`(1)/(2) ` of `(3)/(5) ` of `(4)/(9) ` of `5820=?`

Options

A. 766
B. 777
C. 776
D. 767

Explanation

To solve the problem `(1)/(2) of (3)/(5) of (4)/(9) of 5820`, we can break it down step by step.

### Step 1: Write the expression in multiplication form
We need to find:
\[ \frac{1}{2} \times \frac{3}{5} \times \frac{4}{9} \times 5820 \]

### Step 2: Multiply the fractions
First, we can multiply the fractions together:
\[ \frac{1 \times 3 \times 4}{2 \times 5 \times 9} \]

Calculating the numerator:
\[ 1 \times 3 = 3 \]
\[ 3 \times 4 = 12 \]
So, the numerator is 12.

Calculating the denominator:
\[ 2 \times 5 = 10 \]
\[ 10 \times 9 = 90 \]
So, the denominator is 90.

Now we have:
\[ \frac{12}{90} \]

### Step 3: Simplify the fraction
We can simplify \(\frac{12}{90}\) by finding the greatest common divisor (GCD) of 12 and 90, which is 6.
\[ \frac{12 \div 6}{90 \div 6} = \frac{2}{15} \]

### Step 4: Multiply by 5820
Now we need to multiply this simplified fraction by 5820:
\[ \frac{2}{15} \times 5820 \]

### Step 5: Perform the multiplication
To multiply, we can first divide 5820 by 15:
\[ 5820 \div 15 = 388 \]

Now, multiply by 2:
\[ 388 \times 2 = 776 \]

### Final Answer
Thus, the final answer is:
\[ \boxed{776} \]