Find `(-4)/(5) xx 3/7 xx (15)/(16) xx ((-14)/9)`

Options

A. `2/6`
B. `2/8`
C. `2/10`
D. `1/2`

Explanation

To solve the expression \((-4/5) \times (3/7) \times (15/16) \times (-14/9)\), we will follow these steps:

### Step 1: Rearranging the Expression
Using the commutative property of multiplication, we can rearrange the terms for easier calculation. We can group the fractions as follows:
\[ (-4/5) \times (15/16) \times (3/7) \times (-14/9) \]

### Step 2: Multiply the Numerators and Denominators
Now, we will multiply the numerators together and the denominators together:
\[ \text{Numerator: } (-4) \times 15 \times 3 \times (-14) \]
\[ \text{Denominator: } 5 \times 16 \times 7 \times 9 \]

### Step 3: Calculate the Numerator
Calculating the numerator:
\[ (-4) \times 15 = -60 \]
\[ -60 \times 3 = -180 \]
\[ -180 \times (-14) = 2520 \]
So, the numerator is \(2520\).

### Step 4: Calculate the Denominator
Calculating the denominator:
\[ 5 \times 16 = 80 \]
\[ 80 \times 7 = 560 \]
\[ 560 \times 9 = 5040 \]
So, the denominator is \(5040\).

### Step 5: Form the Fraction
Now we can form the fraction:
\[ \frac{2520}{5040} \]

### Step 6: Simplify the Fraction
To simplify \(\frac{2520}{5040}\), we can divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 2520 and 5040 is 2520:
\[ \frac{2520 \div 2520}{5040 \div 2520} = \frac{1}{2} \]

### Final Answer
Thus, the final answer is:
\[ \frac{1}{2} \]

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