Question 1137916
<pre>
Given 2 < a < 3 and 5 < b < 6 Find:
a. __ < a-b < __

 5 <  b <  6 

multiplying through by -1 flips inequalities:

-5 > -b > -6 

That is equivalent to

-6 < -b < -5

We add that term by term to 2 < a < 3

 2 < a   <  3 
-6 <  -b < -5
-------------
-4 < a-b < -2





b. __ < a/b < __

 
{{{5 < b < 6}}}
 
is an interval of all positive numbers,
The interval of reciprocals are in the opposite 
order of inequality:

{{{1/5 > 1/b > 1/6}}}

and that is equivalent to

{{{1/6<1/b<1/5}}}

So we multiply 2 < a < 3 term by term by that:

{{{matrix(6,5,
2,""<"",a,""<"",3,
1/6,""<"",b,""<"",1/5,
"",and,we,get,"",
2/6,""<"",a/b,""<"",3/5,
"",which,reduces,to,"",
1/3,""<"",a/b,""<"",3/5)}}}

Edwin</pre>