What is the value of `(0.55 xx 4.5)/(0.81)` ?

Options

A. `3.555`
B. `(55)/(18)`
C. `3.05`
D. `(55)/(81)`

Answer

To solve the expression \((0.55 \times 4.5) / 0.81\), we will follow these steps:

### Step 1: Rewrite the expression
We start with the expression:
\[ x = \frac{0.55 \times 4.5}{0.81} \]

### Step 2: Convert decimals to fractions
To simplify the calculation, we can convert the decimals into fractions:
\[ 0.55 = \frac{55}{100}, \quad 4.5 = \frac{45}{10}, \quad 0.81 = \frac{81}{100} \]
Now substituting these values into the expression gives:
\[ x = \frac{\left(\frac{55}{100} \times \frac{45}{10}\right)}{\frac{81}{100}} \]

### Step 3: Simplify the expression
We can simplify the expression by multiplying by the reciprocal of the denominator:
\[ x = \frac{55 \times 45}{100 \times 10} \times \frac{100}{81} \]
The \(100\) in the numerator and denominator cancels out:
\[ x = \frac{55 \times 45}{10 \times 81} \]

### Step 4: Further simplification
Now, we can simplify \(10\) in the denominator:
\[ x = \frac{55 \times 45}{810} \]

### Step 5: Factor and reduce
Next, we can factor \(45\) and \(810\):
\[ 45 = 3 \times 15, \quad 810 = 3 \times 270 \]
Thus, we can cancel \(3\):
\[ x = \frac{55 \times 15}{270} \]

### Step 6: Simplify further
Now we can simplify \(15\) and \(270\):
\[ 15 = 3 \times 5, \quad 270 = 3 \times 90 \]
Canceling \(3\) gives:
\[ x = \frac{55 \times 5}{90} \]

### Step 7: Calculate the final value
Now we can calculate:
\[ x = \frac{275}{90} \]
To simplify further, we can divide both the numerator and denominator by \(5\):
\[ x = \frac{55}{18} \]

### Final Result
Thus, the value of \((0.55 \times 4.5) / 0.81\) is:
\[ \frac{55}{18} \]