Visual representation of adding 45 and 32 using an open number line.

Problem:

The task is to solve the addition problem \( 45 + 32 \) using an open number line.

Solution:

#### Step 1: Understand the Open Number Line
An open number line is a visual tool used to represent numbers and perform arithmetic operations. It helps break down the addition process into smaller, manageable steps.

#### Step 2: Start at 45
We begin at the number 45 on the open number line.

#### Step 3: Add 32 in Parts
The number 32 can be broken down into parts for easier addition. Here, we break it into:
- \( +10 \)
- \( +10 \)
- \( +10 \)
- \( +2 \)

This breakdown makes it easier to add step by step.

#### Step 4: Perform the Addition Step by Step

1. Start at 45:
- Current position: 45

2. Add 10:
- Move 10 units to the right from 45.
- \( 45 + 10 = 55 \)
- New position: 55

3. Add another 10:
- Move 10 units to the right from 55.
- \( 55 + 10 = 65 \)
- New position: 65

4. Add another 10:
- Move 10 units to the right from 65.
- \( 65 + 10 = 75 \)
- New position: 75

5. Add the remaining 2:
- Move 2 units to the right from 75.
- \( 75 + 2 = 77 \)
- Final position: 77

#### Step 5: Write the Final Answer
After completing all the steps, we arrive at the final sum:
\[ 45 + 32 = 77 \]

Final Answer:

\[
\boxed{77}
\]

Explanation:

The open number line method breaks down the addition into smaller, more manageable steps. By adding 10 repeatedly and then the remaining 2, we can visualize the process and ensure accuracy. This method is particularly helpful for understanding place value and mental math strategies.