Number Substitution in 50÷10+9×0: Which Value Can Change Without Affecting the Result?

To solve this problem, we need to understand the order of operations and the special properties of 0 in arithmetic operations.

Step 1: Calculate the current value of the expression
The given expression is $50:10+9\times0$.

Following the order of operations (division and multiplication before addition):
- First, perform the division: $50:10 = 5$
- Next, perform the multiplication: $9 \times 0 = 0$
- Finally, perform the addition: $5 + 0 = 5$

So the current result of the expression is $5$.

Step 2: Analyze which number can be substituted
Now we need to determine which number can be replaced without changing the result of $5$.

Let's examine each number:

• If we change 50: The division $50:10$ would give a different result, changing the final answer.
• If we change 10: The division $50:10$ would give a different result, changing the final answer.
• If we change 9: We would have $x \times 0$ for any number $x$. Since any number multiplied by 0 equals 0, we still get $0$, and the final result remains $5 + 0 = 5$.
• If we change 0: The multiplication $9 \times 0$ would become $9 \times y$ where $y \neq 0$, which would change the final answer.

Step 3: Apply the zero property of multiplication
The key insight is that any number multiplied by 0 equals 0. This is expressed as: $a \times 0 = 0$ for any real number $a$.

Therefore, the number 9 can be substituted with any other number, and the expression will still equal $5$ because the multiplication by 0 will always yield 0.

The answer is 9.