Final answer:
1/4 of the remaining 4/5 of cookies being not peanut butter are cinnamon sugar, which means 1/5 of all the cookies in the jar are cinnamon sugar.
Step-by-step explanation:
If 1/5 of the cookies in a jar are peanut butter cookies, then 4/5 of the cookies are not peanut butter. Out of these, 1/4 are cinnamon sugar cookies. To find the fraction of all the cookies that are cinnamon sugar, we multiply these two fractions.
First, let's calculate the fraction of the remaining cookies:
- Calculate the remaining cookies: 4/5 (since 1/5 are peanut butter).
- Determine the cinnamon sugar cookies: 1/4 of the remaining 4/5 cookies are cinnamon sugar.
- Calculate the fraction for cinnamon sugar cookies: (1/4) * (4/5) = 1/5.
Therefore, 1/5 of all the cookies are cinnamon sugar.