Find: c. `3 (4)/(5) xx (35)/( 38)`

Options

A. `3 (3)/(2)`
B. `3 (1)/(2)`
C. `3 (1)/(5)`
D. `3 (1)/(4)`

Answer

To solve the problem \( 3 \frac{4}{5} \times \frac{35}{38} \), we will follow these steps:

### Step 1: Convert the mixed fraction to an improper fraction
To convert the mixed fraction \( 3 \frac{4}{5} \) into an improper fraction, we use the formula:
\[ \text{Improper Fraction} = \left(\text{Whole Number} \times \text{Denominator} + \text{Numerator}\right) / \text{Denominator} \]
Here, the whole number is 3, the numerator is 4, and the denominator is 5.

Calculating:
\[ 3 \times 5 + 4 = 15 + 4 = 19 \]
So, \( 3 \frac{4}{5} = \frac{19}{5} \).

### Step 2: Write the multiplication expression
Now we can rewrite the multiplication expression:
\[ \frac{19}{5} \times \frac{35}{38} \]

### Step 3: Multiply the fractions
To multiply the fractions, we multiply the numerators together and the denominators together:
\[ \frac{19 \times 35}{5 \times 38} \]

Calculating the numerator:
\[ 19 \times 35 = 665 \]
Calculating the denominator:
\[ 5 \times 38 = 190 \]
So, we have:
\[ \frac{665}{190} \]

### Step 4: Simplify the fraction
Now, we need to simplify \( \frac{665}{190} \). We can find the greatest common divisor (GCD) of 665 and 190.

First, we can factor both numbers:
- \( 665 = 5 \times 133 \)
- \( 190 = 5 \times 38 \)

We can see that both the numerator and denominator have a common factor of 5. So we divide both by 5:
\[ \frac{665 \div 5}{190 \div 5} = \frac{133}{38} \]

### Step 5: Convert back to a mixed number (if needed)
To convert \( \frac{133}{38} \) back to a mixed number, we divide 133 by 38:
- \( 133 \div 38 = 3 \) (whole number part)
- Remainder: \( 133 - (3 \times 38) = 133 - 114 = 19 \)

Thus, we can express \( \frac{133}{38} \) as:
\[ 3 \frac{19}{38} \]

### Final Answer
The final answer is:
\[ 3 \frac{19}{38} \]

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