(A new question of the week) Last time we looked at a classic problem for which there is a nice formula, namely counting all divisors of a given number. This time, we will examine a question from last August where we have to count the number of divisors of a specific type, making it more …
How many divisors (also called factors) does a number have? We’ve answered many questions about that over the years, sometimes by just guiding a student to discover it, sometimes either deriving the formula for them or just showing and using it. Let’s look at a few.
Last week we looked at some questions that arose leading up to the year 2000, triggered by the 20th anniversary of that event. Now we’ll start from a different question about that year, to look at the story of leap years.
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 …
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 …
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 …
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 …
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 …
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 »