To solve the given question about the binary tree representing an arithmetic expression, assuming an in-order traversal, let's break it down:

1. What is In-Order Traversal?

In an in-order traversal, you visit:

• Left subtree
• Root node
• Right subtree

2. In-Order Traversal of the Binary Tree

For the provided tree:

• Start from the leftmost subtree and move upwards and then to the right.
• The traversal results in: $3 + 1 \times 9 - 2 \times 5 - 3 \times 7 + 4 \times 6$

3. Expression Evaluation

According to the traversal: $3 + (1 \times 9) - (2 \times 5) - (3 \times 7) + (4 \times 6)$

Simplify step-by-step:

• $1 \times 9 = 9$
• $2 \times 5 = 10$
• $3 \times 7 = 21$
• $4 \times 6 = 24$

Substitute these back into the expression: $3 + 9 - 10 - 21 + 24$

Now calculate:

• $3 + 9 = 12$
• $12 - 10 = 2$
• $2 - 21 = -19$
• $-19 + 24 = 5$

Final Answer:

The result of the arithmetic expression, assuming in-order traversal, is: $\boxed{5}$

Would you like further explanation on any part of this process?

Related Questions:

1. What are the key differences between in-order, pre-order, and post-order traversals?
2. How would the expression differ if the traversal method were pre-order or post-order?
3. Can you generalize how an arithmetic binary tree evaluates expressions?
4. How does operator precedence play into binary tree evaluations?
5. What are practical applications of binary trees in computing?

Tip:

When traversing arithmetic trees, always consider operator precedence and the order of operations to ensure accurate evaluations.