Month: September 2019

Order of Operations: Why?

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 …

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Order of Operations: Trigonometric Functions

(An archive question of the week) Last time we looked at some details that are rarely mentioned in stating the conventions for interpreting algebraic expressions. I couldn’t fit a discussion of the most complicated case: trigonometric functions, which when written without parentheses, as they traditionally have been, can raise several issues. (Much of the same …

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Order of Operations: Neglected Details

The basic statement of the order of operations covers the five main operations (exponents, multiplication, division, addition, and subtraction). But what about other operations like square roots? How about trigonometric functions? And are operations at the same level always carried out left to right? Here are some questions about the details we don’t often mention.

Order of Operations: Common Misunderstandings

Last time I started a series looking at the Order of Operations from various perspectives. This time I want to consider several kinds of misunderstandings we often see.

Order of Operations: The Basics

The order of operations in algebra (also called operator precedence) is a very common source of questions; I count at least 50 archived discussions explicitly about the topic (not just mentioning it in passing), in addition¬†to the Ask Dr. Math FAQ on the subject.¬† I’ll devote the next few posts to looking at various aspects …

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Perimeter Magic Polygons

Last time we looked at the classic puzzle of magic squares. Many questions we get are about similar kinds of puzzles, and here I want to look at “magic polygons” (triangles, squares, pentagons) in which, unlike the traditional magic squares, only the edges count. These are a common subject of elementary-level questions.

Magic Squares: Logical Thinking

I’m looking at various common puzzles, and ways to think about them logically. Today, we’ll examine basic magic squares: not the standardized methods you can look up, but how a kid can work them out when seeing them for the first time. Often they are not even told they have a name, so there is …

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Monkeys and Coconuts: Several Ways to Solve

Here is another puzzle we have received and answered many times. (I count 7 that have been archived.) It has several variations, which make it even more interesting. The story varies, too; sometimes the monkeys are the stars, other times they just get the leftovers. Someone could to an interesting folklore study on this one.