Simplify:- 3/7 of 4/5 of 5/8 of 490 = ?

Options

A. a. 115
B. b. 105
C. c. 108
D. d. 116

Answer

To simplify the expression \( \frac{3}{7} \) of \( \frac{4}{5} \) of \( \frac{5}{8} \) of \( 490 \), we can follow these steps:

### Step 1: Write the expression in multiplication form
We can express the problem as:
\[ \frac{3}{7} \times \frac{4}{5} \times \frac{5}{8} \times 490 \]

### Step 2: Simplify the fractions step by step
First, we can simplify \( \frac{5}{8} \times 490 \):
\[ 490 = 5 \times 98 \quad \text{(since \( 490 \div 5 = 98 \))} \]
So,
\[ \frac{5}{8} \times 490 = \frac{5 \times 490}{8} = \frac{5 \times 5 \times 98}{8} = \frac{2450}{8} \]

### Step 3: Simplify \( \frac{2450}{8} \)
Now, we can simplify \( \frac{2450}{8} \):
\[ \frac{2450}{8} = 306.25 \quad \text{(but we will keep it as a fraction for now)} \]

### Step 4: Combine the remaining fractions
Now we will multiply the remaining fractions:
\[ \frac{3}{7} \times \frac{4}{5} \times \frac{2450}{8} \]

### Step 5: Cancel out common factors
We can simplify this step by step:
1. \( \frac{4}{8} = \frac{1}{2} \)
2. \( \frac{2450}{7} = 350 \) (since \( 2450 \div 7 = 350 \))

Now we have:
\[ \frac{3}{5} \times 350 \times \frac{1}{2} \]

### Step 6: Calculate the final multiplication
Now we can multiply:
\[ 350 \div 5 = 70 \]
So,
\[ \frac{3}{2} \times 70 = 3 \times 35 = 105 \]

### Final Answer
Thus, the simplified value is:
\[ \boxed{105} \]