`(14)/(19)xx(57)/(70)xx(20)/(21)=?`

Options

A. `(2)/(7)`
B. `4/7`
C. `2/9`
D. `3/7`

Explanation

To solve the expression \(\frac{14}{19} \times \frac{57}{70} \times \frac{20}{21}\), we can follow these steps:

### Step 1: Write the expression
We start with the expression:
\[ \frac{14}{19} \times \frac{57}{70} \times \frac{20}{21} \]

### Step 2: Multiply the numerators and the denominators
We can multiply the numerators together and the denominators together:
\[ \frac{14 \times 57 \times 20}{19 \times 70 \times 21} \]

### Step 3: Calculate the numerator
First, we calculate the numerator:
\[ 14 \times 57 = 798 \]
Now, multiply this result by 20:
\[ 798 \times 20 = 15960 \]
So, the numerator is \(15960\).

### Step 4: Calculate the denominator
Now, we calculate the denominator:
\[ 19 \times 70 = 1330 \]
Now, multiply this result by 21:
\[ 1330 \times 21 = 27930 \]
So, the denominator is \(27930\).

### Step 5: Write the fraction
Now we can write the fraction:
\[ \frac{15960}{27930} \]

### Step 6: Simplify the fraction
To simplify \(\frac{15960}{27930}\), we can find the greatest common divisor (GCD) of 15960 and 27930.

After performing the GCD calculation, we find that:
\[ \frac{15960 \div 3990}{27930 \div 3990} = \frac{4}{7} \]

### Final Answer
Thus, the simplified result of the expression is:
\[ \frac{4}{7} \]

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