Back in the 1960s, Popular Science frequently included inserts focusing on topics of interest to their readers.

Since this was a science magazine in the days before pocket calculators were common, there were many times that the inserts focused on making mental calculations easier. Thanks to Google books, these are available once again!

Our first jump takes us all the way back to the January 1961 issue, which features excerpts from Lester Meyer's book, High Speed Math. The great body of the 14-page book digest focuses on shortcuts for multiplication, but towards the end, there are tips about addition, subtraction, division, and knowing when to use given shortcuts:



Later that same year, in November, they returned to this idea with an insert called “Math and Memory Short Cuts”. This particular book, for some unknown reason, was scanned in reverse page order. Despite that minor flaw, the insert is still readable. Instead of straight math shortcuts, this insert focused on math and memory techniques that were handy in the home workshop.



Popular Science returned to pure math shortcuts in December 1964, with their book digest of Isaac Asimov's Quick and Easy Math. This 7-page feature was arranged in the more traditional order of tips for addition, subtraction, multiplication, and division. If you're only familiar with Asimov's fiction writing, you might be surprised at the clarity he can bring to instructional writing:



Our final insert comes from the March 1967 issue, in an insert titled “High-Speed Math Short Cuts” This one is dedicated almost entirely to quick multiplication and division techniques, including a handy reference table giving the results of 1000 ÷ n for every integer n from 1 to 999, plus tips on using the table to handle larger numbers!



Obviously, these techniques were far more essential in the days before pocket calculators were common. However, the techniques are still useful, so they're fun to explore. You never know when and where you'll find that perfect shortcut for frequently-encountered problems!