QuestionUse the property of addition to simplify and find the sum of $[5.5 + (-2.3)] + [(-5.5) + 2.3]$ .

Studdy Solution

STEP 1

Assumptions1. We are asked to find the sum of $[5.5+(-.3)]+(-5.5+.3)$ . We are asked to use the Inverse Property of Addition to solve the problem

STEP 2

The Inverse Property of Addition states that the sum of a number and its additive inverse (the negative of the number) is zero. In other words, for any number $a$ , we have $a + (-a) =0$ .

STEP 3

Looking at the given expression, we can see that it is in the form $a + b + (-a + c)$ , where $a =5.5$ , $b = -2.3$ , and $c =2.3$ .

STEP 4

We can rearrange the terms in the expression to group $a$ and $-a$ together, and $b$ and $c$ together, using the Commutative Property of Addition, which states that the order of addition does not affect the sum. $[.+(-2.3)]+(-.+2.3) =. -. + (-2.3 +2.3)$

STEP 5

Now, we can apply the Inverse Property of Addition to simplify the expression. $5.5 -5.5 + (-2.3 +2.3) =0 +0$

STEP 6

Finally, we can add the two zeros together to find the sum of the original expression.
$0 +0 =0$ So, the sum of $[5.5+(-2.3)]+(-5.5+2.3)$ is0.

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