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 »
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!
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.
(An archive question of the week) My title is tongue-in-cheek, as we’ll be looking at the Chinese Remainder Theorem, which is really a Chinese theorem about remainders, not a theorem about “Chinese remainders”. But we’ll work on a problem that can be solved with or without knowledge of the theorem, and with various doses of …