(Originais Teachy 2024) - Question Hard of Mathematics

During a field trip to the Serra do Cipó National Park, a group of 6th-grade students is challenged to calculate the amount of garbage collected by visitors, aiming to raise awareness about the importance of environmental conservation. The trip monitor explained that the students could help separate recyclable from non-recyclable waste, providing the following information: 'So far, we have collected 3/4 of an aluminum can, 5/8 of a plastic bottle, and 7/12 of a cardboard packaging.' To calculate the total amount of garbage collected, students need to compare the fractions of each type of material and estimate which type of material was collected in greater quantity in order to prioritize proper separation and disposal. Considering the challenge proposed, determine which type of material was collected in greater quantity and justify your answer, identifying the fraction corresponding to that quantity.