A System of Exponential Equations
What do you do when you are given a problem that starts with a “lie” and ends with a wrong answer? We’ll go in several directions with this problem, a system of two exponential equations in two variables.
Rolling Dice: Three Probability Problems
Last week we examined three probability problems that had problems. Looking further back, I find that Jonathan, who asked the first of those questions, asked a group of questions about rolling multiple dice in 2022. They provide some additional lessons about easy mistakes to make.
How to Think Through Probability Problems
It’s been a while since we’ve looked at probability. Here, we’ll look at three questions that we received last year. In each case, we have to detect an error! They’re good examples of what can go wrong, and what to do when your answer appears to be wrong.
When Percentages Don’t Make Sense
Last week’s question led to a number of previous questions, which would have made it too long. Here we’ll look at the last couple references we gave, dealing with percentages of a negative base. This time, the problems will be mostly about money.
Percentage Change in Temperature?
Continuing to look at past questions that didn’t make it into the blog, I find a question about percentage change in temperature, which nicely ties together a couple older topics that have long been on my list to cover. Let’s do that now.
Fun With a Functional Equation
Looking back at interesting questions I had to skip over when there were too many to choose, I found this interesting discussion of a functional equation.
Trigonometric Equations: Finding All Solutions
A recent question dealt with how to write the general solution to a trigonometric equation. I want to combine that with an older question that will set the stage for the issue. This topic was touched on in Trigonometric Equations: An Overview.
Dividing Decimals: How and Why
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
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.
Adding or Subtracting Decimals: How and Why
Recently a teacher (Hi, Edite!) asked for help teaching how to divide decimals; in particular, she wanted to be able to provide a deeper understanding of the process, giving a good reason for what we do. Here I want to start a long-delayed series on operations with decimals, doing exactly this for all four basic …