Simplify the following expression `[8 xx 5 -3 " of "(2(3)/(5) div 1(2)/(5) xx 5 -3) ] xx (7)/(2)`.

Options

A. 552
B. 814
C. 208
D. 352

Answer

To simplify the expression `[8 * 5 - 3 * (2(3)/(5) ÷ 1(2)/(5) * 5 - 3)] * (7)/(2)`, we will follow the order of operations (BODMAS/BIDMAS).

### Step-by-Step Solution:

1. **Identify the Expression**:
The expression is:
\[ 8 \times 5 - 3 \times \left( \frac{2 \times 3}{5} \div \frac{1 \times 2}{5} \times 5 - 3 \right) \times \frac{7}{2} \]

2. **Calculate the Inner Bracket**:
We first simplify the expression inside the brackets:
\[ \frac{2 \times 3}{5} \div \frac{1 \times 2}{5} \]
To divide fractions, we multiply by the reciprocal:
\[ = \frac{2 \times 3}{5} \times \frac{5}{1 \times 2} = \frac{6}{5} \times \frac{5}{2} = \frac{6 \times 5}{5 \times 2} = \frac{6}{2} = 3 \]

3. **Substitute Back into the Expression**:
Now substitute back into the expression:
\[ 8 \times 5 - 3 \times (3 \times 5 - 3) \]

4. **Simplify the Inner Expression**:
Calculate \(3 \times 5 - 3\):
\[ = 15 - 3 = 12 \]

5. **Substitute Again**:
Substitute back again:
\[ 8 \times 5 - 3 \times 12 \]

6. **Calculate Each Part**:
Calculate \(8 \times 5\) and \(3 \times 12\):
\[ 8 \times 5 = 40 \]
\[ 3 \times 12 = 36 \]

7. **Combine the Results**:
Now combine the results:
\[ 40 - 36 = 4 \]

8. **Final Multiplication**:
Now multiply by \(\frac{7}{2}\):
\[ 4 \times \frac{7}{2} = \frac{28}{2} = 14 \]

### Final Answer:
The simplified value of the expression is \(14\).

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