`(3)/(5) "of" (4)/(7) "of" (5)/(9) "of" (21)/(24) "of" 504=?`

Options

A. 63
B. 39
C. 96
D. 84

Explanation

To solve the expression \((3/5) \text{ of } (4/7) \text{ of } (5/9) \text{ of } (21/24) \text{ of } 504\), we can follow these steps:

### Step 1: Rewrite the expression
We start by rewriting the expression using multiplication:
\[ x = \frac{3}{5} \times \frac{4}{7} \times \frac{5}{9} \times \frac{21}{24} \times 504 \]

### Step 2: Multiply the fractions
We can multiply the fractions together first:
\[ x = \left(\frac{3 \times 4 \times 5 \times 21}{5 \times 7 \times 9 \times 24}\right) \times 504 \]

### Step 3: Simplify the fractions
Notice that the \(5\) in the numerator and denominator cancels out:
\[ x = \frac{3 \times 4 \times 21}{7 \times 9 \times 24} \times 504 \]

### Step 4: Calculate the numerator and denominator
Calculating the numerator:
\[ 3 \times 4 = 12 \]
\[ 12 \times 21 = 252 \]

Calculating the denominator:
\[ 7 \times 9 = 63 \]
\[ 63 \times 24 = 1512 \]

So now we have:
\[ x = \frac{252}{1512} \times 504 \]

### Step 5: Simplify \(\frac{252}{1512}\)
We can simplify \(\frac{252}{1512}\):
\[ \frac{252 \div 252}{1512 \div 252} = \frac{1}{6} \]

### Step 6: Multiply by 504
Now we multiply by \(504\):
\[ x = \frac{1}{6} \times 504 \]

### Step 7: Calculate the final answer
Calculating the final multiplication:
\[ x = \frac{504}{6} = 84 \]

Thus, the final answer is:
\[ \boxed{84} \]