Question 697295
Here is a counterexample to show
that 

b. {{{4/9}}} < {{{a/b}}} < {{{7/9}}}

is not always true:

Suppose a = 6 and b = 7.5 

4 < a < 7 < b < 9 because 4 < 6 < 7 < 7.5 < 9 
However 
a/b = 6/7.5 = .8 
and 
7/9 = 0.7778 (rounded to 4 decimal places) 

So {{{a/b}}} > {{{7/9}}},
and thus this is a case when choice b.
is false.

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The second response above gives a 
counterexample of choice c.

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Here is a counterexample to show
that 

d. {{{4/7}}} < {{{a/b}}} < 1

is not always true:

Suppose a = 4.2 and b = 8 

4 < a < 7 < b < 9 because 4 < 4.2 < 7 < 8 < 9 
However 
a/b = 4.2/8 = .525 
and 
4/7 = 0.5714 (rounded to 4 decimal places) 

So {{{a/b}}} > {{{4/7}}},
and thus this is a case when choice d.
is false.

This is also a counterexample for choice e.

Edwin</pre>