It's certainly not an appropriate characterization to state "before the invention of calculators people did math using the "slide rule.""
The slide rule is a useful computing device. It still works just fine. I have quite a collection, since most folks don't know anything about them and they will sell them to me at a yard sale for 50¢. I like to keep one in my car, just to calculate averge speeds and average gas mileage. It's much less of a theft risk than a fancy calculator. Who would steal a slide rule?
The slide rule never was intended as a substitute for a brain, just like a calculator has no such design consideration. My mother consistently embarrassed her colleagues by calculating adequate approximations before the others found their slide rules.
The most interesting fact about slide rules, I think, is that it knows nothing of magnitude. It is the user's responsibility to keep track of the decimal.
Examples.
2*6 =
200 * 0.6 =
2000000 * 60000 =
0.00002 * 0.0000006 =
Slide Rule operation is EXACTLY the same for all of these problems.
