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.

Real Estate Agent Job Description

Real estate agents liaise between home owners and buyers to conduct the sale, purchase or rent of properties. They work for brokers and play a major role in assisting people buy or sell residential, commercial or industrial property. They keep and maintain an up-to-date account of property listing and other relevant housing information to stay abreast with properties available on the real estate market. They subscribe to several listing services to advertise and market properties up for sale. They also contact property and market properties up for sale. They also contact property owners to obtain information regarding a property.

As part of their responsibilities, estate agents present sales and purchase offers to clients for consideration. They advise them on property rates, legal requirements and general market trend. They also interview clients to determine their property preference or specification. Usually, they prepare a list of properties that best match the needs and requirements of clients. They visit and inspect properties in order to establish precise property value. They also proffer recommendations to clients on properties that best suit their budget and preference.

Most estate agents oversee the preparation of closing statements, purchase agreements, representation contracts and other necessary documents required for estate trade. They conduct negotiations between property sellers and buyers to establish price and other terms of sales. They also liaise with pest control operators, home inspectors etc. to ensure the terms and conditions stated in a purchase agreement are met prior to the closing of sales.

In fulfilling their role, real estate agents oversee the closing of property sales, they ensure payment is complete and appropriate documents signed. They maintain contact with clients to offer them real estate services/products and assist with the resolution of issues. They also provide consultation services to clients to recommend strategies for the speedy sale of property. They often conduct training programs for junior/trainee sales agents to enhance their sales skill. This job position requires at least a high school diploma, state license for practice and an aptitude for sales. Qualities needed for the job include persuasion, interpersonal skills and problem-solving skills.

Real Estate Agent Job Description Sample

Given below is a sample of the job description usually handed real estate agents by most employers:

  • Act as liaisons to conduct real estate trade between property buyers and sellers
  • Present sales offers to clients as well as bid on available properties
  • Carry out investigations to determine client credit status and ability to complete payment
  • Inspect properties to appraise its value and estimate the worth on the property market
  • Interact with clients to identify their requirements and proffer recommendations on properties that best suit their budgets
  • Assist home sellers in promoting their buildings on property listing services to attract clients for purchase
  • Prepare and deliver sales pitches to clients in order to secure real estate contract
  • Provide clients with a list of properties available for sale to assist them in making choice selection
  • Conduct price negotiations between property buyers and sellers to ensure a fair bargain for both parties
  • Provide clients with a tour of residential, industrial or commercial properties to showcase and explain property features
  • Carry out investigations to confirm clients have clear property titles
  • Provide appropriate reply to client’s enquiries concerning property appraisals, financing, maintenance etc.
  • Examine property premises to recommend maintenance measure required to improve the face value
  • Assist clients in evaluating mortgage options to obtain the best rate and terms
  • Attend conventions, conferences and seminars to improve existing job knowledge and expand personal network.

If you are a recruiter needing the best real estate agent to hire, you can use the sample job description above in making one for your company, for use in hiring and assigning duties to the successful candidates.

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.

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.