We’ve been celebrating a new year with some examination of dates: the fact that 2020 is a new decade (sort of) and a leap year (definitely), and now, some details about how the whole Gregorian calendar works. Some of this is collected in the Ask Dr. Math FAQ on The Calendar and the Days of …
(A new question of the week) We had a long discussion last August about domain and range of functions involving either quadratic functions or restricted domains (or both). Two Math Doctors got involved, offering different ways to approach the same problem. I’ve edited the discussion to avoid some intermingling of topics. A quadratic inequality Here …
(A new question of the week) A question from last August gave us some nice problems reminiscent of the Binomial Theorem, which were very deserving of discussion. Three problems The question came from Arsh: I have some coefficient problems which I am unable to solve. I don’t know if a single concept will work for …
(A new question of the week) As we approach a new year, I want to start cleaning up a backlog of recent questions, and start posting more typical interactions, rather than waiting for the most momentous. Many of these will therefore be relatively short! This one goes back to last July, but it connects to …
To finish up this long series on the order of operations, I want to look at where the “rules” came from, which will also demonstrate why some aspects are not fully agreed upon, finishing up the discussion from last time. The “rules” are only descriptive First, here are a couple paragraphs from the 2017 answer …
I want to close this series with a topic that arises constantly, both in classrooms and on social media: How do you evaluate an expression like or , where the multiplication is indicated without a specific symbol? There are several reasons one might want to interpret this differently than the rule we’ve discussed, that multiplication …
(An archive problem of the week) Last time we looked at the subtle distinction between the order of operations, which defines the meaning of an expression, and properties that allow us to do something other than what an expression literally says. Here I want to look at one longer discussion that brings out these issues …
Order of Operations: Fractions, Evaluating, and Simplifying Read More »
Some questions we have been asked about the order of operations go beyond the what and why, pondering the relationship of the conventions both to theoretical matters (properties of operations) and to practical matters (evaluating and simplifying expressions). We will see here an important distinction between meaning and processes. PEMDAS vs properties, I: Meaning vs. …
Last time we looked at some questions about why we need rules for Order of Operations at all, with some hints in the answers as to why the rules we use make sense. This time I want to survey some deeper explanations. Why not just left to right? First, an overview of reasons for the …
Having looked at what the order of operations convention means, another common question is, why is it what it is? We’ll look at some basic ideas here, focusing on why we need a convention at all, and why the one we have makes sense; then next time we’ll dig in a little deeper, examining some …