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.

Choosing Ringbearer Gifts Does Not Have to Be A Bear

The significance of wedding rings is best illustrated in people's fear of losing them. There are people who boast of having never removed their wedding ring since their wedding day, though this is sometimes due to changes to their weight since they said, "I do." But really, how important are wedding rings? Moreover, how many times have we heard of what a nightmare it is to lose your ring? We hear stories of people losing their rings in the labyrinth of pipes underneath the kitchen sink. Then, there was the movie "American Wedding," in which wacky Steve Stiffler accidentally feeds the bride's wedding ring to a dog. Clearly, wedding rings are very important. Consequently, even though the ringbearer is one of the shortest members of the bridal party, his is the task of the tallest order. So, when you choose ringbearer gifts, keep in mind the critical role that your ringbearer plays.

The Ringbearer
The use of ringbearers is fairly modern. They tend to be young brothers or nephews of the bride or groom, and usually range in age from 5 to 10. In weddings that are formal, the ringbearer, or pageboy, has one of two different functions. First, the ringbearer might carry the bridal party's rings on a huge white satin pillow. Boys will be boys, and almost anything could happen during his waddle down the aisle. Usually, the best man himself secures the rings, or thread is used to attach the rings onto the ringbearer's pillow.

Another function of the ringbearer is to carry the bride's train, if it is lengthy.

The Basics
Whether the ringbearer totes the rings or holds the train, make him feel special through your choice of ringbearer gifts. For example, consider what your ringbearer likes. Here are some ringbearer gifts that might ring well with him.

Ring Bearer Fun Box Gift: This is decorated to look like a Ringbearer's tuxedo. Inside it is fun games, cookies, and candies.

Ringbearer Baseball Cap: This will remind the boy that he was in the starting lineup of the wedding ceremony.

Space Magic Cookie Pot: This is a bouquet that is packed with cookies and candies. What kid says no to sweets?

Ringbearer Activity Tote Bag: This is a fabric bag with several gift items inside.

Personalized Gifts
Aside from the obvious height difference, kids and adults are not too different from each other. Like adults, kids want to feel special, too. Personalized ringbearer gifts help you do just that. Here are a few personalized ringbearer gifts to consider.

Personalized Baseball: This will make any little leaguer feel like a big leaguer. The ball is mounted on a walnut-finish stand.

Ringbearer T-shirt: This will let your mini lord of the rings remember the special day. How could he not with his name is printed on the shirt?

Personalized Silver Plated Yo-Yo: Give a new twist to the old toy! Each time your ringbearer uses this ringbearer gift, he will remember his walk down the aisle.

Being the ringbearer in a wedding can be daunting for any youngster. Help your ringbearer enjoy the task by giving him a well-thought out ringbearer gift. Carefully chosen ringbearer gifts will make your wedding day one that will always ring a bell in your little ringbearer's mind.

Dedicated Hosting Servers – Choosing the Best

What are dedicated hosting servers?

Dedicated hosting servers, as the name implies, are servers leased to a single client and not shared with any others. In other words, if you were to sign up to a dedicated hosting plan, the server would be devoted and committed entirely to hosting your websites.

Why should I use dedicated hosting?

Dedicated hosting has a variety of advantages over shared hosting, particularly if you plan to run an ecommerce website or if you prefer a high level of control over resources.

The key advantages can be briefly summarised as follows:

  • CONTROL: over operating system and software applications
  • RELIABILITY: Reliability: quicker server response time and better performance as the server is not taxed by sharers
  • SECURITY: extremely high security is provided and you can implement your own security measures
  • RESOURCES: greater bandwidth available, ideal for high traffic and resource-intensive websites

What do I need to use dedicated hosting?

MANAGEMENT SKILLS

Although dedicated web hosting gives you the opportunity to fully manage your server, web hosts will provide varying levels of management for you, depending on your host and plan. In these cases, you will not need a high level of management skills.

FINANCES

Expect to pay more for dedicated web hosting that for shared.

What should I look for in a dedicated server?

RAM

It is crucial to have enough RAM. You should aim for at least 2 GB of RAM and the more the better. The number of concurrent users able to visit your site will be greatly affected by the amount of RAM you have. If you do not have enough RAM, under a significant load from a number of simultaneous users accessing your site, your site will crash (i.e. the Slashdot effect). This can particularly be a problem if you have database driven applications.

PROCESSOR

Choosing the best processor for your needs is also important. Intel Xeons and AMD Opterons are the current standard in server CPU architecture. Other CPUs are most likely outdated or are standard desktop CPUs and may not perform as well as the former under a significant network load.

DISK SPACE

Choose a plan with the amount you will need. Unless you will be serving up file and data archives and/or audio and video content (i.e. streaming media, mp3 downloads, etc) then disk space should not be a concern as all plans provide more than adequate amounts of disk space (e.g. 250 GB+). If you anticipate expansion, look into the flexibility of upgrade options.

BANDWIDTH (Monthly Transfer)

Look for 1000-2000 GB+, depending on your needs.

DATA CONNECTION SPEED

Look for 1000 Mbps, particularly if you are streaming video or have a large number of concurrent users. Otherwise 100 Mbps might suffice.

OPERATING SYSTEMS

Look for which are offered and what costs are involved. Many Linux distributions and BSD systems are available for free from the open source community, while Microsoft Windows Server involves a cost. Expect operating system updates to be provided.

MANAGEMENT / EASE OF USE

Look for how much management is included in the plan price. For ease of use, look for free inclusion of cPanel (web based administration). Look for hosts supporting server configuration, software, application, security and anti-virus updates, firewall services and monitoring. Be wary of the term “fully managed” as this means different things to different hosts. Investigate thoroughly.

SOFTWARE

What options do you have? What is included? Microsoft products? Look for control panel software.

SUPPORT

Look for 24 hours a day, 7 days a week, 365 days a year phone / email technical support.

BACKUP AND RESTORATION

Look for what backup and restoration options are provided. Some plans come with two hard drives, allowing an easy back up solution.

IP ADDRESSES

Look for more than one, particularly if you plan to do ecommerce.

UPTIME GUARANTEE

Look for hosts guaranteeing 99.9 to 100% uptime and find out their compensation if it is not reached.

WEB HOSTING PRICE

Find out if there is a setup fee. Expect to pay $200+ per month for hosting.

Who provides top rated web hosting?

No doubt you will read different opinions in different places, but based on the criteria outlined above, I have identified a few stand-out dedicated web hosts with excellent reputations for quality and reliability. You will find details of these hosts at Web Host Choice [http://webhostchoice.info]

What Are the Top 10 Tips for Small Business Branding?

Managing a business is not an easy job but promoting your business may be as hard as anyone else could ever imagine. And some small business owners thought that they have only limited things in order to manage and promote their business then they are definitely wrong. And some think that branding is for big businesses only then I will prove you wrong. And despite the business size, branding can be as effective as it can be. Here are the top 10 tips for small business branding.

The first one is to focus on the thing that you would like to establish, people won’t be attracted if you promote everything and anything under the sun, being an expert on one thing is what matters the most for the clients, making clients confused can never be a good idea, make them think on one important thing that stands your business.

The second one, is consistency on your performance. No one would love to patronize a company that doesn’t have consistency on its performance or on its quality. If you commit something to some clients, make sure you’ll do it, first impressions really lasts so better make sure to impress them positively and maintain it in order for you to have their loyalty.

The third one is to make an overview of your business at least on a one page document, letting them know how your business is running and what are your goals, mission and vision are very important tools in achieving for their approval, just be sure to make it brief and concise, no one will last if you write on plenty of flowering words, better to put on true informations.

The fourth one is, good treatment between you and your employees and between clients and employees as well, nothing can beat that.

The fifth one is, to remember that branding needs straight direction and longer maintenance and that there should be straight connection between the actual and the desired image.

The sixth one, join locally organized events and be one of the committees, it’s a good way to establish your image and business.

The seventh one is to blog, blogging is one of the great tools in establishing your business, making other people have an idea about it.

The eight one, you don’t have to depend everything to your logo, logo doesn’t make up the whole part of the business, so never spend too much time and effort on it, its just a part of the business.

And having your own company website is on the ninth place because obviously almost all people uses web, and the last one is not to depend too much on blogs, you must explore more over.

That’s the top 10 tips for small business branding Just don’t be afraid to give a try and to plan big for your business. And searching for branding tips can be easily done when you are eager to do it.