Choose all properties that were used to simplify the following problem:

Question

[38 + 677] + (-38)

[677 + 38] + (-38)

677 + [38 + (-38)]

677 + 0

677

additive identity
additive inverse
commutative property of addition
associative property of addition
distributive property

Answer 1

To simplify the problem step by step, the following properties were used:

1. Additive Inverse: This is used in the expression \( 38 + (-38) \), which equals 0.

2. Additive Identity: This is used in \( 677 + 0 \), since adding 0 does not change the value of 677.

3. Commutative Property of Addition: This property is used in rearranging the terms as seen in the expressions \( [38 + 677] + (-38) \) and \( [677 + 38] + (-38) \), as addition can be done in any order.

4. Associative Property of Addition: This property is used when grouping the terms, allowing us to change the way we group the numbers, as seen in the transitions from one expression to the next.

Therefore, the properties used to simplify the problem are:

• Additive identity
• Additive inverse
• Commutative property of addition
• Associative property of addition