Find the value of the expression
`(3)/(5) xx (3)/(14) xx (15)/(2) xx (-7)/(9).`

Options

A. `(-7)/(8)`
B. `(-5)/(6)`
C. `(-3)/(4)`
D. `(-3)/(5)`

Answer

To find the value of the expression \(\frac{3}{5} \times \frac{3}{14} \times \frac{15}{2} \times \frac{-7}{9}\), we will simplify it step by step.

### Step 1: Write the expression clearly
We have:
\[ \frac{3}{5} \times \frac{3}{14} \times \frac{15}{2} \times \frac{-7}{9} \]

### Step 2: Multiply the numerators and denominators
The product of the numerators is:
\[ 3 \times 3 \times 15 \times (-7) \]
The product of the denominators is:
\[ 5 \times 14 \times 2 \times 9 \]

### Step 3: Calculate the numerator
Calculating the numerator:
\[ 3 \times 3 = 9 \]
\[ 9 \times 15 = 135 \]
\[ 135 \times (-7) = -945 \]
So, the numerator is \(-945\).

### Step 4: Calculate the denominator
Calculating the denominator:
\[ 5 \times 14 = 70 \]
\[ 70 \times 2 = 140 \]
\[ 140 \times 9 = 1260 \]
So, the denominator is \(1260\).

### Step 5: Write the fraction
Now we can write the fraction:
\[ \frac{-945}{1260} \]

### Step 6: Simplify the fraction
To simplify \(\frac{-945}{1260}\), we need to find the greatest common divisor (GCD) of 945 and 1260.

The GCD of 945 and 1260 is 315. Now we divide both the numerator and the denominator by 315:
\[ \frac{-945 \div 315}{1260 \div 315} = \frac{-3}{4} \]

### Final Answer
Thus, the value of the expression is:
\[ \frac{-3}{4} \]

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