Let's look at it algebraically:
2n/(n - 1) can be divided (see image of long division)
--> 2 + 2/(n-1)
2 is always an integer
2/(n-1) is an integer when n = 3, 2, 0, -1

#TryMathLive #ProblemSolving

And on TW, Susan Russo used difference of two squares, which I hadn't thought of.
Cool!
https://twitter.com/Dsrussosusan/status/1628146466098188289?s=20

#MTBoS #iTeachMath #TryMathLive #MathEd #MathStratChat

I am happy with those 3 versions of mentally computing 83 x 97.

Please share your #ProblemSolving strategies here or on the post https://karendcampe.wordpress.com/2023/02/04/february-calendar-problems/

More #MathStratChat on Wednesdays from @pwharris
& mental math Mondays from @howie_hua

#MTBoS #iTeachMath #TryMathLive

Here's another multiplication using the area model to show double distribution.
Same four partial products as above:
80•90 + 80•7 + 90•3 + 7•3
Total = 8051

#MathStratChat #TryMathLive #MTBoS #iTeachMath #ProblemSolving #MathEd

How about decompose with a target number?

83 • 97
83•(100 – 3)
83•100 – 83•3
8300 – 249 [bc 80•3 + 3•3]
8300 – (250 – 1)
8300 – 250 + 1
8050 + 1 = 8051

#MathStratChat #TryMathLive #MTBoS #iTeachMath #ProblemSolving