Cumulative Practice
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Recall the properties of addition.
G
We want to determine which property is represented by the given equation. Let's begin by recalling some facts about the properties of addition.
| Property | Description | Using Algebra |
|---|---|---|
| Commutative Property of Addition | Changing the order of addends does not change the sum. | a+b=b+a |
| Associative Property of Addition | Changing the grouping of addends does not change the sum. | (a+b)+c=a+(b+c) |
| Additive Inverse Property | The sum of a number and its additive inverse, or opposite, is 0. | a+(- a)=0 |
| Addition Property of Zero | The sum of any number and 0 is equal to the number itself. | a+0=a |
We will consider each of the properties one at a time.
- 80 + 30 + (- 30)= - 80 + [ 30+ (- 30)] Looking at the equation, we can see that we do not change the order of addends. This means that the equation does not represent the Commutative Property of Addition.
We want to know whether the following equation represents the Associative Property of Addition. - 80 + 30 + (- 30)= - 80 + [30+(- 30)] On the right side of the equation, we are changing the grouping of addends. This means that the equation does represent the Associative Property of Addition, which corresponds to answer G. Even though we found that answer G is correct, let's review the remaining answers, just to be sure.
Let's start by considering the given equation. - 80 + 30 + (- 30)=- 80 + [ 30+ (- 30)] Looking at the equation, we can see that 30 is the additive inverse of (- 30). This means that we can rewrite the equation in the following way. - 80 + [ 30+ (- 30)] ⇔ - 80 + 0 Notice that - 80 is not the additive inverse of 0. By the Substitution Property of Equality, we also know that - 80 is not the additive inverse of 30 + (- 30). This means that the initial equation does not represent the Additive Inverse Property, so option H is not correct.
Finally, we want to check if the equation represents the Addition Property of Zero. - 80 + 30 + (- 30)= - 80 + [ 30+ (- 30)] Looking at the equation, we can see that we are adding he negative numbers - 80 and - 30 and the positive number 30. None of the addends are equal to 0. This means that the equation does not represent the Additive Property of Zero, so option I is not correct. The only correct option is G.