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.

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Cheap Holiday Deals to Stalis Provide Perfect Holidays For All

Family holidays to Stalis are about as popular as couples holidays, beach holidays, 18 – 30′s holidays, and mature holidays to Stalis. In fact, it is difficult to find a group that can’t appreciate holidays spent in Stalis. Greek island holidays seldom have as much to offer visitors as you will find in the resort of Stalis-a resort that offers a little bit of everything you could possibly want from a beach holiday and a little bit more.

First of all, you should check out various package holidays to Stalis. You might be able to learn a little more about the possibilities that holidays to Stalis present for the entire family simply by taking in the long list of package options that are available to you. More importantly, in these economic times, packages are a great way to make cheap holiday deals to Stalis and other locations on Crete.

The nightlife in Stalis is rather lively though not nearly as dominating as the nightlife and club activities are in Malia. Stalis is a more well-rounded option for holiday fun than those resorts that are designed to appeal to party crowds or even those that attract more mature holiday crowds. What you have in Stalis is a healthy mix that makes it a worthy choice for family holidays.

The beaches of Stalis provide excellent opportunities for families that enjoy beach holidays and are content to spend the entire time on the beach. There is much more to this charming resort than a few beaches though so you don’t risk running out of things to do. Popular excursions to enjoy from Stalis include mini trains to Malia, boat trips to Santorini, and the traditional villages that can be found further inland. Greek island holidays are about experiencing the best Greece has to offer. Don’t miss out on the cultural treasure chest waiting for you away from the primary resorts.

Cheap holiday deals to Stalis are a great way to enjoy the very best of Crete. Don’t miss out on package holidays and prices that are lower in price now than they have been in years. Family holidays to Stalis may be the perfect way for you and your family to enjoy Greek island holidays. Make your plans today and you could be enjoying the beautiful views and gorgeous waters of Crete before you know it.

Fast Weight Loss Diets That Shrink Belly Fat

Getting a Firm Belly

A lot of importance is placed upon tight flat stomachs. Marketing campaigns are always promoting items that will accomplish this. Although many individuals want to lose their belly fat, due to appearances, one main reason to reduce this fat is your health! However, experts are now saying that it is okay to have a little fat, as long as you are not overweight.

Belly flab and high blood pressure, as well as high cholesterol, heart disease, and type 2 diabetes have been linked to belly fat. In order to be at no health risk, men should not have a waist measuring more than 40 inches, and women must have a 35 inch waist or less.

Below are some good techniques to help you reduce dangerous abdominal fat and get a firm belly:

· Exercise More, Eat Better

Calories do not have to be burnt at a gym or workout class; this can be done when you participate in everyday activities. For example, yard work burns several hundred calories per hour. Whereas organized sports, like football, burn even more. Another great activity to burn calories is swimming. Still another way to burn calories is to engage in walking.

Your fat-burning metabolism will kick into overdrive with Cardio exercise. All you need is persistence and perseverance; the trick is to find an activity you like. If you stick to it, the pounds will melt away. It’s also imperative to alter your routine to ward off boredom, as well as to get maximum calorie burning results.

In order to get a firm belly, there are different exercises that you can implement into your schedule. The American Council on Exercise did a study to find out the best types of exercise to incorporate into any weight loss program. Their findings included supine bicycle, captain’s chair leg lifts, and vertical leg crunches. These exercises are thought to work the abs more than any other exercises. Other good exercises include twisting crunches and exercise ball crunches. These activities should be done several times a week in order to obtain a slimmer waistline. Detailed step-by-step tutorials for each exercise can be found on the internet. However, if you are an outside person and your yard needs mowed, this activity will move all those muscles in the right way. However you must engage in this activity at least 20 minutes, non- stop.

Different foods can help you get a firm belly. Foods high in protein and fiber are slenderizing, however sugary carbs increase belly fat rather quickly. You should look for a diet consisting of complex carbs, unsaturated fats, and lean protein sources; a classic example is the South Beach diet. The diet solution has a high success rate and is a natural way of losing weight.

· Reduce Stress

The reducing of stress can be accomplished at the same time that you are losing belly fat. This can be done through the implementation of yoga. Yoga has a two-fold effect on our bellies, as follows:

1. It reduces stress levels. Stress very often leads to weight gain. Stress-induced weight gain often results in belly fat. In this way, stress reduction can give you a flatter stomach and at the same time, actually lower your risk for many diseases.

2. Yoga also tones the muscles in your stomach. A yoga routine that includes supine poses and other postures will work the abdominal muscles. You might want to check out a yoga DVD or video tape, or you can also try to go through some yoga tutorials.

All in all, it takes time and effort to get that dream belly, but it sure is worth it!

The iPhone 4 – New Features, New Design, Brand New All in One Gadget

The new iPhone is finally here. More technology packed then ever before, it sets new benchmarks for other mobile phones manufacturers that have been overwhelmed by the success of Apple's iPhone.

But I guess you're more interested in the features of then new phone rather than the impact it has on the business world so let me share with you the novelties it brings along.

Design:

The new iPhone is thinner, sleeker and better looking then its predecessors. The stainless steel looks good and refined giving it a more futuristic look. The metal buttons add to the overall feel of sturdiness without dramatically increasing the weight. It is heavier then the iPhone 3GS by only 0.1 ounces and it feels great in the hand.

Technology:

But the most obvious improvement is by far the new screen. The "Retina" is a 3.5 inch display which looks absolutely superb, mainly because its pixels are only 78 micrometers wide. It has four times more pixels then the previous version and it is by far the best display I have ever seen on a handheld device. The zoom is flawless and not a single bit of detail is lost in the process.

The "camera system" (as Steve Jobs called it) is comprised of a 5MP capturing device on the back and a VGA one on the front. The image can be shifted between cameras at any time during a video call. Apple calls this "Face Time" and although it has been praised by company officials it is pretty hard to believe it will revolutionize mobile communications or set a trend for other manufacturers to follow. It is undetected a clever feature but it is overshadowed by other technological marvels such as the flawless screen.

iMovie:

iMovie is an app that allows complex video editing like nothing I have seen before on a mobile phone. You can trim out a section of a movie, add a musical soundtrack to any clip, insert pictures in movies and many more. It costs $ 4.99 in the Apple applications store but it is really worth the money.

Conclusion:

The iPhone 4 is a great device with major improvements from the previous versions. Technology packed but also a looker it will unduly become a favorite among geeks and fashion savvy teens alike. A true all in one that certainly describes your attention.