Question 871085
If by 0.67 you mean a repeating decimal, it must be
{{{"0.66666 . . ."=2/3}}}
 
It would be easy to use a calculator to get an approximate decimal value for
all the fractions and compare those approximate decimal values, but I assume calculators are not allowed.
 
Two of the fractions given can be simplified, and simplifying may help.
{{{69/99=3*23/(3*33)=23/33}}}
{{{24/33=3*8/(3*11)=8/11}}}
 
We can easily compare {{{6/11}}} and {{{2/3}}} to each other and to
B. {{{69/99=23/33}}} and C. {{{24/33}}} ,
if we express all four fractions with {{{33}}} as a denominator
{{{6/11=6*3/(11*3)=18/33}}} and {{{2/3=2*11/(3*11)=22/33}}}
{{{6/11=18/33<22/33<23/33<24/33}}} shows us that
{{{6/11<2/3}}} and that
the answer is neither B. nor C.
 
{{{6/11=6*5/(11*5)=30/55}}} ,
So {{{26/55<30/55=6/11<2/3}}} and D. is not the answer either.
 
The answer must be {{{highlight(A)}}} because that's all that is left.
 
Let's verify, anyway.
To compare {{{11/18}}} to {{{2/3}}} and {{{6/11}}} we can use as a common denominator
{{{198=18*11=3*6*11=3*66}}}
{{{11/18=11*11/(18*11)=121/198}}}
{{{2/3=2*66/(3*66)=132/198}}}
{{{6/11=6*18/(11*18)=108/198}}}
{{{6/11=108/198<121/198<132/98=2/3}}} so {{{6/11<highlight(11/18)<2/3}}}