Simplify: `14/25xx35/51xx34/49`

Answer

To simplify the expression \( \frac{14}{25} \times \frac{35}{51} \times \frac{34}{49} \), we can follow these steps:

### Step 1: Write the expression
We start with the expression:
\[ \frac{14}{25} \times \frac{35}{51} \times \frac{34}{49} \]

### Step 2: Factor the numerators and denominators
Next, we can factor the numbers:
- \( 14 = 2 \times 7 \)
- \( 25 = 5 \times 5 \)
- \( 35 = 5 \times 7 \)
- \( 51 = 3 \times 17 \)
- \( 34 = 2 \times 17 \)
- \( 49 = 7 \times 7 \)

So, we rewrite the expression using these factors:
\[ \frac{2 \times 7}{5 \times 5} \times \frac{5 \times 7}{3 \times 17} \times \frac{2 \times 17}{7 \times 7} \]

### Step 3: Combine the fractions
Now we can combine the fractions:
\[ \frac{(2 \times 7) \times (5 \times 7) \times (2 \times 17)}{(5 \times 5) \times (3 \times 17) \times (7 \times 7)} \]

### Step 4: Simplify the expression
Now we can cancel out common factors from the numerator and denominator:
- The \( 5 \) in the numerator and one of the \( 5 \) in the denominator cancel out.
- The \( 7 \) in the numerator and one of the \( 7 \) in the denominator cancel out.
- The \( 17 \) in the numerator and the \( 17 \) in the denominator cancel out.
- The \( 2 \) remains in the numerator, and we have \( 7 \) remaining in the denominator.

After canceling, we have:
\[ \frac{2 \times 7}{5 \times 3 \times 7} = \frac{2}{15} \]

### Step 5: Final answer
Thus, the simplified form of the expression \( \frac{14}{25} \times \frac{35}{51} \times \frac{34}{49} \) is:
\[ \frac{2}{15} \]

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