Evaluate: d. `3 (5)/(8) xx (24)/( 49)`

Answer

To evaluate the expression \( 3 \frac{5}{8} \times \frac{24}{49} \), we will follow these steps:

### Step 1: Convert the mixed fraction to an improper fraction
The mixed fraction \( 3 \frac{5}{8} \) can be converted to an improper fraction.

To do this:
- Multiply the whole number (3) by the denominator (8):
\[ 3 \times 8 = 24 \]
- Add the numerator (5) to this result:
\[ 24 + 5 = 29 \]
- Therefore, \( 3 \frac{5}{8} \) can be written as:
\[ \frac{29}{8} \]

### Step 2: Write the expression with improper fractions
Now, we can rewrite the original expression using the improper fraction:
\[ \frac{29}{8} \times \frac{24}{49} \]

### Step 3: Multiply the fractions
To multiply two fractions, we multiply the numerators together and the denominators together:
\[ \frac{29 \times 24}{8 \times 49} \]

### Step 4: Calculate the numerator and the denominator
First, calculate the numerator:
\[ 29 \times 24 = 696 \]
Next, calculate the denominator:
\[ 8 \times 49 = 392 \]

So, we have:
\[ \frac{696}{392} \]

### Step 5: Simplify the fraction
To simplify \( \frac{696}{392} \), we need to find the greatest common divisor (GCD) of 696 and 392.

Calculating the GCD:
- The GCD of 696 and 392 is 8.

Now, divide both the numerator and the denominator by their GCD:
\[ \frac{696 \div 8}{392 \div 8} = \frac{87}{49} \]

### Final Answer
Thus, the evaluated result is:
\[ \frac{87}{49} \]

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