We can replace the idea of movement with stacked number lines and a slider.
You can think of this as two rulers. To represent \(a + b\text{,}\) slide the top ruler over by spaces, then move the slider to the position on the upper ruler. The value on the bottom ruler marked by the slider gives the result. Here is what \(3 + 4\) would look like.
Draw a stacked number line diagram to calculate \(3 + (-2)\text{.}\)
Although this may seem like an artificial construction, this idea basically mimics the way that calculations were done with slide rules. Unfortunately, there is one piece missing, which is the application of logarithms. And logarithms go beyond the scope of this course. But one of the core features of logarithms is that it converts multiplication into addition. And that is the trick that makes slide rules work.
Slide rules have been replaced by calculators, but it’s of historical interest that slide rules were the calculators of their day, which spanned from the early 1600s through the mid-1900s. Slide rules were phased out during the 1970s when pocket calculators started to become cheap enough for the average person to be able to purchase one.
