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.

The Pros and Cons of Hiring a Real Estate Attorney

When one one gets involved in a property dispute in their city, why is it that the last resort happens to be the real estate attorney? Well, this is because most of the cases involve great professionalism and sometimes legal proceedings to help you get what you deserved, or protect you from the intricate lawsuits. While no property agent and adviser can guide you with total solicitation, the lawyer comes with greater benefits from all perspective. Every good thing has some flaws, and that goes same with the property lawyers as well. Let's find out what are the pros and cons of the real estate lawyers.

You can not be the master of all trades! No person is self competent to handle all the issues of his life, and especially when it comes in dealing with property related issues, which require higher professionalism, experience and legal expertise in dealing with the lawful proceedings. Moreover, you have higher chances of falling prey to the vandalism and deceit of the real estate agents. So, why do not you leave it to the more experienced ones, the real estate attorney!

Advantages of hiring the real estate lawyer

  • If you are a beginner, property dealing business can be quite complex and deceptive. You are unaware of most of the laws relating to the real estate industry, and various local laws. The property attorney comes as a rescue in guiding you with relevant solicitation. For all your property transactions and transactions, the lawyer will make you well versed in all the intricacies of the property business.
  • You are not an expert in understanding various terms, legal issues, nuances and intricacies of a purchase or sale contract. A lawyer helps in preventing you from blindly signing it without fully understanding the terms of contract. He prepares and reviews all the necessary property documentation on your behalf, and takes the necessary actions.
  • A large number of tax issues, environmental restrictions, condo association by-laws and other petty issues can make your property a deal into a distracting deal. A proper lawyer takes you out of such dungeon.
  • Helps you get the best deals and prices for your transaction. Protects you from fraudulent property lawsuits. If you get to purchase a damaged property without your prior notice, and if the seller is aware of it, with the help of your lawyer you can file petition against such lawyer and get restitution for such damage.

Disadvantages of hiring the real estate lawyer

  • Hiring a lawyer can involve higher service charges and contingency fees, adding an extra burden to you transaction.
  • Reliability and competency of a lawyer comes as a question. While all the lawyers would promise greater quality service and 100% success rate, the same may not be the case. You can end up paying more charges for such fraud and misery.

However, it is recommended to hire a competent property attorney for your property issues, or you can end up to more vandalism and fraud.

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.

Vacations in Punta Chame With Romantic Ambiance and White Sand Beaches

When you feel that the hectic schedule of life is burdening you with myriads of tensions and anxieties which are affecting your potentialities and performance it's advisable to take a short holiday from work or business and spend some quality time with your near and dear ones at a beautiful location. There are many exotic places where you can go for a dream holiday but if you prefer the realms of nature, white long stretches of sand and pristine beaches which create that romantic and mystic ambience which you enjoy the most then you are most welcome for a vacation in Punta Chame which will surely live up to your expectations and give you a wonderful and memorable holiday.

With romance in the air and elegance and beauty all around you are sure to feel the adrenaline rising and if you are a sports freak then along with natural beauty and romantic ambience you have the option of water sports like Kite surfing where you can ride the crest of the huge waves and enjoy the deep blue pacific all around you. Punta Chame is a beautiful finger shaped peninsula which is located from a short distance from the famous tourist destination the Panama City which welcomes tourist all year around with beautiful locations and a pleasant climate. Along with the enjoyment if you are looking for a wonderful accommodation to match your mood and offer a luxurious living then Punta Chame hotel is the ideal option where you various services which are sure to give you a wonderful time during the vacations. The rooms of these hotels have beautifully decorative interiors with white bed linens and exotic decoration which will add to the fun and enthusiasm in the air as well as in your relationship.

The whole view reminds you of country living where you will find horses, cattle and rolling mountains and also huge stretches of green pastures and with the ocean on the other side you can enjoy and ideal holiday with lots of privacy and no disturbance from the outside world . The beautiful palm trees on the ocean side where the blue waves peeks through the long trees is a wonderful view which is made even more enchanting when the cool breeze blows on the mountainside and there are huge waves on the oceanic surface.

So if you are looking for an idyllic holiday which can refresh your mind and still some new and memorable experiences for your lifetime then a vacation at Punta Chame is must.