State if this statement is always, sometimes, or never true. Use examples to explain.
“The result of subtracting a negative integer from a negative integer is a positive integer.”
-10 - (-5) = -5 NOT true in this case
+10 - (-15) = +5 YES in this case
So sometimes :)
-6 - (-2) = -4
-2 - (-6) = +4
To determine whether the statement is always, sometimes, or never true, let's break it down and examine it.
The statement is: "The result of subtracting a negative integer from a negative integer is a positive integer."
To subtract a negative integer from a negative integer, we can apply the rule of signs:
- When subtracting a negative number, it is equivalent to adding the positive counterpart of that number.
Let's consider some examples:
1. (-4) - (-2) = (-4) + (+2) = -2
In this example, subtracting a negative integer from a negative integer results in a negative integer, not a positive integer. Therefore, the statement is sometimes true, but not always.
2. (-9) - (-7) = (-9) + (+7) = -2
Again, subtracting a negative integer from a negative integer results in a negative integer, not a positive integer. So, the statement is sometimes true, but not always.
In all the examples we considered, subtracting a negative integer from a negative integer did not yield a positive integer, but rather a negative integer.
Therefore, the statement "The result of subtracting a negative integer from a negative integer is a positive integer" is never true.