Problem

$1$

$.$

$4$

$$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

$$

$$seconds$.$ We may want to display this as

$$

:

$$

$,$

$$where

$$

$$is the integer number of minutes and

$$

$$is the number of

seconds

$($

$0$

$)$

$<=$

$$

$<$

$($

$6$

$0$

$)$

$.$

$$Come up with expressions for

$$

$($

$$

$)$

$$and

$$

$($

$$

$)$

$$that calculate these values. Test your expressions by calculating them for tin

$\{$

$3$

$.$

$5$

$,$

$1$

$2$

$0$

$,$

$1$

$8$

$5$

$,$

$3$

$6$

$1$

$0$

$.$

$5$

$,$

$4$

$1$

$0$

$3$

$8$

$.$

$1$

$3$

$\}$

$$seconds$.$ Optional challenge: Try doing the same for

$$

:

$$

:

$$

$,$

$$where

$$

$$is the integer number of hours and where

$0$

$<=$

$$

$<$

$6$

$0$

$.$

$$Problem

$1$

$.$

$5$

$$A classroom has

$3$

$0$

$$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

$$

$,$

$$come up with: a

$)$

$$An expression

$$

$($

$$

$)$

$$that calculates the corresponding row number, b

$)$

$$An expression

$$

$($

$$

$)$

$$that calculates

the corresponding column number. Test your expressions by calculating

$$

$($

$$

$)$

$$and

$$

$($

$$

$)$

$$for nin

$\{$

$1$

$,$

$4$

$,$

$5$

$,$

$1$

$4$

$,$

$2$

$5$

$,$

$2$

$6$

$\}$

$.$

$$Hint: Try subtracting

$1$

$$from each

seat number then dividing by the number of columns. What do you notice about the results?

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