Question

Which properties of operations could be used to show that (-5p+ 9) + (-2+ p) is equivalent to (-5p) +p+9 - 2?​

Answer 1

• The Commutative and Associative properties of addition

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Using the Commutative property of addition, which states that the order of addends does not affect the sum, you can rewrite:

• (-2 + p) as (p - 2)

Now, the expression becomes:

• (-5p + 9) + (p - 2)

Next, apply the Associative property of addition, which states that the grouping of addends does not affect the sum.

You can rearrange the terms as follows:

• [(-5p + 9) + p] - 2

Then, combine the like terms:

• (-5p + p) + 9 - 2

Now the expression matches the given form:

• (-5p) + p + 9 - 2

This shows that the two expressions are equivalent using the Commutative and Associative properties of addition.