Arithmetic Expression Solved

The problem requires finding the value that replaces the question mark in the given arithmetic expression. The expression is:

$$8974 + 3567 – 8976 – 3565 + 8652 = ?$$

We need to perform the addition and subtraction operations to determine the final result.

Calculation Steps Overview

Let's break down the calculation using two common methods:

Rearranging Terms for Calculation

One way to simplify is to group the positive numbers and the negative numbers separately:

• Positive Terms: 8974, 3567, 8652
• Negative Terms: –8976, –3565

Rewrite the expression by grouping:

$$ (8974 + 3567 + 8652) + (–8976 – 3565) $$

First, sum the positive terms:

• $8974 + 3567 = 12541$
• $12541 + 8652 = 21193$

Next, sum the absolute values of the negative terms:

• $8976 + 3565 = 12541$
• So, the sum of negative terms is $-12541$.

Now, combine these sums:

$$ 21193 – 12541 = 8652 $$

Pairing Numbers for Calculation

Alternatively, we can pair numbers that are close to each other to simplify the calculation:

Rearrange the expression to form pairs:

$$ (8974 – 8976) + (3567 – 3565) + 8652 $$

Calculate the result of each pair:

• $8974 – 8976 = -2$
• $3567 – 3565 = 2$

Substitute these results back into the rearranged expression:

$$ (-2) + (2) + 8652 $$

Simplify the expression:

$$ 0 + 8652 = 8652 $$

Final Answer Calculation

Both methods correctly show that the result of the calculation $8974 + 3567 – 8976 – 3565 + 8652$ is 8652. This is the value that should replace the question mark.