Simplify : 5 - 6.5 `div` 13 + 2.3 `xx` 0.8 + 0.4

Options

A. 6.83
B. 6.74
C. 7.38
D. 5.38

Answer

To simplify the expression \( 5 - 6.5 \div 13 + 2.3 \times 0.8 + 0.4 \), we will follow the order of operations, often remembered by the acronym PEMDAS/BODMAS (Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

### Step-by-Step Solution:

1. **Identify the operations**: The expression contains subtraction, division, multiplication, and addition.
\[ 5 - 6.5 \div 13 + 2.3 \times 0.8 + 0.4 \]

2. **Perform the division first**:
\[ 6.5 \div 13 = 0.5 \]
Now substitute this back into the expression:
\[ 5 - 0.5 + 2.3 \times 0.8 + 0.4 \]

3. **Next, perform the multiplication**:
\[ 2.3 \times 0.8 = 1.84 \]
Now substitute this back into the expression:
\[ 5 - 0.5 + 1.84 + 0.4 \]

4. **Now, perform the addition and subtraction from left to right**:
- First, calculate \( 5 - 0.5 \):
\[ 5 - 0.5 = 4.5 \]
- Now add \( 1.84 \):
\[ 4.5 + 1.84 = 6.34 \]
- Finally, add \( 0.4 \):
\[ 6.34 + 0.4 = 6.74 \]

5. **Final answer**:
\[ 6.74 \]

### Summary of the Steps:
- **Step 1**: Identify operations.
- **Step 2**: Perform division.
- **Step 3**: Perform multiplication.
- **Step 4**: Perform addition and subtraction from left to right.
- **Step 5**: State the final answer.