To solve the expression \((0.56 + 0.64) \cdot 5 + 31.64\), let's follow the order of operations (PEMDAS/BODMAS):

1. **Addition inside the parentheses**:  
   \( 0.56 + 0.64 = 1.20 \)

2. **Multiplication**:  
   \( 1.20 \cdot 5 = 6.00 \)

3. **Addition**:  
   \( 6.00 + 31.64 = 37.64 \)

Thus, the final result is:

\[
\boxed{37.64}
\]

Would you like more details, or do you have any questions?

Here are some related questions to consider:

1. How would the result change if the multiplication was done before the addition inside the parentheses?
2. What happens if we replace the multiplication by division in the original expression?
3. How would the outcome be affected if we changed the numbers inside the parentheses?
4. Can you find another expression with a similar structure that results in 40?
5. What is the significance of using parentheses in mathematical expressions?

**Tip:** Remember, parentheses in math ensure that certain operations are performed first, following the order of operations.

Learn how to solve the mathematical expression (0.56 + 0.64) * 5 + 31.64 with a detailed step-by-step solution. This problem covers arithmetic operations, including addition and multiplication, following the order of operations (PEMDAS/BODMAS). Suitable for students in Grades 5-7.

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