Fraction is composed of ("count")/("size indicator")
Count is obvious needs no explanation.
Size indicator is how many of what you are counting it takes to make a whole of something
color(red)("You can not "ul("directly")" add or subtract the counts")color(red)("unless the size indicators are the same ")
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
" "("count")/("size indicator")" "->" "("numerator")/("denominator")
Lets make the size indicator (denominator) of 1/4 the same as that of 3/8
Multiply 1/4 by 1 but where 1=2/2. This does not change the inherent value but it does change the way 1/4 looks.
So color(brown)((1/4xx1)+3/8)color(blue)(" "->" "(1/4xx2/2)+3/8)
but (1/4xx2/2)+3/8" is the same as "2/8+3/8
=5/8