To determine how much pie each person at the party will receive, we start by understanding that there are 9 pies and 36 people. We need to find out the fraction of one pie that each person will get.
1. We begin by setting up the fraction representing the amount of pie per person:
[tex]\[
\frac{\text{Total number of pies}}{\text{Total number of people}} = \frac{9}{36}
\][/tex]
2. Next, we need to simplify this fraction to its lowest terms. We do this by finding the greatest common divisor (GCD) of 9 and 36.
- The factors of 9 are 1, 3, 9.
- The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36.
- The greatest common factor is 9.
3. We then divide the numerator and the denominator of the fraction by their GCD:
[tex]\[
\frac{9 \div 9}{36 \div 9} = \frac{1}{4}
\][/tex]
Thus, each person at the party will receive [tex]\(\frac{1}{4}\)[/tex] of a pie.
Therefore, the fraction of one pie each person will receive is:
[tex]\(\frac{1}{4}\)[/tex]
