Model $2$ Dividing Numbers

Table A

$9/4$ evaluates to $2\mathrm{.}25$

$10/4$ evaluates to $2\mathrm{.}5$

$11/4$ evaluates to $2\mathrm{.}75$

$12/4$ evaluates to $3\mathrm{.}0$

$13/4$ evaluates to $3\mathrm{.}25$

$14/4$ evaluates to $3\mathrm{.}5$

$15/4$ evaluates to $3\mathrm{.}75$

$16/4$ evaluates to $4\mathrm{.}0$

Table B

$9//4$ evaluates to $2$

$10//4$ evaluates to $2$

$11//4$ evaluates to $2$

$12//4$ evaluates to $3$

$13//4$ evaluates to $3$

$14//4$ evaluates to $3$

$15//4$ evaluates to $3$

$16//4$ evaluates to $4$

Table C

$9\%4$ evaluates to $1$

$10\%4$ evaluates to $2$

$11\%4$ evaluates to $3$

$12\%4$ evaluates to $0$

$13\%4$ evaluates to $1$

$14\%4$ evaluates to $2$

$15\%4$ evaluates to $3$

$16\%4$ evaluates to $0$

Questions:

$9.$ For each operator in Model $2,$ identify the symbol and describe the type of numerical result.

$10.$ If the result of the $/$ operator were rounded to the nearest integer, would this be the same as the result of the $//$ operator? Explain how the results in Table A compare to Table B$.$

$11.$ If the table included more rows, list all numbers $//4$ would evaluate to $2$ and all the numbers $//4$ would evaluate to $4.$

$12.$ Based on the results of Table C$,$ propose another number $\%4$ evaluates to $0,$ and explain what all these numbers have in common.

$13.$ Consider the expressions in Table C that evaluate to $1.$ How do the left operands in these expressions $($i$.$e$.,9,13)$ differ from those that evaluate to $0?$

$14.$ Describe the reason for the repeated sequence of numbers $(0,1,2,3)$ for the result of $\%4.$

$15.$ Recall how you learned to do long division in elementary school. Finish solving for $79-$: $5$ below. Which part of the answer is $79//5,$ and which part is $79\%5?$

$16.$ Imagine that you are given candy mints to divide evenly among your team members.

a$)$ If your team receives $11$ mints, how many mints would each student get, and how many are left over? Write a Python Expression to compute each result.

b$)$ If your team receives $2$ mints, how many mints would each student get, and how many are left over? Write a Python expression to computes this result.

$17.$ Python has three division operators: "floor division", "remainder", and "true division".

Which operator $($symbol$)$ corresponds to each name?