`(5)/(8)xx2(3)/(5) div (4)/(9)=?`

Options

A. `2(13)/(27)`
B. `1(11)/(27)`
C. `2(23)/(32)`
D. `3(21)/(32)`

Explanation

To solve the expression \(\frac{5}{8} \times 2 \frac{3}{5} \div \frac{4}{9}\), we will follow these steps:

### Step 1: Convert the mixed number to an improper fraction
The mixed number \(2 \frac{3}{5}\) can be converted to an improper fraction.

\[ 2 \frac{3}{5} = 2 \times 5 + 3 = 10 + 3 = \frac{13}{5} \]

### Step 2: Rewrite the expression
Now we can rewrite the original expression using the improper fraction:

\[ \frac{5}{8} \times \frac{13}{5} \div \frac{4}{9} \]

### Step 3: Change division to multiplication
To divide by a fraction, we multiply by its reciprocal:

\[ \frac{5}{8} \times \frac{13}{5} \times \frac{9}{4} \]

### Step 4: Simplify the expression
Now we can simplify the expression step by step. First, we can cancel out the \(5\) in the numerator and denominator:

\[ \frac{1}{8} \times \frac{13}{1} \times \frac{9}{4} \]

Now, we multiply the fractions:

\[ \frac{1 \times 13 \times 9}{8 \times 4} = \frac{117}{32} \]

### Step 5: Convert to a mixed number
To convert \(\frac{117}{32}\) to a mixed number, we divide \(117\) by \(32\):

\[ 117 \div 32 = 3 \quad \text{(whole number)} \]
\[ 117 - (32 \times 3) = 117 - 96 = 21 \quad \text{(remainder)} \]

So, we can express \(\frac{117}{32}\) as:

\[ 3 \frac{21}{32} \]

### Final Answer:
The final answer is \(3 \frac{21}{32}\).

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