19. There are three grades in Mona's middle school-sixth, seventh. and eighth. One-third of the students are in sixth grade and \( \frac{1}{4} \) are in seventh grade. What fraction of the schools' students are in eighth grade?

To find the fraction of students in eighth grade, we first need to determine the fractions of students in the sixth and seventh grades. If one-third of the students are in sixth grade, that's represented as \( \frac{1}{3} \), and if one-fourth are in seventh grade, that's represented as \( \frac{1}{4} \). To combine these fractions, we need a common denominator. The least common multiple of 3 and 4 is 12. Converting the fractions gives: - Sixth grade: \( \frac{1}{3} = \frac{4}{12} \) - Seventh grade: \( \frac{1}{4} = \frac{3}{12} \) Adding these fractions together: \[ \frac{4}{12} + \frac{3}{12} = \frac{7}{12} \] Now, to find the fraction of students in eighth grade, we take the total fraction (1, or \( \frac{12}{12} \)) and subtract the combined fraction of sixth and seventh grades: \[ 1 - \frac{7}{12} = \frac{5}{12} \] Thus, the fraction of the school's students that are in eighth grade is \( \frac{5}{12} \).