The next topic in our survey of fractions is the fact that two different fractions can represent the same number – that is, they can be equivalent, though they are written differently. At first, this may seem strange to students: the number 5 only has one “name”, so why should 1/2 and 2/4 be different …
Last time we looked at what improper fractions (and, to some extent, mixed numbers) are. There are many situations where we need to rewrite one of these forms as the other – mixed numbers are most convenient for talking about numbers in real life, while improper fractions are easiest for doing operations like addition. Let’s …
Improper Fractions and Mixed Numbers: Converting Read More »
In working through topics pertaining to fractions, I find that questions about improper fractions are common. Today we’ll look at questions about the definition of the term, and next time we’ll move on to mixed numbers and how to convert between the two forms.
Last time, we looked at what fractions are, and saw that fractions and decimals are two different ways to handle numbers less than 1 (or between integers). Here, we’ll look at several questions about why we need both forms, and whether one is better than the other. The comparison and contrast turns out to be …
We’ve looked at some specific ideas about fractions (their proper definition, their relationship to decimals, and how to divide them); it’s time to go through this topic from the beginning. Here we’ll look at how they are introduced to beginners, and how to keep them from hurting our brains!
(A new question of the week) A few months ago, I wrote about Ranking a Word Among Its Permutations, that is, finding where a word would be found in an ordered list of all possible “words” made by permuting its letters. The problem in general requires a (sometimes lengthy) algorithm. A month or so later, …
Last time, we looked at the basic definition of independent events. This time I want to explore some deeper questions about the concept.
The concept of independent events can be both very simple and easily misunderstood. We’ll be looking at several explanations of the idea, starting with the basics and then digging into some deeper questions that are often overlooked.
(An archive question of the week) We’ve been looking at some issues involving frequency distributions and the classes used in them. Let’s look at a related concept with some similar issues, namely the cumulative distribution function (CDF), also called an ogive (more on that name at the end of the post!).
(A new question of the week) A recent question raised a different issue about grouped frequency distributions than we have discussed previously: What do you do when the last class is labelled something like “30 or more”? As we’ll see, there is no one right answer!