Proving Proportions, Problematic Products
(A new question of the week) A recent question provided an opportunity to examine some ideas about ratios, and also ways to tame a potentially huge product.
Multiplying Vectors I: The Scalar Product
Having covered the basics of defining and adding vectors, multiplying by scalars and finding unit vectors, it’s time to look at multiplying vectors together. What makes this entirely unlike working with numbers is that there are two ways (in fact, more than two!) to multiply two vectors. We’ll look at one of those today, the …
Vector Basics: Describing Directions
We’re looking at the concept of vectors at an introductory level. Last week we looked at how they are defined in this context (as quantities with magnitude and direction), and how they are added (which is really part of the definition). Our collection of answers from Ask Dr. Math this time focuses on the ideas …
A Rate Problem: Two Speeds, Two Ways
(A new question of the week) A question we got at the end of March asked about a standard kind of algebra word problem that can be solved in a couple very different ways. It illustrates several choices that can be made (both about the meaning of the problem and how to solve it), as …
Vector Basics: Adding Arrows
Because we have had a number of questions about vectors recently, I thought it might be time to look at various facets of that topic. Here, we will start with some ideas about what vectors, and their most basic operations, are. Next week, we’ll get into the far more interesting topic of multiplying vectors.
Angle Between Vectors: A Tricky Problem
A new question of the week We haven’t done much with vectors here, though there have been many problems of that sort lately. Let’s look at a recent question that touches on the basics, yet is by no means a simple problem.
Decimals, Commas, Thousands, and Lakhs
I’ll finish this series on place value and writing numbers, with a question that’s not quite as simple as you might think: why we use commas and decimal points as we do. Americans may be surprised at some of the answers – and some of the questions.
Decimals in Word Form: Subtleties
Last time we looked at how to convert a number between decimal and word form. Now we’ll move into some tricky cases such as where to use “and” or a hyphen, to eliminate ambiguity.
Decimals in Word Form: Basics
We’ve been looking at the place value concept, and writing number in expanded form(s); but how about the word form of decimals? This can be confusing at several points. We’ll start with reading a number and writing its word form, and then do the reverse.
What is Expanded Form?
A concept regularly taught along with place value is “expanded form”, a way to write a number that displays each place separately. As we’ll see, there is considerable variation in terminology here, so parents may have to check what form a teacher wants, rather than look it up and expect a single answer!