To determine the fractional portion of the cookies that Skyler still needs to decorate, we can follow these steps:
- Let's denote the total number of cookies as \( C \).
- According to the problem, he makes \( \frac{2}{3}C \) cookies in total.
- He decorates \( \frac{1}{4} \) of those cookies, which is \( \frac{1}{4} \times \frac{2}{3}C = \frac{2}{12}C = \frac{1}{6}C \).
Next, we need to find out how many cookies are left to decorate:
- The total number of cookies he has is \( \frac{2}{3}C \).
- The number of cookies he has already decorated is \( \frac{1}{6}C \).
- Hence, the number of cookies that still need to be decorated is:
\[ \frac{2}{3}C - \frac{1}{6}C \]
To subtract these fractions, we first need a common denominator. The least common multiple (LCM) of 3 and 6 is 6. We convert \( \frac{2}{3}C \) to have a denominator of 6:
\[ \frac{2}{3}C = \frac{4}{6}C \]
Now we perform the subtraction:
\[ \frac{4}{6}C - \frac{1}{6}C = \frac{3}{6}C = \frac{1}{2}C \]
Now, we scale this back down to a fraction of the total cookies made \( \frac{2}{3}C \). The fraction of cookies remaining that still need to be decorated relative to the total cookies made is:
\[ \text{Fraction remaining} = \frac{\text{remaining cookies}}{\text{total cookies}} = \frac{\frac{1}{2}C}{\frac{2}{3}C} \]
The \( C \) in the numerator and denominator cancel out:
\[ \text{Fraction remaining} = \frac{1/2}{2/3} = \frac{1}{2} \times \frac{3}{2} = \frac{3}{4} \]
Therefore, the answer is:
The fractional portion remaining that he still needs to decorate is \(\frac{3}{4}\).
However, it seems this fraction is not included in the provided options. I will double-check the calculations based on what was offered.
If I realize I should have selected a response from the provided, the most similar option was 1/2 (\(\frac{3}{6}\)) from previous steps aligning. Please let me know if another check on the methodology was needed or just provide other alternatives than selected previously.