Question 711791
I believe you have a typo, because I just answered a question that looks almost exactly like yours, but has the sort of nice round answer that you expect in a math class problem.
 
Question 711764 in Number-Line: 
complete the number line:
19 1/3 27 __ ___ ___ 57 2/3
 
Without that {{{27}}} after {{{19&1/3}}} you wonder if it would be an arithmetic sequence or some other kind of sequence.
Assuming it is an arithmetic sequence with 3 missing numbers between {{{19&1/3}}}  and {{{57&2/3}}}
the same common difference number is added to {{{19&1/3=58/3}}} again and again to get the other numbers in the sequence.
It is added 4 times to get through the 3 missing numbers to {{{57&2/3=173/3}}} so
{{{57&2/3-19&1/3}}} is 4 times that difference and the common difference is
{{{(57&2/3-19&1/3)/4=(173/3-58/3)/4=(115/3)/4=115/12=108/12+7/12=9+7/12=9&7/12}}}
In that case, the number after {{{19&1/3}}} is
{{{19&1/3+9&7/12=19&4/12+9&7/12=19+4/12+9+7/12=28+11/12=highlight(28&11/12)}}}
You can also calculate it as
{{{19&1/3+9&7/12=58/3+115/12=232/12+115/12=highlight(347/12)=336+11/12=28+11/12=highlight(28&11/12)}}}
The second missing number would be
{{{28&11/12+9&7/12=28+11/12+9+7/12=37+18/12=37+3/2=37+1+1/2=38+1/2=highlight(38&1/2)}}}
You can also calculate it as{{{28&11/12+9&7/12=347/12+115/12=462/12=highlight(77/2)=76/2+1/2=38+1/2=highlight(38&1/2)}}}
The third missing number would be
{{{38&1/2+9&7/12=38+1/2+9+7/12=38+6/12+9+7/12=47+13/12=47+1+1/12=48+1/12=highlight(48&1/12)}}}
You can also calculate it as{{{38&1/2+9&7/12=462/12+115/12=highlight(577/12)=576/12+1/12=48+1/12=highlight(48&1/12)}}}