Find the Replaceable Number in 6×2+5×0 Without Changing the Result

To solve this problem, let's first evaluate the given expression and then determine which number can be substituted without changing the result.

Step 1: Evaluate the expression
The expression is: $6\times2+5\times0$
Following the order of operations (multiplication before addition):
$6\times2 = 12$
$5\times0 = 0$
Therefore: $6\times2+5\times0 = 12 + 0 = 12$

Step 2: Analyze each number's role
Now let's examine what happens if we change each number:

• If we change the 6: The product $6\times2$ would change, affecting the final result.
• If we change the 2: The product $6\times2$ would change, affecting the final result.
• If we change the 5: The product $5\times0$ would still equal $0$ (since any number times 0 equals 0), so the result remains $12 + 0 = 12$.
• If we change the 0: The product $5\times0$ would no longer be $0$, which would change the final result.

Step 3: Apply the property of zero
The key property here is that any number multiplied by 0 equals 0. Since the term $5\times0$ equals $0$ regardless of what number is in place of the 5, we can substitute any number for 5 without changing the result of the expression.

For example:
$6\times2+100\times0 = 12 + 0 = 12$
$6\times2+(-3)\times0 = 12 + 0 = 12$

Therefore, the number that can be substituted without changing the result is 5.