`(2.5 xx 3 + 7.5 div 2.5 - "0.5 of 3")/(47 + 12 div 1.5 - "6 of 2" xx 3) = ?`

Options

A. `(3)/(17)`
B. `(9)/(19)`
C. `(4)/(11)`
D. `(3)/(11)`

Answer

To simplify the expression `(2.5 x 3 + 7.5 ÷ 2.5 - "0.5 of 3")/(47 + 12 ÷ 1.5 - "6 of 2" x 3)`, we will follow the order of operations (BODMAS/BIDMAS):

1. **Calculate the numerator:**
- First, calculate `2.5 x 3`:
\[ 2.5 \times 3 = 7.5 \]
- Next, calculate `7.5 ÷ 2.5`:
\[ 7.5 \div 2.5 = 3 \]
- Then, calculate `"0.5 of 3"` which is `0.5 x 3`:
\[ 0.5 \times 3 = 1.5 \]
- Now, substitute these values into the numerator:
\[ 7.5 + 3 - 1.5 \]
- Perform the addition and subtraction:
\[ 7.5 + 3 = 10.5 \]
\[ 10.5 - 1.5 = 9 \]

2. **Calculate the denominator:**
- First, calculate `12 ÷ 1.5`:
\[ 12 \div 1.5 = 8 \]
- Next, calculate `"6 of 2"` which is `6 x 2`:
\[ 6 \times 2 = 12 \]
- Then, substitute these values into the denominator:
\[ 47 + 8 - (12 \times 3) \]
- Calculate `12 x 3`:
\[ 12 \times 3 = 36 \]
- Now, substitute this value into the denominator:
\[ 47 + 8 - 36 \]
- Perform the addition and subtraction:
\[ 47 + 8 = 55 \]
\[ 55 - 36 = 19 \]

3. **Final step: Divide the numerator by the denominator:**
\[ \frac{9}{19} \]

Thus, the final answer is:
\[ \frac{9}{19} \]