Evaluate: c. `(14)/(25 ) xx (20)/( 49)`

Answer

To evaluate the expression \( \frac{14}{25} \times \frac{20}{49} \), we can follow these steps:

### Step 1: Write the expression
We start with the expression:
\[ \frac{14}{25} \times \frac{20}{49} \]

### Step 2: Factor the numerators and denominators
Next, we can factor the numbers where possible:
- \( 14 = 2 \times 7 \)
- \( 20 = 4 \times 5 \)
- \( 25 = 5 \times 5 \)
- \( 49 = 7 \times 7 \)

So, we can rewrite the expression as:
\[ \frac{2 \times 7}{5 \times 5} \times \frac{4 \times 5}{7 \times 7} \]

### Step 3: Combine the fractions
Now, we can combine the fractions:
\[ \frac{2 \times 7 \times 4 \times 5}{5 \times 5 \times 7 \times 7} \]

### Step 4: Cancel out common factors
We can cancel the common factors in the numerator and the denominator:
- The \( 7 \) in the numerator cancels with one \( 7 \) in the denominator.
- The \( 5 \) in the numerator cancels with one \( 5 \) in the denominator.

After canceling, we have:
\[ \frac{2 \times 4}{5 \times 7} \]

### Step 5: Calculate the remaining multiplication
Now, we multiply the remaining numbers:
- The numerator: \( 2 \times 4 = 8 \)
- The denominator: \( 5 \times 7 = 35 \)

So, we have:
\[ \frac{8}{35} \]

### Final Answer
Thus, the evaluated expression is:
\[ \frac{8}{35} \]

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