The inverse property of addition states that for any real number [tex]\(a\)[/tex], there exists another real number [tex]\(-a\)[/tex] such that their sum is zero. This property helps us understand how a number can be "canceled out" by its additive inverse.
Let's break down the given examples:
1. [tex]\(5 + (-5) = 0\)[/tex]
Here, [tex]\(a = 5\)[/tex]. The number [tex]\(-5\)[/tex] is called the additive inverse of [tex]\(5\)[/tex]. When you add [tex]\(5\)[/tex] and [tex]\(-5\)[/tex], the result is zero, demonstrating the inverse property of addition.
2. [tex]\(-1.33 + 1.33 = 0\)[/tex]
In this example, [tex]\(a = -1.33\)[/tex]. The number [tex]\(1.33\)[/tex] is the additive inverse of [tex]\(-1.33\)[/tex]. Adding these two numbers together yields zero, once again illustrating the inverse property of addition.
From these examples, we can deduce the following general statement about the inverse property of addition for any real number [tex]\(a\)[/tex]:
[tex]\[ a + (-a) = 0 \][/tex]
Thus, the statement that best describes the property is:
[tex]\[ a + \square = 0 \][/tex]
where [tex]\(\square\)[/tex] should be filled with [tex]\(-a\)[/tex].
So, the complete statement should be:
[tex]\[ a + (-a) = 0\][/tex]
This expresses the inverse property of addition clearly and concisely for any real number [tex]\(a\)[/tex].
