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: Write down the expression
We start with the expression:
\[ \frac{-4}{5} \times \frac{3}{7} \times \frac{15}{16} \times \frac{-14}{9} \]

### Step 2: Multiply the fractions
When multiplying fractions, we can multiply the numerators together and the denominators together:
\[ \frac{-4 \times 3 \times 15 \times -14}{5 \times 7 \times 16 \times 9} \]

### Step 3: Simplify the expression
Now, we will simplify the expression by canceling common factors in the numerator and denominator.

1. **Cancel \(15\) and \(5\)**:
\[ 15 \div 5 = 3 \quad \text{(Now we have: } \frac{-4 \times 3 \times 3 \times -14}{1 \times 7 \times 16 \times 9}\text{)} \]

2. **Cancel \(3\) and \(9\)**:
\[ 9 \div 3 = 3 \quad \text{(Now we have: } \frac{-4 \times 1 \times 3 \times -14}{1 \times 7 \times 16 \times 3}\text{)} \]

3. **Cancel \(14\) and \(7\)**:
\[ 14 \div 7 = 2 \quad \text{(Now we have: } \frac{-4 \times 1 \times 3 \times 2}{1 \times 16 \times 3}\text{)} \]

4. **Cancel \(4\) and \(16\)**:
\[ 16 \div 4 = 4 \quad \text{(Now we have: } \frac{-1 \times 1 \times 3 \times 2}{1 \times 4 \times 3}\text{)} \]

5. **Cancel \(3\) in the numerator and denominator**:
\[ 3 \div 3 = 1 \quad \text{(Now we have: } \frac{-1 \times 1 \times 2}{1 \times 4 \times 1}\text{)} \]

### Step 4: Final multiplication
Now we multiply the remaining numbers:
\[ \frac{-1 \times 2}{4} = \frac{-2}{4} \]

### Step 5: Simplify \(-2/4\)
\[ \frac{-2}{4} = \frac{-1}{2} \]

### Step 6: Convert to positive
Since we have two negative signs, we can convert it to positive:
\[ \frac{-1}{2} = \frac{1}{2} \]

### Final Answer
The final answer is:
\[ \frac{1}{2} \]

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