(Originais Teachy 2023) - Question Easy of Mathematics

João is organizing a birthday party and wants to make a larger quantity of his favorite cake recipe. The original recipe yields a cake with 20 slices and uses 3 cups of flour, 2 cups of sugar, and 1 cup of oil. João wants to make a cake with 40 slices. a) How many cups of flour, sugar, and oil should he use to make a cake that yields 40 slices? b) If he wanted to make a cake with 60 slices, what would be the quantity of cups of each ingredient? c) João noticed that the number of cake slices is always half the number of cups of water used in the recipe. How many cups of water are needed for a cake of 80 slices?

In a science project, students need to measure different volumes of liquids for their experiments. The scale used to measure the volume of water can only measure in multiples of 100 milliliters. When measuring, the scale shows 450.725 grams of water. We know that the density of water is 1 g/ml. (1) Round the volume measured by the scale to the nearest milliliter. (2) Explain why the scale provided a number in grams instead of milliliters and how you used the density of water to convert the measurement back to volume in milliliters.

Imagine you have 432 candies and want to separate them into containers of 100, 10, and individual units to facilitate counting. How would you make this separation? Explain your answer by showing how the number 432 can be decomposed into powers of 10.