Find the value of `2 xx { ( 3.6 xx 0.48 xx 2.50)/( 0.12 xx 0.09 xx 0.5) }`

Options

A. 800
B. 500
C. 900
D. 1600

Answer

To solve the expression \( 2 \times \left( \frac{3.6 \times 0.48 \times 2.50}{0.12 \times 0.09 \times 0.5} \right) \), we will follow these steps:

### Step 1: Write the expression clearly
We start with the expression:
\[ 2 \times \frac{3.6 \times 0.48 \times 2.50}{0.12 \times 0.09 \times 0.5} \]

### Step 2: Convert decimals to fractions
To simplify the calculations, we can convert the decimals to fractions:
- \( 3.6 = \frac{36}{10} = \frac{18}{5} \)
- \( 0.48 = \frac{48}{100} = \frac{12}{25} \)
- \( 2.50 = \frac{250}{100} = \frac{25}{10} = \frac{5}{2} \)
- \( 0.12 = \frac{12}{100} = \frac{3}{25} \)
- \( 0.09 = \frac{9}{100} = \frac{9}{100} \)
- \( 0.5 = \frac{5}{10} = \frac{1}{2} \)

Now substituting these values into the expression gives:
\[ 2 \times \frac{\left(\frac{18}{5} \times \frac{12}{25} \times \frac{5}{2}\right)}{\left(\frac{3}{25} \times \frac{9}{100} \times \frac{1}{2}\right)} \]

### Step 3: Simplify the numerator and denominator
Calculating the numerator:
\[ \frac{18 \times 12 \times 5}{5 \times 2 \times 25} = \frac{18 \times 12}{2 \times 25} \]

Calculating the denominator:
\[ \frac{3 \times 9 \times 1}{25 \times 100 \times 2} = \frac{27}{5000} \]

### Step 4: Combine the fractions
Now we have:
\[ 2 \times \frac{\frac{18 \times 12}{2 \times 25}}{\frac{27}{5000}} = 2 \times \frac{18 \times 12 \times 5000}{2 \times 25 \times 27} \]

### Step 5: Cancel out common factors
The \(2\) in the numerator and denominator cancels out:
\[ = \frac{18 \times 12 \times 5000}{25 \times 27} \]

### Step 6: Calculate the values
Now we can calculate:
- \(18 \times 12 = 216\)
- \(25 \times 27 = 675\)

So we have:
\[ = \frac{216 \times 5000}{675} \]

### Step 7: Simplify the fraction
Now we can simplify:
\[ = \frac{1080000}{675} \]

### Step 8: Perform the division
Now we divide:
\[ = 1600 \]

### Final Step: Multiply by 2
Finally, we multiply by 2:
\[ = 2 \times 1600 = 3200 \]

Thus, the final value is:
\[ \boxed{3200} \]