Question bank: Comparisons between fractions

In preparation for a birthday party, João and Maria are dividing a rectangular cake into equal parts to avoid waste. João cut the cake into 5 vertical slices, while Maria cut the cake into 8 horizontal slices. They realized that they each got 4 equal slices following the other's cut. João claims that his slices are larger than Maria's, while she disagrees, arguing that hers are larger. To settle the matter, decide who is right by comparing the fractions representing the parts of the cake each one has and expressing them in ascending order of size.

A pizzeria offers two different promotions: in the first one, a large pizza is divided into 8 equal slices, and in the second one, an extra-large pizza is divided into 12 equal slices. If you want to compare a promotion that offers 'x' slices of the large pizza with one that provides 'y' slices of the extra-large pizza, and you know that x and y are integers greater than zero, answer: (1) Given that x/y is a proper fraction, what would be the smallest number of slices you could receive in the promotion of the large pizza for each slice you receive in the promotion of the extra-large pizza? (2) If the promotion of the large pizza sells 'a' units and the promotion of the extra-large pizza sells 'b' units, and knowing that 'a' and 'b' are integers greater than zero and that a/b results in an irreducible fraction, determine in terms of 'a' and 'b' how many times more slices are sold in the promotion of the large pizza than in the promotion of the extra-large pizza.

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.

Isabella, Marcelo, and Heitor are distributing flyers for a school event. Isabella distributed 5/8 of the total, Marcelo distributed 1/4 of the total, and Heitor distributed the rest. a) Determine the fraction of flyers that Heitor distributed. b) Arrange the fractions representing the amount of flyers distributed by each student from smallest to largest. c) Which student distributed the most flyers?

At a birthday party, two identical rectangular cakes were cut into different pieces. One cake was cut into 50 equal pieces, and the other cake was cut into 60 equal pieces. One third of the guests took a piece of the first cake, while half of the guests took a piece of the second cake. (1) Calculate and compare the amount of pieces each group of guests took. (2) Determine from which cake a larger fraction of the total was served. Explain the reasoning behind your conclusion.