`((-9)/(16)xx(8)/(15))=?`

Options

A. `(-3)/(10)`
B. `(-4)/(15)`
C. `(-9)/(25)`
D. `(-2)/(5)`

Answer

To solve the expression \((-9/16) \times (8/15)\), we can follow these steps:

### Step 1: Write the expression
We start with the expression:
\[ \frac{-9}{16} \times \frac{8}{15} \]

### Step 2: Multiply the numerators and denominators
We can multiply the numerators together and the denominators together:
\[ \frac{-9 \times 8}{16 \times 15} \]

### Step 3: Simplify before multiplying
Before we multiply, we can simplify the fractions. We notice that \(8\) and \(16\) have a common factor. We can divide both by \(8\):
\[ \frac{-9 \times 1}{2 \times 15} \]
Now, we have:
\[ \frac{-9}{2 \times 15} \]

### Step 4: Simplify the denominator
Next, we can multiply the denominator:
\[ 2 \times 15 = 30 \]
So now our expression looks like:
\[ \frac{-9}{30} \]

### Step 5: Simplify the fraction
Now we can simplify \(-9/30\). The greatest common divisor (GCD) of \(9\) and \(30\) is \(3\). We can divide both the numerator and the denominator by \(3\):
\[ \frac{-9 \div 3}{30 \div 3} = \frac{-3}{10} \]

### Final Answer
Thus, the simplified form of the expression is:
\[ \frac{-3}{10} \]

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