4/7 of 2/3 of 5/6 of 5/8 of 1008 is

Options

A. a. 200
B. b. 144
C. c. 64
D. d. 400

Answer

To solve the problem \( \frac{4}{7} \) of \( \frac{2}{3} \) of \( \frac{5}{6} \) of \( \frac{5}{8} \) of \( 1008 \), we can follow these steps:

### Step 1: Convert "of" to multiplication
We can rewrite the expression by replacing "of" with multiplication:
\[ \frac{4}{7} \times \frac{2}{3} \times \frac{5}{6} \times \frac{5}{8} \times 1008 \]

### Step 2: Multiply the fractions
Now, we can multiply the fractions together:
\[ \frac{4 \times 2 \times 5 \times 5}{7 \times 3 \times 6 \times 8} \times 1008 \]

### Step 3: Calculate the numerator
Calculating the numerator:
\[ 4 \times 2 = 8 \]
\[ 8 \times 5 = 40 \]
\[ 40 \times 5 = 200 \]
So, the numerator is \( 200 \).

### Step 4: Calculate the denominator
Calculating the denominator:
\[ 7 \times 3 = 21 \]
\[ 21 \times 6 = 126 \]
\[ 126 \times 8 = 1008 \]
So, the denominator is \( 1008 \).

### Step 5: Simplify the fraction
Now we can simplify the fraction:
\[ \frac{200}{1008} \times 1008 \]
When we multiply \( \frac{200}{1008} \) by \( 1008 \), the \( 1008 \) cancels out:
\[ 200 \]

### Final Answer
Thus, the final answer is:
\[ \boxed{200} \]