`108div36of 1/3+2/5xx(3)3/4=?`

Options

A. (8)3/4
B. (6)1/4
C. (2)1/2
D. (10)1/2

Answer

To solve the expression \( 108 \div 36 \text{ of } \frac{1}{3} + \frac{2}{5} \times 3 \frac{3}{4} \), we will follow the order of operations (BODMAS/BIDMAS) which stands for Brackets, Orders (i.e., powers and square roots, etc.), Division and Multiplication (from left to right), Addition and Subtraction (from left to right).

### Step-by-Step Solution:

1. **Convert "of" to multiplication**:
The term "of" in mathematics typically means multiplication. Thus, we can rewrite the expression:
\[ 108 \div 36 \times \frac{1}{3} + \frac{2}{5} \times 3 \frac{3}{4} \]

2. **Convert the mixed fraction to an improper fraction**:
The mixed fraction \( 3 \frac{3}{4} \) can be converted to an improper fraction:
\[ 3 \frac{3}{4} = \frac{3 \times 4 + 3}{4} = \frac{12 + 3}{4} = \frac{15}{4} \]
Now the expression becomes:
\[ 108 \div 36 \times \frac{1}{3} + \frac{2}{5} \times \frac{15}{4} \]

3. **Perform the division**:
First, we calculate \( 108 \div 36 \):
\[ 108 \div 36 = 3 \]
Now substitute back into the expression:
\[ 3 \times \frac{1}{3} + \frac{2}{5} \times \frac{15}{4} \]

4. **Multiply \( 3 \times \frac{1}{3} \)**:
\[ 3 \times \frac{1}{3} = 1 \]
Now the expression is:
\[ 1 + \frac{2}{5} \times \frac{15}{4} \]

5. **Multiply \( \frac{2}{5} \times \frac{15}{4} \)**:
\[ \frac{2 \times 15}{5 \times 4} = \frac{30}{20} = \frac{3}{2} \]
Now substitute back:
\[ 1 + \frac{3}{2} \]

6. **Convert 1 to a fraction**:
\[ 1 = \frac{2}{2} \]
Now the expression is:
\[ \frac{2}{2} + \frac{3}{2} = \frac{2 + 3}{2} = \frac{5}{2} \]

7. **Convert to a mixed number**:
\[ \frac{5}{2} = 2 \frac{1}{2} \]

### Final Answer:
The final answer is \( 2 \frac{1}{2} \).