Question

use properties of operations to write two expressions that are equivalent to $\frac{3}{4}n + left(8 + 1\frac{1}{3}z
ight).$

Explanation:

Step1: Use Commutative Property of Addition

The commutative property of addition states that \(a + b = b + a\). Applying this to \(\frac{3}{4}n+(8 + \frac{1}{3}z)\), we can swap the order of the two addends:
\((8+\frac{1}{3}z)+\frac{3}{4}n\)

Step2: Use Associative Property of Addition

The associative property of addition states that \(a+(b + c)=(a + b)+c\). Applying this to \(\frac{3}{4}n+(8+\frac{1}{3}z)\), we can group \(\frac{3}{4}n\) and \(8\) first:
\((\frac{3}{4}n + 8)+\frac{1}{3}z\)

Answer:

Two equivalent expressions are \((8+\frac{1}{3}z)+\frac{3}{4}n\) and \((\frac{3}{4}n + 8)+\frac{1}{3}z\) (answers may vary depending on other properties used, like distributing if there was a multiplication, but here with addition properties these are valid).