Consider the ratio written like a fraction:
Count of sandwichescount of people→46
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
For ratios, when multiplying or dividing, what we do to the bottomwe do to the top.
So to change 46 into what we want we apply
4÷66÷6=231← Count of sandwichescount of people
So each person ends up with 23 of a sandwich
Now see where the shortcut comes from 46=23 of a sandwich