Problem $1\mathrm{.}4$

The modulo operator is useful for values that loop through a fixed cycle $($like the days of a week or the

minutes in an hour$).$ Consider an elapsed time of $t$ seconds. We may want to display this as $m$:$s,$ where

$m$ is the integer number of minutes and $s$ is the number of seconds Come up with

expressions for $m(t)$ and $s(t)$ that calculate these values.

Test your expressions by calculating them for tin$\{3\mathrm{.}5,120,185,3610\mathrm{.}5,41038\mathrm{.}13\}$ seconds.

Optional challenge: Try doing the same for $h$:$m$:$s,$ where $h$ is the integer number of hours and where

Problem $1\mathrm{.}5$

A classroom has $30$ numbered seats arranged in six rows and five columns as shown.

Col. $1$ Col. $2$ Col. $3$ Col. $4$ Col. $5$

For any given seat $n,$ come up with:

a$)$ An expression $R(n)$ that calculates the corresponding row number,

b$)$ An expression $C(n)$ that calculates the corresponding column number.

Test your expressions by calculating $R(n)$ and $C(n)$ for nin$\{1,4,5,14,25,26\}.$

Hint: Try subtracting $1$ from each seat number then dividing by the number of columns. What do you

notice about the results?