Balu and pumba shared ½ of a cake. balu got to eat twice as much cake as pumba. what fraction of the whole cake did balu eat?

Balu had 1/3 of the whole cake.

Let x represent how much Pumba had, therefore 2x = Balu's portion
3x = 1/2
0.5 divided by 3 is 0.167, which is Pumba's portion of the whole cake.
Balu had twice as much, so multiply this number by 2 to get 0.33, which is equal to 1/3 as a fraction.

You could also draw it out. Imagine the 1/2 that Balu and Pumba shared was cut into 3 equal slices. Balu had 2 slices and Pumba had 1, since Balu had twice as much cake as Pumba. Then, imagine the other half that Balu and Pumba did not have was cut into thirds as well. There would be 6 slices total  and Balu had 2 of them. 2/6 can be reduced to 1/3

Hope this helps!