## A Negative Times a Negative Makes a Positive Number

In high school we were introduced to negative numbers. Why high school? Why not earlier? Because we cannot picture in our minds what a negative number is. We know what positive numbers are. For instance, if we have three apples and someone gives us four more apples, we know we now have seven apples. And as to multiplication, if we have three groups of four three apples each, we know we have 12 apples. But can you visualize what a negative apple might be? How can you demonstrate negative times negative makes positive? Pure Numbers Forget units for the moment. We will concentrate on pure numbers. In the above example, the four groups of three apples becomes simply 4(3) = 12. Suppose, instead of 4(3) we make on of the…

## Mathematical Powers – a Simple Insight

[caption id="attachment_14363" align="alignright" width="380"] Squaring - the Power of 2[/caption] Multiplication is one of the simpler operations we perform on numbers. As kids we had to learn the multiplication tables, one times two equals two, two times two equals three, three times two equals six, and so forth. It didn’t take long before most of us were comfortable multiplying simple numbers. But sometimes we multiply the same number times itself. In that case, we can write out the multiplication in the usual way, or we can write it in terms of mathematical powers. Mathematical Powers – a Simple Illustration Let’s consider the example of three times three. That can be written either 3 x 3 = 9, or in powers notation, 32 = 9 This tells us three to the…