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.

Tips For Weight Loss Reexamined

When you hear the word weight loss, the images you conjure up are giving up on food, skipping one meal in a day and trying to bury your hunger in whatever manner you can.

No longer are these true as a means of going for that weight loss you so desire. A lot of things have been redefined and re-examined in the weight loss arena and a lot of old theories of dieting and controlling your hunger are no longer valid. Come to think of these, a lot of these have been even dismissed by medical specialists as dangerous and unhealthy.

So what are your options if you want to lose weight? Well, if you have heard about stories of actresses going on a crash course diet and getting thin in ten days then you have only heard about one side of the story. There are stories which are not told that these actresses suffer from numerous health related issues because of their dieting binge or because of the rapid loss of weight. So better be careful if you are going to pursue weight loss that way.

Do not despairs as there are unhealthy and more meaningful ways of losing weight which will not take you down the unhealthy path. These tips for weight loss will help you lose weight in a manner which is also medically viable and can be sustained by the body. But the fact of the matter that the inner motivation still has to come from you.

The first foremost tip for weight loss is that you should drink lots of water. Drink eight to ten glasses of water everyday. This helps in two ways first you lose excess toxins from the body and secondly your metabolism rate go high. As a corollary to that since you have had so much water you will not be hungry as much as you were earlier. This should be your number one fad diet if you are a aficionado of fad diets that come and go every year.

The second tip is a combined tip of exercise and discipline. Exercise regularly and exercise smart. Never ever give up. They say a habit is formed in 21 days and that means for the first 21 days you should attend to be disciplined and will exercise regularly. After 21 days it will become your habit and then you should strive for more and more strenuous exercises each day. If you have issues going to the gym try using home based equipment like Wii Fit or Yoga at home or cycling at home for doing some exercises at home. Increase the difficulty levels and you will see weight loss happening.

Hopefully these tips will help you reduce significant quantity amount over a period of time. Remember there is no magic formula.

Instant High Paying Jobs For Teens

So you have a teen on the hunt for a half decent job but what are their options these days. Everyone is telling them to baby sit or get a paper delivery job but both are time consuming and pay third world country rates when it comes to money in their pocket. It is even harder trying to land a job position that has been advertised somewhere as employers receive hundreds and hundreds of applications when advertising in the current job market.

A recent study shown that it is now taking the average person 4 – 7 months to find new employment and they expect that period of time to lengthen substantively over the next few years.

So what can I do you say, well thanks to modern technology all this is about to change. The days of searching endlessly for employment are fast coming to an end as the internet slowly takes over and starts filling this increasing need in the teen job market. When it comes to jobs for teens it is now possible for them to land their dream job in under ten minutes no matter who they are. When they take a job online there are no lengthy, intimidating interviews to go through and their application is always accepted no matter where you live or what qualifications they may or may not have. When you compare this to the difficulty of applying for and getting a normal advertised job it is no wonder that thousands of teens are switching to paid online jobs.

Paid online work beats traditional jobs hands down every time. Online jobs these days mostly consist of completing online survey's as these are generally higher paying when it comes to the types of work you can do online and they make fantastic jobs for teens. Most of these places are free to join and once they have signed up they can then start taking surveys and get very well paid for it. Most teens that are doing these surveys are at least $ 10 for a twelve minute survey with the money getting transferred to their account on completion.

The surveys themselves are extremely easy to complete and there is an unlimited number of different types of surveys that can be taken. There are no set times that they have to work, teens can quickly and easily work at their own pace as often or as little as they like each week, it's up to them. By just taking 3 surveys per day, 5 days per week, a teen is capable of earning $ 150.00 per week. Just try finding a job anywhere else that pay's as well as this that will hire them instantly.

Which survey companies they end up joining makes a huge difference to how much money they make. Pick the wrong ones and they could end up working for $ 2 – $ 5 per hour and getting very frustrated. Out of all the "Free To Join" paid survey sites online today there are only a small list of survey companies that have the genuine higher paying surveys available on a daily basis. Joining all of these top 7 companies ensures that they have and endless supply of high paying surveys to take every day when they log in.

So the choice is up to them, with the state of the current job market are they going to keep blogging.

How to Choose Your Motorcycle GPS Systems

Location, location, location are not just words used in real estate. When riding your motorcycle it's a great idea to know where you are and where you are going. Global positioning systems or GPS have come a long way in the last twenty years in helping riders find their way along the highways and byways of traveling. Choosing the right GPS for your motorcycle can depend on what features you desire.

The physical dimensions of the GPS device can be up to 5.7 "x 4.2" giving you a large enough screen to view your roadway, directions, watch a video on screen, or just use the split screen to see your next turn. The buttons for almost anything you need are right there on your large screen. In case you want to find your location at the moment just go to the Menu. From there push the "Where Am I" button on the touch screen and you will be able to read your exact location.

GPS devices are generally pre-loaded with maps of the United States including all cities, towns, highways, and local points of interest. This allows the rider to find any destination, landmark, or address in the continental United States. To help with guidance GPS devices have voice control which allows you to talk to the GPS and ask for directions, turns, or the next filling station on your route. The device also gives you audible turn by turn.
instructions, highways intersections, distance to your turn, and what lane you need to be in to make your next turn.

Wifi capability is available if you need to make reservations at a restaurant, check your stock portfolio, or just look up a local movie theater. The Wifi feature also allows you to get the local weather and traffic information so that you can either get out of the rain if need be or detour around an accident in the road several miles ahead. The colorful touch screen can be a valuable benefit to you when trying to finding your way to local events, route planning, and uploading those points of interest you would like to see along the way.

To give you further enjoyment on your ride the GPS device has Blue tooth Stereo as an added feature. This allows for many hours of listening comfort while you ride. If you enjoy music as most people do you'll want to choose some of your own favorites. An MP3 player gives you the flexibility while you drive. You can easily hook into the side of the GPS with your jack and listen to your music or get directions to your brother's barbecue.

For most of us in today's market we would not want to be without our cell phones. Blue tooth technology has allowed GPS devices to have hands free phone service. Use the touch screen to accept a phone call and talk to the GPS device to find a number and make a call. Hands free phone service is easy and very versatile.

When you've reached your destination GPS device can be removed and used to find your way on that hike up the mountain and back. Your exact location where your bike was left can be found by easily using your touch screen and directions. Global Positioning Systems (GPS) are the best idea for the motorcycle rider.