Fractions and Rational Numbers – What is the Difference?

Most of us go through years of school math courses and still are confused about some basic things. For example: Why can not you divide by zero? Why is .999 … equal to 1, and not a bit less?

There are loads of these kinds of questions, that would not be a cause of frustration at all, if they were taught reasonably and clearly.

Unfortunately most of these things are supposed to be covered in elementary school, and most elementary school teachers do not have a good understanding of basic math concepts. Instead they are supposedly to teach just a collection of "skills."

One of the simplest concepts that is usually left inadequately explained is the difference between fractions and rational numbers. Let's see if we can clear it up now.

A fraction is a number that expresses part of a whole as a quotient of integers (where the denominator is not zero).

A rational number is a number that can be expressed as a quotient of integers (where the denominator is not zero), or as a repeating or terminating decimal. Every fraction fits the first part of that definition. Therefore, every fraction is a rational number.

But even though every fraction is a rational number, not every rational number is a fraction.

Why? Consider this:

Every integer (all the whole numbers, including zero, and their negatives ….- 3, -2, -1, 0, 1, 2, 3 …) is a rational number , because it can be expressed as a quotient of integers, as in the case of 4 = 8/2 or 1 = 3/3 or -3 = 3 / -1 and so on. So integers such as 4 or 1 can be expressed as the quotient of integers.

But an integer is not a fraction . 4 is an integer, but it is not a fraction. 4 is not expressed as the quotient of integers. The difference here is in the wording.

A fraction is a number that expresses part of a whole. An integer does not express a part. It only expresses a whole number.

A rational number is a number that can be expressed as a quotient of integers, or as part of a whole, but fraction is a number that is (must be) expressed as a quotient of integers, or as part of a whole – there is a difference. The difference is subtle, but it is real.

There are slightly different variations of the definition of a fraction, including, "A fraction is the ratio of two whole numbers, or to put it simply, one whole number divided by another whole number."

That definition also shows that an integer is not a fraction, because an integer is not a ratio. It can be expressed as a ratio, but it is not a ratio in itself; it can be divided by another whole number, but it i s not being divided.

In a nutshell, the fractions are a subset of the rational numbers. The rational numbers contain the integers, and fragments do not.

Technical Writing – How to Write Project Justification Documents

As part of building the overall project scope a technical author will first need to lay out the justification documentation. This document which can also be considered a “business case” lays out the fundamental reasons for implementing the project. Here’s a simple guide on creating a project justification.

State the Problem

Businesses don’t carry out projects for fun; they perform them in order to solve a specific issue or issues. You need to describe the problem clearly and accurately at the start of your document so that you can then present the solution to that problem.

For example if you intend to implement a new HRMS (Human Resource Management System) your problem may be; “The HR team currently spends nearly 80% of its time on non-productive administrative tasks, reducing the effectiveness of the function dramatically.”

State the Solution

This should be a simple statement to define your project. This enables your reader to understand what it is you’re proposing.

“We intend to implement an automated HRMS system to reduce manual administration by half.”

Supply Supporting Information

The problem and solution aren’t going to justify your project to the stakeholders and decision makers, so you need to provide the right level of information to enable them to support your recommendation.

Examples of the kind of information you should use:

  • Market Demand – Not always the strongest argument, but if you can show that all your competitors are implementing similar systems, it certainly suggests that it may be worth considering in your organisation.
  • Business Need – In this example the business need is clear, the HR team are spending the majority of their work time on non-specialist tasks and that costs money.
  • Customer Demands - what is it that your customers are screaming out for? Don’t forget to include internal customers as well as external ones.
  • Technological Progression – what’s going on in the world around you, is there are compelling case to be told in terms of the way IT and systems are developing?
  • Legal – Don’t forget the all important obligation to the law, if you can show that your project brings compliance or makes it easier to comply with those requirements you have a stronger case.

Writing a business case or project justification is an essential part of the larger project scoping process. Ideally you should write this early in the lifecycle of your project to help you obtain funding and support. You will also then be able to clearly identify the objectives of your task so that team members have a clear message to take away.

Culinary Arts Education – Degrees For a Job in the Hospitality Industry

There are many people that dream of a career in the hospitality industry and the most popular job is, of course, the head chef. To attain this role within a quality restaurant you will need to go through a culinary arts education course that will prepare you for working as a professional chef. These courses include the actual hands on preparation of food as well as the theories and lessons you will need to work in the industry. The courses run for anywhere from three to five years and even longer in you choose to complete a double degree.

There are many schools offering culinary education including everything from local community colleges through to world class cooking schools such as Le Cordon Bleu. Most of these schools offer professional degrees in culinary arts and will provide you with an opportunity to get a great job in the industry. However, it is more than likely you will need to get experience as an assistant, or sous chef, before you will be promoted or offered a job as a head chef. Like most other graduates you will need to make your way up the industry until you reach the top.

It is important to compare the different culinary arts education courses that are offered. Consider that some of the courses will not offer a formal degree so it is a good idea to put plenty of research into your decision. Create a short list of schools as it is a good idea to apply to more than one school in case you are not accepted by your first choice.

Old School Online Gaming

Ever wondered what your parents and the adults played for fun back in their day? Or before the existence of Nintendo Wii's, Playstations, and World of Warcraft, what were the games that people played with the computer? Online gaming back then was not as high-tech as what you play now but they delivered the same amount of fun that today's online games give you. Take a journey down old time geekery and see what was deemed as hi-tech back then:

1. # TradeWars 2002
A space game developed in 1984. In TW2002, the player is a galaxy trader where the main objective is to gain control of a limited set and amount of resources, as you travel in different sectors of the galaxy. Using your earned wealth in trading, you can upgrade your spaceship, get better weapons and fight for control of planets and starbases.

2. # MUDs
Also known as Multi-User Dungeon, this is a text-based multiplayer real-time virtual world that started in 1978. It combined elements such as role-playing games, hack and slash, player versus player, interactive fiction, and online chat with a fantasy setting populated by fictional races and monsters. The objective of the game is to slay monsters, explore a fantasy world, complete quests, go on adventures, create a story by role-playing, and advance the character.

3. # MUSHes
MUSH, generally called a Multi-User Shared Hallucination, is somewhat of a text-based Second Life where you can create anything you want, be anyone you want, and do anything that you want in a multi-user game. With the popularity of MUDs in the 1980s, many variations emerged such as TinyMUD in 1989. MUSH was then created by Larry Foard who used TinyMUD's code and added a different programming language.

4. # Hunt
The old school Before Doom, created in 1985 by Conrad C. Huang and Gregory S. Couch, is represented using ASCII characters on an 80×24 terminal screen. Hunt is a multiplayer game where each player wanders around a maze, killing off other players using guns, bombs, and slime. Players can also form a team. The maze, when destroyed, regenerates over time, during which "deflectors" appear, changing the direction of the projectile. Sometimes a "wandering bomb" appears, exploding when contact is made.

5. # Empire 3.84
Considered as the grandfather of all Internet games, Empire 3.84 is a risk-like conquer-the-world game with its original version appearing in 1971 on a PDP-11/45 mainframe computer at Harvard University. It gained popularity for being cited as one of Sid Meier's inspiration for Civilization PC game series.

6. # BBS Door Games
Since the technology in the old days was pretty much text-based, online games back then usually were also text-based games played over the modem on an amateur-run bulleting board system (BBS). Supporting only one phone line, there was not WiFi back then, so players usually had to take turns when playing, but still they can compete against each other.

7. # FIBS
The First Internet Backgammon Server pretty much tells us what it is, it's the first backgammon server on the Internet. Started in 1992, it has become one of the most popular online games to play backgammon against other players around the globe.