Dividing Decimals: How and Why

Arithmetic / December 19, 2024

We have looked at how we add, subtract, and multiply decimals. Now we’ll conclude with division: what we do, why we do it, and how we don’t really need to do it that way.

Multiplying Decimals: How and Why

Arithmetic / December 13, 2024

We’ve looked at how to add or subtract decimals. Now let’s move on to multiplication; we’ll look at three answers to the same sort of question.

Ratios and Areas: An Unusual Pie Chart Problem

Geometry / November 28, 2024

Here is a short problem with several levels of difficulty. The problem itself is poorly designed, as we’ll see, but still provides several useful lessons, dealing with measurement, rounding, and ratios.

Solving Equations with Newton’s Method

Calculus / November 22, 2024

Last time we solved some of the equations connected with a segment of a circle using Newton’s Method. Let’s take a closer look at the method – how it works, why it works, and a few caveats.

Proving a Radical Expression Is Rational

Algebra / October 17, 2024

It can be tricky deciding how to approach a proof; this problem, whose answer requires going in a very different direction than you might expect, provides some interesting insights into the nature of proof. The proof itself, in fact, is far less interesting than the process of getting there!

Turning a Maximization Problem Inside-Out

Calculus / October 10, 2024

Here is an interesting question we got recently, that turns a common maximization problem (the open-top box) inside-out. What do you do when you’re given the answer and have to find the problem? We’ll hit a couple snags along the way that provide useful lessons in problem-solving.