Question 113721
<pre><font size = 4><b>
If {{{s/t}}} = {{{u/v}}}, then {{{(s+t)/t}}} = ?

First we do it the long way, and then we look
at a shortcut.

{{{(s+t)/t}}} =

{{{s/t+t/t}}} =

{{{s/t+1}}}

Substitute {{{u/v}}} for {{{s/t}}} since
they are given to be equal.

{{{u/v+1}}}

Write the 1 as {{{v/v}}}

{{{u/v+v/v}}}

Write that as 

{{{(u+v)/v}}}

This is the correct answer. HOWEVER,
you are probably supposed to do it
by a short cut rule of proportions:

The rule is:
<font color = "red">
<i>If you have a proportion, then you may add
the denominators to the numerators on both
sides and the result is still a proportion</i>
</font>
So you can do this problem using this short cut:

Start with this:

{{{s/t}}} = {{{u/v}}}

Notice that you want to find {{{(s+t)/t}}}. So
you notice that this is {{{s/t}}} with the
denominator t added to the numerator {{{s}}}.  Therefore
you can just do that same thing on the right and
add the denominator {{{v}}} to the numerator u and get

{{{(s+t)/t}}} = {{{(u+v)/v}}}

Edwin</pre>