Simplify: 8 + 3 -` ( 5/2xx1/3)` of `12/5+4/3xx3/8`

Options

A. 9.5
B. 10
C. 9
D. 19

Answer

To simplify the expression \( 8 + 3 - \left( \frac{5}{2} \times \frac{1}{3} \right) \text{ of } \left( \frac{12}{5} + \frac{4}{3} \times \frac{3}{8} \right) \), we will follow the order of operations (BODMAS/BIDMAS).

### Step-by-Step Solution:

1. **Calculate the value of \( 8 + 3 \)**:
\[ 8 + 3 = 11 \]

**Hint**: Always start by simplifying the addition or subtraction outside the brackets.

2. **Calculate \( \frac{4}{3} \times \frac{3}{8} \)**:
\[ \frac{4}{3} \times \frac{3}{8} = \frac{4 \times 3}{3 \times 8} = \frac{12}{24} = \frac{1}{2} \]

**Hint**: When multiplying fractions, multiply the numerators together and the denominators together.

3. **Now substitute back into the expression**:
\[ 11 - \left( \frac{5}{2} \times \frac{1}{3} \right) \text{ of } \left( \frac{12}{5} + \frac{1}{2} \right) \]

4. **Calculate \( \frac{12}{5} + \frac{1}{2} \)**:
- Find a common denominator (which is 10):
\[ \frac{12}{5} = \frac{24}{10}, \quad \frac{1}{2} = \frac{5}{10} \]
\[ \frac{24}{10} + \frac{5}{10} = \frac{29}{10} \]

**Hint**: To add fractions, convert them to have a common denominator.

5. **Calculate \( \frac{5}{2} \times \frac{1}{3} \)**:
\[ \frac{5}{2} \times \frac{1}{3} = \frac{5 \times 1}{2 \times 3} = \frac{5}{6} \]

**Hint**: Again, multiply the numerators and denominators for fractions.

6. **Now calculate \( \frac{5}{6} \text{ of } \frac{29}{10} \)**:
\[ \frac{5}{6} \times \frac{29}{10} = \frac{5 \times 29}{6 \times 10} = \frac{145}{60} \]
- Simplifying \( \frac{145}{60} \):
\[ \frac{145 \div 5}{60 \div 5} = \frac{29}{12} \]

**Hint**: When calculating "of", you multiply the two fractions.

7. **Substitute back into the expression**:
\[ 11 - \frac{29}{12} \]

8. **Convert 11 to a fraction with a denominator of 12**:
\[ 11 = \frac{132}{12} \]

9. **Now perform the subtraction**:
\[ \frac{132}{12} - \frac{29}{12} = \frac{132 - 29}{12} = \frac{103}{12} \]

**Hint**: When subtracting fractions, ensure they have the same denominator.

10. **Final Result**:
\[ \frac{103}{12} \]

### Final Answer:
The simplified expression is \( \frac{103}{12} \).