Casting Out Nines: What and How

This old technique for checking arithmetic is both easy and hard to describe: easy to explain in advanced terms, but hard to explain in elementary terms. We’ll try to do it all here, but a fuller explanation of the “why” will come next week.

A Bad System of Nonlinear Equations

(A new question of the week) Sometimes a problem that looks complicated turns out to have a simple answer. And sometimes that simple answer turns out to be too simple for its own good. Today’s problem is an example of this.

Finding the Radius of a Sphere

(An archive question of the week) An interesting question came to us in 2016, where rather than using a well-known formula, it was necessary to work out both what data to use, and how to calculate the desired radius.

Challenging Rate Questions

(New question of the week) A conversation last week went through a number of interesting questions, starting with a couple on percentages, and moving into some that I would call rate questions. I will extract these, which I think will be useful for others. (The rest could, too, but there was just too much there …

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Rounding: Contextual Issues

Previously, I discussed how to round a number to the nearest whole number [or tenth, ten, etc.]. I focused there on what to do when you are simply told to do it — what “round to nearest” means, and how that determines whether you round a particular number up or down. I also pointed out …

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