal. Thus, we rewrite the equation as:
\[ \frac{4}{9} \times \frac{1}{x} = \frac{-8}{15} \]

### Step 3: Cross-multiply to solve for \( x \)
To eliminate the fraction, we can cross-multiply:
\[ 4 \times 15 = -8 \times 9x \]
This simplifies to:
\[ 60 = -72x \]

### Step 4: Isolate \( x \)
Now, we need to isolate \( x \). We do this by dividing both sides by -72:
\[ x = \frac{60}{-72} \]

### Step 5: Simplify the fraction
To simplify \( \frac{60}{-72} \), we can divide both the numerator and the denominator by their greatest common divisor (GCD), which is 12:
\[ x = \frac{60 \div 12}{-72 \div 12} = \frac{5}{-6} = -\frac{5}{6} \]

### Conclusion
Thus, the value of \( x \) is:
\[ x = -\frac{5}{6} \]