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 $\frac{6}{8}x+y$.

Step-by-step solution

:Given information

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

To simplify using commutative property of addition.

: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 $a\times b=b\times a$

Step 3: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

$$\begin{gathered} \frac{5}{8}x+\frac{5}{12}y+\frac{1}{8}x+\frac{7}{12}y=\frac{5}{8}x+\frac{1}{8}x+\frac{5}{12}y+\frac{7}{12}y \\ =\frac{6}{8}x+\frac{12}{12}y \\ =\frac{6}{8}x+y \end{gathered}$$