Question

1. the equation 4(2x + 3y) = 4(3y + 2x) is an example of which property?

a distributive property
b commutative property of addition
c associative property of addition
d identity property for addition

Explanation:

Step1: Recall properties of addition

The commutative property of addition states that for any two numbers \(a\) and \(b\), \(a + b = b + a\). In the given equation \(4(2x + 3y)=4(3y + 2x)\), we can see that inside the parentheses, \(2x + 3y\) is rewritten as \(3y + 2x\), which follows the commutative property of addition (since we are just swapping the order of \(2x\) and \(3y\) in the addition within the parentheses, and the multiplication by 4 is applied to both sides).

Step2: Eliminate other options

• Distributive property involves \(a(b + c)=ab + ac\), which is not the case here.
• Associative property of addition is \((a + b)+c = a+(b + c)\), which is about grouping, not order.
• Identity property for addition is \(a + 0 = a\), which is not relevant here.

Answer:

B. commutative property of addition