We can use signed numbers to represent time relative to a chosen point in time. We can think of this as starting a stopwatch. The positive times are after the watch starts, and negative times are times before the watch starts.

Three points are labeled on a number line. The numbers negative 10 through 10, in increments of 1, are indicated. A dot at negative 4 is labeled "4 seconds before the start time". A dot at 0 is labeled "start time". A dot at 7 is labeled "7 seconds after the start time".

If a car is at position 0 and is moving in a positive direction, then for times after that (positive times), it will have a positive position.

Number line. 7 evenly spaced tick marks. Scale negative 15 to 15, by 5's. Three equal sized arrows pointing to the right, one from 0 to 5, 5 to 10, and 10 to 15.

$5 \boldcdot 3 = 15$

For times before that (negative times), it must have had a negative position.

A blank horizontal number line from negative 15 to 15 by 5’s. Above the number line with three arrows pointing right and a dot are plotted. The first arrow points from negative 15 to negative 10. The second arrow points from negative 10 to negative 5. The third arrow points from negative 5 to 0. A dot is above 0.

$5 \boldcdot \text-3 = \text-15$

If a car is at position 0 and is moving in a negative direction, then for times after that (positive times), it will have a negative position.

A blank horizontal number line from negative 15 to 15 by 5’s. Above the number line with three arrows pointing left and a dot are plotted. The first arrow points from 0 to negative 5. The second arrow points from negative 5 to negative 10. The third arrow points from negative 10 to negative 15. A dot is above 0.

$\text-5 \boldcdot 3 = \text-15$

For times before that (negative times), it must have had a positive position.

A blank horizontal number line from negative 15 to 15 by 5’s. Above the number line with three arrows pointing left and a dot are plotted. The first arrow points from 15 to 10. The second arrow points from 10 to 5. The third arrow points from 5 to 0. A dot is above 0. 

$\text-5 \boldcdot \text-3 = 15$

Here is another way of seeing this:

• A positive number times a positive number always results in a positive number.
• A negative number times a positive number or a positive number times a negative number always results in a negative number.
• A negative number times a negative number always results in a positive number.