# Fractions

## 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: 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. How can you have more than 9 ninths? First, here is …

## Fractions vs. Decimals: Pros and Cons

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 …

## Fractions: What Are They, and Why?

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! Parts of a whole Although, as …

## Order of Operations: Fractions, Evaluating, and Simplifying

(An archive problem of the week) Last time we looked at the subtle distinction between the order of operations, which defines the meaning of an expression, and properties that allow us to do something other than what an expression literally says. Here I want to look at one longer discussion that brings out these issues …