Question 823840
That is a very convenient way of doing those calculations, but I would say that the way the numbers like {{{5&5/5}}} are written is unusual.
 
{{{6=5+1}}} and since {{{1=5/5}}}
{{{6=5+5/5}}} .
Everyone writes {{{5+2/5}}} as {{{5&2/5}}} ,
but I had never seen 
{{{5+5/5}}} written as {{{5&5/5}}} .
I would not call it wrong, but it is unusual.
That said, to subtract {{{4&1/5=4+1/5}}} from {{{6=5+5/5}}} ,
you could subtract the {{{4}}} from the {{{5}}} to get {{{6-5=1}}} ,
and the {{{1/5}}} from the {{{5/5}}} to get {{{5/5-1/5=4/5}}} .
 
{{{3=2+1=2+3/3}}}
If someone writes {{{2+3/3}}} as {{{2&3/3}}} , I will think it is weird,
but I will not complain.
So the same person will probably write
{{{3-2&1/3=2&3/3-2&1/3=0&2/3=2/3}}}
One {{{2}}} is subtracted from the other,
and the {{{1/3}}} is subtracted from the {{{3/3}}} .
 
The way shown above is the way I do the calculations when I have to do them in my head.
The way I was taught to do that kind of calculation is harder.
The teacher would make us transform the both numbers into fractions with the same denominator.
Then we would subtract.
After that we would transform the fraction back into a mixed number if necessary.
So we would write
{{{6-4&1/5=30/5-21/5=9/5=4&1/5}}}
We were expected to transform in our heads, and sometimes we would make mistakes.
In our heads we had to do the following:
{{{6=6*5/5=30/5}}} , {{{4&1/5=4+1/5=4*5/5+1/5=(4*5+1)/5=(20+1)/5=21=5}}} , and
{{{9/5=(5+4)/5=5/5+4/5=1+4/5=1&4/5}}}