Question

You and five of your friends go back to your place for lunch between classes. Your roommate has eaten approximately \(\frac{1}{4}\) of an apple pie you made. Your friends all want pie. What fractional part of the remaining pie can each of them have, if you decide not to have any?

Short answer

Answer: Each friend will get 3/20 of the pie.

Step-by-step solution

Calculate the remaining pie

First, we need to determine the remaining pie. We know that 1/4 of the pie is already eaten, so we need to subtract this from the whole pie (1). So we have \(1 - \frac{1}{4}\).

Simplify the fraction

In order to subtract the fraction from 1, we need to find a common denominator. The denominators are already the same (4), so we just need to perform the subtraction: \(1 - \frac{1}{4} = \frac{4}{4} - \frac{1}{4}\).

Perform the subtraction

Now, we just need to subtract the numerators to find the remaining pie: \(\frac{4}{4} - \frac{1}{4} = \frac{3}{4}\). So, there is \(\frac{3}{4}\) of the pie left.

Divide the remaining pie among five friends

Now, we need to divide the remaining pie (\(\frac{3}{4}\)) by the number of friends (5). To divide a fraction by a whole number, we can simply multiply the fraction by the reciprocal of the whole number: \(\frac{3}{4} \times \frac{1}{5}\).

Simplify the new fraction

Now we just need to multiply the fractions to find how much pie each friend will get: \(\frac{3}{4} \times \frac{1}{5} = \frac{3 \times 1}{4 \times 5} = \frac{3}{20}\). Each friend will get \(\frac{3}{20}\) of the pie.