Question 120259
<font size = 5 color = "red"><b>SOLUTION BY EDWIN:</font></b>

Average... 
Determine the average of the two real numbers x/3 and 2x/5.

<pre><b>
Use the formula

                          FIRST NUMBER + SECOND NUMBER 
AVERAGE OF TWO NUMBERS = ------------------------------
                                       2


AVERAGE OF TWO NUMBERS = {{{(x/3 + (2x)/5)/2}}}

Write the 2 on the bottome as {{{2/1}}} so everything
will be a fraction:

AVERAGE OF TWO NUMBERS = {{{(x/3 + (2x)/5)/(2/1)}}}

Put parentheses around all terms top and bottom:

AVERAGE OF TWO NUMBERS = {{{((x/3) + ((2x)/5))/((2/1))}}}


The LCD of all three denominators 3,5,and 1 is 15,
so multiply every term on top and bottom by 15, written
as {{{(15/1)}}}:
(15/1)
AVERAGE OF TWO NUMBERS = {{{((15/1)(x/3) + (15/1)((2x)/5))/(15/1)(2/1)}}}

Cancel the 3 into the 15 in the first term on top.
Cancel the 5 into the 15, getting 3 in the second term on top.

                           5          3 
AVERAGE OF TWO NUMBERS = {{{((cross(15)/1)(x/cross(3)) + (cross(15)/1)((2x)/cross(5)))/(15/1)(2/1)}}}

So we end up with

AVERAGE OF TWO NUMBERS = {{{(5x + 6x)/30}}} or

AVERAGE OF TWO NUMBERS = {{{(11x)/30}}}

Edwin</pre>