Combinatorics and Coefficients
(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.
2020 and the Y0K Problem
The arrival of 2020 has brought to mind the various controversies at the start of the year 2000, also called Y2K. As a software engineer responsible for date-sensitive communications within large computer systems, I well recall being on call that Saturday, in case something went wrong. I also recall all the questions we got in …
Does a Linear Function Have to be Continuous?
(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 …
One More Way to Find GCF and LCM
There are so many ways to find a Least Common Multiple that I had to omit one method we have been asked about several times. This one doesn’t require finding prime factors, but focuses on division by whatever factors you see. Divide everything by whatever works The first reference to the method I have found …
Many Ways to Find the Least Common Multiple
Last time, we looked at three ways to find a GCF (Greatest Common Factor). Here we’ll see the corresponding ways to find an LCM (Least Common Multiple); next time we’ll examine another method, which in its full form finds both at once. (Note that the Least Common Denominator of fractions is just the Least Common …
Three Ways to Find the Greatest Common Factor
Last time, we looked at simplifying a fraction, and the GCF (Greatest Common Factor, also called GCD for Greatest Common Divisor, or HCF for Highest Common Factor) came up. At the end I referred to a source for information about the Euclidean Algorithm for calculating it, and it seems fitting here to look at that …
How Do You Simplify a Fraction?
Last time we examined the basic concept of equivalent fractions – the fact that different fractions can represent the same value. We saw that there will be one way to write a fraction that is “in lowest terms” – no other fraction with the same value will involve smaller numbers, and all the others can …
How Do Equivalent Fractions Work?
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 …
Improper Fractions and Mixed Numbers: Converting
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 »
Improper Fractions: What Are They, and Why?
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.