Question 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 answer

To solve the problem, we need to find the fractional portion of the cookies that Skyler made but has not yet decorated.

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

He can only decorate \( \frac{1}{4} \) of these cookies. The amount of cookies that he decorates is given by:

\[ \text{Decorated cookies} = \frac{1}{4} \times \frac{2}{3}C = \frac{2}{12}C = \frac{1}{6}C. \]

Next, we need to find the portion of cookies that remains undecorated. This is calculated by subtracting the decorated cookies from the total cookies he made:

\[ \text{Undecorated cookies} = \frac{2}{3}C - \frac{1}{6}C. \]

To perform this subtraction, we need a common denominator. The least common multiple of \( 3 \) and \( 6 \) is \( 6 \). We can convert \( \frac{2}{3}C \) into sixths:

\[ \frac{2}{3}C = \frac{4}{6}C. \]

Now we can perform the subtraction:

\[ \frac{4}{6}C - \frac{1}{6}C = \frac{4 - 1}{6}C = \frac{3}{6}C = \frac{1}{2}C. \]

Now, we find the fractional portion of cookies that Skyler still needs to decorate compared to the total number he originally made, which is \( C \):

\[ \text{Fraction remaining to decorate} = \frac{\text{Undecorated cookies}}{\text{Total cookies}} = \frac{\frac{1}{2}C}{C} = \frac{1}{2}. \]

Therefore, the fractional portion remaining that he still needs to decorate is

\[ \boxed{\frac{1}{2}}. \]