What is the value of `[100 div 50 - 25 - 55 "of" ((1)/(3) xx (11)/(9))]` ?

Options

A. `-(1156)/(27)`
B. `-(1382)/(27)`
C. `-(1321)/(27)`
D. `-(1226)/(27)`

Answer

To solve the expression `[100 div 50 - 25 - 55 "of" ((1)/(3) xx (11)/(9))]`, we will follow the order of operations known as BODMAS/BIDMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction).

### Step-by-Step Solution:

1. **Identify the Expression**:
The expression is:
\[ 100 \div 50 - 25 - 55 \text{ of } \left(\frac{1}{3} \times \frac{11}{9}\right) \]

2. **Calculate the Division**:
First, we perform the division:
\[ 100 \div 50 = 2 \]
So, the expression now becomes:
\[ 2 - 25 - 55 \text{ of } \left(\frac{1}{3} \times \frac{11}{9}\right) \]

3. **Calculate the Multiplication Inside the Bracket**:
Next, we calculate the multiplication:
\[ \frac{1}{3} \times \frac{11}{9} = \frac{11}{27} \]
Now the expression is:
\[ 2 - 25 - 55 \text{ of } \frac{11}{27} \]

4. **Interpret "of" as Multiplication**:
The term "55 of" means multiplication:
\[ 55 \times \frac{11}{27} = \frac{605}{27} \]
Now the expression is:
\[ 2 - 25 - \frac{605}{27} \]

5. **Convert Whole Numbers to Fractions**:
To perform the subtraction, we convert the whole numbers to fractions with a common denominator (27):
\[ 2 = \frac{54}{27}, \quad 25 = \frac{675}{27} \]
Now the expression is:
\[ \frac{54}{27} - \frac{675}{27} - \frac{605}{27} \]

6. **Combine the Fractions**:
Now we can combine the fractions:
\[ \frac{54 - 675 - 605}{27} = \frac{54 - 1280}{27} = \frac{-1226}{27} \]

7. **Final Result**:
The final value of the expression is:
\[ -\frac{1226}{27} \]