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#