Polly buys 14 cupcakes for a party. The bakery puts them into boxes that hold 4 cupcakes each.a. How many boxes will be needed for Polly to bring all the cupcakes to the party? Explain how you know.b. If the bakery completely fills as many boxes as possible, what fraction of the last box is empty? How many more cupcakes are needed to fill this box?

Answer:Part a) The number of boxes needed will be 4part b) The fraction of the box that is empty is [tex]\frac{1}{2}[/tex]Part c) Are needed 2 cupcakes to fill the last boxStep-by-step explanation:Part a) How many boxes will be needed for Polly to bring all the cupcakes to the party?To find out the number of boxes needed, divide the total number of cupcakes by 4 (maximum number of cupcakes that fit in each box).so[tex]\frac{14}{4}=3.5\ box[/tex]Round upThe number of boxes needed will be 4Part b) If the bakery completely fills as many boxes as possible, what fraction of the last box is empty?we know thatThe maximum number of cupcakes per box is 4The first three boxes have 4 cupcakes The last box has [tex]14-3(4)=2\ cupcakes[/tex]The fraction of the box that is empty is equal to the number of cupcakes missing to fill the box divided by the cupcake capacity of the box[tex]\frac{2}{4}=\frac{1}{2}[/tex]Part c) How many more cupcakes are needed to fill this boxSubtract the number of cupcakes in the box from the cupcake capacity of the boxThe last box has 2 cupcakesThe cupcake capacity of the box is 4so[tex]4-2=2\ cupcakes[/tex]thereforeAre needed 2 cupcakes to fill the last box