#color(blue)("Dealing with a lot of those zeros")#

What follows is where the shortcut of cancelling comes from.

#72000 -> 72xx1000#

#4900000-> 4900xx1000#

#(72xx1000)/(4900xx1000)" "=" "72/4900xx1000/1000#

But #1000/1000=1# and anything multiplied by 1 does not change its value.

#72/4900xx1000/1000" "=" "72/4900xx1" "=" "72/4900#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#color(blue)("Dealing with what is left")#

#72/4900" "=" "(72-:8)/(49000-:8) = 9/6125#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#color(blue)("This is one way to find a common factor - there are other methods")#

Observe that the highest #ul("common")# factor is #2xx2xx2=8#