### Home > CC3MN > Chapter 2 > Lesson 2.1.9 > Problem2-86

2-86.

When you want to convince someone that $8x+(2x−3)$ is equivalent to $(8x+2x)−3$, you can support your claim with the Associative Property of Addition.

Determine if the following statements are true or false. If true, justify your conclusion by stating the appropriate algebraic property. If false, explain how you know.

1. $(81)(38)=(38)(81)$

Notice that the only difference between the left side and the right side of the equation is the placement of the factors.
Does this change the product? How do you know?

True; Commutative Property of Multiplication

1. $27+0=27$

Does adding zero to a number ever change its value? What is this property called?

1. $3−5=5−3$

Unlike addition and multiplication, subtraction is not commutative.
Meaning that the order of the terms matters.

1. $19.4·1=19.4$

$\left(a\right)\left(1\right)=a$

True; Identity Property of Multiplication