Question

Use the Commutative and Associative Properties

In the following exercises, simplify$\frac{5}{8}x+\frac{5}{12}y+\frac{1}{8}x+\frac{7}{12}y$

Short answer

The simplified form of the expression$\frac{5}{8}x+\frac{5}{12}y+\frac{1}{8}x+\frac{7}{12}y$using the commutative property is .

Step-by-step solution

Step 1  . Given information

Given :$\frac{5}{8}x+\frac{5}{12}y+\frac{1}{8}x+\frac{7}{12}y$.

Simplify using commutative property of addition.

Step 2  . Description of the commutative property

Commutative property:

when adding or multiplying two real numbers changing the order gives the same result.

addition: if a and b are two real numbers then $a+b=b+a$

Multiplication: if a and b are two real numbers then$a\times b=b\times a$

. simplifying the expression using commutative property.

According to the given question use the commutative property of addition to write like terms and then add ,then the expression becomes$$\begin{gathered} \frac{5}{8}x+\frac{5}{12}y+\frac{1}{8}x+\frac{7}{12}y=\frac{5}{8}x+\frac{1}{8}x+\frac{5}{12}y+\frac{7}{12}y \\ =\frac{6}{8}x+\frac{12}{12}y \\ =\frac{6}{8}x+y \end{gathered}$$