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.

In a science project, a 6th-grade class divided a box of pencils among themselves to take notes and make drawings. Maria received 1/4 of the pencils, João 2/5, and Ana 3/10. Considering that the box contained a whole number of pencils, make the necessary comparisons to determine who received the most and the least amount of pencils, and then order the students according to the amount of pencils received, from least to most.

In a biology study, it was observed that a species of plant grows in a way that fills a square area with 1000 square centimeters. Researchers noticed that, in a certain soil, plant A grows occupying exactly half of the area filled by plant B, which grows in a different territory and occupies 1/3 less than plant C. Plant C, in turn, grows filling a fraction of the area occupied by a fourth plant, D, which grows in another environment. Plant D was observed to cover an area of 2400 square centimeters, which is 30% more than the area covered by plant E. Based on this information: (1) Determine the area filled by plant A and plant B. (2) Calculate the area occupied by plant C and plant D. (3) Knowing that plant E occupies the smallest area among those mentioned, present the increasing order of the areas occupied by plants A, B, C, D, and E.

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.

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?