why do oyu change the last two signs when subtracting two negative numbers?
If you add a negative number to something you go left on the number line (minus direction).
5 + (-4) = 5 - 4 = 1
Therefore if you subtract a negative number from something, you go right on the number line (plus direction).
5 - (-4) = 9
When subtracting two negative numbers, you change the last two signs because of the basic arithmetic rules governing the subtraction of signed numbers. The rule states that when subtracting a negative number, it is equivalent to adding the opposite of that number.
To understand why the sign change happens, let's consider an example: -3 - (-5). Here, we have two negative numbers being subtracted.
To solve this, we need to change the operation from subtraction to addition by applying the rule stated above. Instead of subtracting -5, we add its opposite, which is +5. So the expression becomes -3 + 5.
Using the addition of signed numbers, we can solve this as follows:
-3 + 5 = 2
Therefore, -3 - (-5) is equal to 2.
The sign change occurs because subtracting a negative number is equivalent to adding a positive number. This rule helps maintain consistency and predictability in arithmetic operations involving signed numbers.