# Month: June 2022

## Making Sense of Imaginary Numbers

Several recent questions (including last week’s post) involved complex numbers, and made me realize we haven’t yet talked about them here. So let’s start a series on the topic, beginning with how we talk about them to students who are just meeting the idea for the first time, or are troubled by it.

## Partial Fractions: Complex and Trivial Cases

(A new question of the week) We discussed four years ago how to make a partial fraction decomposition of a rational function, and why it can always be done; a question from mid-May brings up two side issues: when you can factor the denominator, and whether a trivial decomposition, which takes no work at all, …

## Abraham Lincoln and the Rule of Three

For the last two weeks, we have examined new and old waysÂ to think about proportions. This time, we’ll look at an old method called the Rule of Three (both “single” and “double”), and how you might have learned to solve these problems 200 years ago without algebra. Be prepared for a deep dive!

## Many Ways to Solve a Proportion

Last week we looked at a set of special rules for working with proportions, which have been largely replaced by the more general “tool” of algebra (the “Swiss army knife” of problem solving, which can do the job of many specialized tools), though the latter can still be useful. We still find that many students …