Six friends share 4 sandwiches equally. What fraction of a sandwich does each friend get?

The same thing but from a different stand point

Consider the ratio written like a fraction:

##("Count of sandwiches")/("count of people")-> 4/6##

But we need the count of sandwiches for 1 person. So we need to change the 6 people into 1 person. To change 6 into 1 divide it by 6

##6-:6=1##

##color(brown)("For ratios, when multiplying or dividing, what we do to the bottom")####color(brown)("we do to the top.")##

So to change ##4/6## into what we want we apply

##(4-:6)/(6-:6)=(2/3)/1 larr" "("Count of sandwiches")/("count of people") ##

So each person ends up with ##2/3## of a sandwich

##color(green)("So you can now see where the shortcut comes from "4/6 = 2/3" of a sandwich"##