`4.59xx 1.8-: 3.6 +5.4 of `(1)/(9) - (1)/(5)` = ?

Options

A. `2.695`
B. 2.705`
C. `3.105`
D. `3.009`

Answer

To solve the expression \( 4.59 \times 1.8 \div 3.6 + 5.4 \left( \frac{1}{9} - \frac{1}{5} \right) \), we will follow the order of operations, often referred to as BODMAS/BIDMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction).

### Step 1: Solve the bracket
First, we need to calculate the expression inside the brackets:
\[ \frac{1}{9} - \frac{1}{5} \]
To subtract these fractions, we need a common denominator. The least common multiple of 9 and 5 is 45.
\[ \frac{1}{9} = \frac{5}{45}, \quad \frac{1}{5} = \frac{9}{45} \]
Now, we can perform the subtraction:
\[ \frac{5}{45} - \frac{9}{45} = \frac{5 - 9}{45} = \frac{-4}{45} \]

### Step 2: Multiply by 5.4
Now we multiply this result by 5.4:
\[ 5.4 \times \left( \frac{-4}{45} \right) = \frac{5.4 \times -4}{45} = \frac{-21.6}{45} \]
To simplify \(-21.6 / 45\):
\[ -21.6 \div 45 = -0.48 \]

### Step 3: Solve the multiplication and division
Next, we calculate \( 4.59 \times 1.8 \div 3.6 \):
First, calculate \( 4.59 \times 1.8 \):
\[ 4.59 \times 1.8 = 8.262 \]
Now, divide this result by 3.6:
\[ 8.262 \div 3.6 = 2.295 \]

### Step 4: Add the results
Now we add the two results together:
\[ 2.295 + (-0.48) = 2.295 - 0.48 = 1.815 \]

### Final Result
Thus, the value of the expression is:
\[ \boxed{1.815} \]