A caterer has prepared 16 trays of hot food for an event. The trays are placed in warming boxes for delivery. Each box can hold 5 trays of food.a. How many warming boxes are necessary for delivery if the caterer wants to use as few boxes as possible? Explain how you know.b. If the caterer fills a box completely before filling the next box, what fraction of the last box will be empty?

Answer: So, you have 16 trays of hot food, and each box can have a maximum of 5 trays.a) if each box can have 5 trays then:1 box can delivery 5 trays, that is not enough.2 boxes can delivery 10 trays, that is not enough3 boxes can delivery 15 trays, almost, but not enough4 boxes can delivery 20 trays, this is it!You also can see it in the next way: 16 trays/5 trays per box = 3.2 boxes.But you can't use a 0.2 of a box, so here we need to round upwards!3.2 rounded upwards is 4.b) If you have 4 boxes, then you have 20 spaces for trays.if each box is filled, you will put the first 15 trays in 3 boxes and fill them, and one leftover tray will go in the fourth box.so this last box has one of five trays, this means that has 4 slots empty.then the empty fraction is the empty slots divided by the total number of slots, this is: 4/5.