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?