Ellen baked 2 dozen cupcakes of which half contained chocolate, two-thirds contained raisins, one-fourth contained chocolate chips, and one-

You just find the largest fraction there.   The only one that is bigger than 1/2 is 2/3 so that is the biggest.

All the others could be subsets of that 2/3  so the largest number that could not have any of these ingredients is 1- 2/3  =  1/3

1/3  of  24 cakes  is   8 cakes.  

I don't know what you did Titanium but I will give you credit for your effort :)

whoa

this is more complicated than expected

its funny how I'm eating a cupcake right now, so I should take the time to answer this question

we know  that 2 dozens=24 cupcakes

half of that is chocolate

so, we make it proportional

1/2 and ?/24

times 1 by 24 and divide it by 2, equals 12

there are 12 chocolate cupcakes overall

now we have to do raisns

we know that it's 2/3 of the remaining

2/3 * ?/12

times 2 by 12=2444 divide that by 3 which equals 8

now, we add 12 and 8

then subtract 24-20=4

so, we have 4 cupcakes remaining

1/4 of it contains chocolate chip

so, 1/4 and ?/4

1*4=4/4=1

now theres 3

1/6 of it contains n u t s

so, 1/6 and ?/3

1*3=3/6=.5

lets just round it anyways since according to my theory, the dog ate half of all the cupcakes

which means 1

now there are only 2 remaining

out of all the cupcakes, 2/24 of them will contain nothing

if you'd like to simplify it, it'd be 1/12

yea!!!!!!!!