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.

Why Holiday Villas Are Popular in Most Holiday Destinations

Holiday villas with swimming pools are becoming a very popular form of holiday accommodation with holiday makers going on a family holiday. You are now able to stay in a villa in most countries in the world.

These holiday homes are especially popular in countries with a warm climate. There is nothing better than sitting outside your holiday villa by the side of the swimming pool with a cool drink.

When choosing a villa for your vacation you need to consider very carefully what sort of holiday that you want. The first thing to consider is what sort of climate that you are looking for. There are typically holiday villas in most climates but there is a much greater selection of villa in the countries that have a warmer climate. You must decide how hot you want it to be and what time of the year you want to go away on your villa holiday.

Having decided on the climate, you must then look to see which country can offer you that climate on your vacations. Some countries may require you to get a visa to spend your vacations there and other countries that you consider for a villa holiday may require certain vaccinations before you go there. Then check how long it will take you to fly to your chosen destination and also if there are flights available.

Once you have done this you can start thinking about what sort of villa accommodation that you are looking for. There are some superb villas available around the world and they vary in price to suite just about every budget.

For holiday makers looking for a relaxing holiday by the beach it is possible to find some stunning villas with swimming pools right by coast. For families looking for a villa in the mountains there are also plenty to choose from with some offering spectacular views over the local countryside.

Most holiday villas have swimming pools. You must check to see if you want a swimming pool with your holiday villa and what size the swimming pool is. Many holiday villas also have outside barbecue areas and outdoor seating areas. In some countries that have mosquitoes you will find that some of the holiday villas have mesh screens around them to keep the bugs out.

It is possible to find holiday villas to suite almost every budget. There are some small two bedroom holiday villas and also some huge holiday home with seven or eight bedrooms. Some families like to go on a villa holiday by themselves and others like to stay in a larger holiday villa and take friends with them.

Atypical villa will have bedrooms with en-suite bathrooms. Typically the master bedroom or suite will be much larger than the other bed rooms in the villa. It will also have the best bathroom in the villa. Typically it will have a walk in shower, large bath and his and hers washbasins and a toilet. Above the washbasins will be a large mirror and below there will be plenty of storage space.

How To Search Google For Country Specific Results

Running an international online business with the capability to service people from any country means that you want your site to perform well not only in local country specific results but also global results. You may not realize this but doing a standard Google search and leaving the "full web" option selected does not necessarily give you your website's true location in the Google global results. It gives you the global results given your location.

For example, the results of doing a full web search in my home city of Brisbane Australia will be different to a full web search from Toronto Canada.

Google gives results based on your location even when you are not stipulating a local result. You can click your local country only result button and get sites that are from your home country, usually determined by the domain name extension, for example .com.au for Australia, .ca for Canada, etc. or the IP address of your web hosting server, or you can click the web option and get global Internet results that vary depending on your computer's location in the world (based on the IP address of the computer you are using to access the Internet).

Think Global

If your business can service the world then you really can not ignore the American marketplace, or if you are in the USA do not forget about Europe, Asia and the rest. Since you need to know how well your site is performing in Google global search results and unfortunately simply ticking the "the web" option in Google when searching can be misleading because your ranking will be different if it was someone in a different country doing the exact same search.

What you want to know is when someone in the UK does a Google search for one of your terms, how high is your website up in the search results? With this little trick you can figure it out.

The Code

All you need to do is add & gl = uk to the URL at the end of the Google search query.

For example:

http://www.google.com/search?hl=en&q=sample+query&meta= & gl = uk

This tells Google to spit out the results for the query based on UK servers.

I can not guarantee 100% conclusively that this works as I expect it does, but it definitely does something and you should try it yourself and see if your site shows up in a different place in the results. The "gl" stands for G eographic L ocation and of course you can exchange the last letters to test different country results around the world.

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.