Skyler is making cookies to donate to the bake sale at his local grocery store. He makes 2/3 of the cookies on a given night and has only enough time to decorate 1/4 of them. What is the fractional portion remaining that he still needs to decorate?(1 point) Responses 11/12 Start Fraction 1/1 over 1/2 End Fraction 1/2 Start Fraction 1 over 2 End Fraction 5/12 Start Fraction 5 over 12 End Fraction 3/7

1 answer

To determine the fractional portion of the cookies that Skyler still needs to decorate, we can follow these steps:

  1. Let's denote the total number of cookies as \( C \).
  2. According to the problem, he makes \( \frac{2}{3}C \) cookies in total.
  3. 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:

  1. The total number of cookies he has is \( \frac{2}{3}C \).
  2. The number of cookies he has already decorated is \( \frac{1}{6}C \).
  3. 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.