To understand what happens when you subtract one negative integer from another, let’s break it down with an example. First, recall that a negative integer is simply any whole number that is less than zero. Examples include -1, -2, -3, and so on.
When you perform the subtraction of two negative integers, such as -5 and -3, you’re actually calculating the difference between two quantities that are both below zero. The operation is represented mathematically as:
-5 - (-3)
Now, subtracting a negative number is equivalent to adding its positive counterpart. Thus, we can rewrite the subtraction as:
-5 + 3
Following through with this operation:
-5 + 3 = -2
The result, -2, is indeed a negative integer. Therefore, when you subtract a smaller negative number from a larger negative number, the result remains negative. However, if you subtract a larger negative number from a smaller one, like -3 and -5:
-3 - (-5)
This becomes:
-3 + 5 = 2
In this case, the result is positive. So, to summarize:
- The difference between any two negative integers can result in a negative integer if the first integer is smaller than the second.
- If the first negative integer is larger, the difference will yield a positive integer.
Understanding this concept helps clarify how operations with negative numbers can lead to results that may initially seem counterintuitive.