Find: d. `4 (4)/(7) xx 5 (3)/(5)`

Options

A. `25 (3)/(8)`
B. `25 (3)/(7)`
C. `25 (2)/(5)`
D. `25 (3)/(5)`

Answer

To solve the problem \( 4 \frac{4}{7} \times 5 \frac{3}{5} \), we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
First, we need to convert the mixed numbers \( 4 \frac{4}{7} \) and \( 5 \frac{3}{5} \) into improper fractions.

For \( 4 \frac{4}{7} \):
- Multiply the whole number (4) by the denominator (7):
\( 4 \times 7 = 28 \)
- Add the numerator (4) to this product:
\( 28 + 4 = 32 \)
- So, \( 4 \frac{4}{7} = \frac{32}{7} \).

For \( 5 \frac{3}{5} \):
- Multiply the whole number (5) by the denominator (5):
\( 5 \times 5 = 25 \)
- Add the numerator (3) to this product:
\( 25 + 3 = 28 \)
- So, \( 5 \frac{3}{5} = \frac{28}{5} \).

### Step 2: Multiply the Improper Fractions
Now we will multiply the two improper fractions:
\[ \frac{32}{7} \times \frac{28}{5} \]

### Step 3: Multiply the Numerators and Denominators
Multiply the numerators together and the denominators together:
\[ \frac{32 \times 28}{7 \times 5} \]

Calculating the numerator:
\[ 32 \times 28 = 896 \]
Calculating the denominator:
\[ 7 \times 5 = 35 \]
So, we have:
\[ \frac{896}{35} \]

### Step 4: Simplify the Fraction
Now we will simplify \( \frac{896}{35} \). We can divide both the numerator and the denominator by their greatest common divisor (GCD).

Calculating:
- \( 896 \div 35 \) gives us \( 25 \) remainder \( 21 \), so we can express it as:
\[ 25 \frac{21}{35} \]
- Now, simplify \( \frac{21}{35} \) by dividing both by 7:
\[ \frac{21 \div 7}{35 \div 7} = \frac{3}{5} \]

Thus, the final answer is:
\[ 25 \frac{3}{5} \]

### Final Answer:
The product of \( 4 \frac{4}{7} \times 5 \frac{3}{5} \) is \( 25 \frac{3}{5} \).

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