To solve the expression \(1 + 2 \left(\frac{3}{4}\right)\), we'll follow the order of operations (PEMDAS/BODMAS), which stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

1. Start with the division inside the parentheses:
   \[
   \frac{3}{4} = 0.75
   \]

2. Next, multiply by 2:
   \[
   2 \times 0.75 = 1.5
   \]

3. Finally, add 1 to the result:
   \[
   1 + 1.5 = 2.5
   \]

### Final Answer:
\[
1 + 2 \left(\frac{3}{4}\right) = 2.5
\]

Would you like more details or have any questions? 

Here are 5 related questions to explore further:
1. How do you apply the order of operations in more complex expressions?
2. What happens if parentheses are nested within other parentheses?
3. How does division of fractions work in general?
4. Can you explain the distributive property of multiplication over addition?
5. How do you handle expressions with exponents and roots?

**Tip:** Always work inside parentheses first when following the order of operations!

This step-by-step guide explains how to solve the arithmetic expression 1 + 2(3 ÷ 4) using the order of operations (PEMDAS/BODMAS). It covers key concepts like parentheses, multiplication, and division, making it suitable for students in Grades 6-8.

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