One way to demonstrate the product of to negative numbers is positive.

  • The fundamental idea is that a product can be illustrated by drawing each factor on two seperate number lines that intersect at a common zero point. The units on the two lines does not have to be the same. I have illustrated -3 and -2.

  • In order to multiply one of the numbers is connected to the unit on the other number line. In the illustration I have connected -3 to 1 on the other line.

  • By a translation by the vector from -3 to -2 this connector is parallel shifted from -3 to -2. In the illustration it is at the same time extende as I have just drawn line segments.

  • The result of the multiplication can now be read from the number line representing the last number; in the case -2. The result is 6 but the important is that it is positive.

  • That this always will be the case should be clear but if not you can study the two triangles that is in the illustration. They are similar. Click this to get an explanation

  • I have made an interactive version on Geogebra tube