#color(blue)("Step 1 - making the numbers easier to handle")#
I am guessing that the decimals are giving you trouble. This is a way round that.
Note that:
#7517.4# is the same as #75174xx1/10#
#1.34# is the same as #134xx1/10^2#
So we have: #75174/134xx1/10-:1/10^2#
#75174/134xx1/10xx10^2#
#75174/134xx10#
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#color(blue)("Step 2 - determine the start value for division")#
#10xx134=1340 larr" not big enough"#
#100xx134=13400 larr" correct count of digits but too small"#
#700xx134=93800larr" too big"#
#500xx134=6" something" larr" start with this one"#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Step 3 - applying the division. This is a different format of long division")#
#" "75174larr" numerator value"#
#color(red)(500)xx134 ->ul(67000) larr" subtract"#
#" "8174#
#color(red)(60)xx134" "->ul(8040) larr" subtract"#
#" "134 #
#color(red)(1)xx134" "->ul(134) larr" sibtract"#
#" "0#
so #75174/134 = color(red)(500+60+1) = 561#
But we still need to deal with the adjustment of #xx10#
So #7517.4/1.34=561xx10 = 5610#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Check by calculator #-> 7517.4/1.34 = 5610#
