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 Secret of Successful Container Gardening

Container gardens are great, and a lot of people are starting to look at container garden ideas today for convenient ways that they can start one. If you don’t have a lot of space but you want to grow some vegetables, flowers, or plants, you need to check out container gardens and how they can work for you. You’ll be amazed how with the right steps and secrets, you’ll know how to grow a container garden that is flourishing and looks outstanding.

Have Containers that Work for You

The great thing with a container garden is that you can use any sort of container that you want. So, if you want to use a container that is a rubber boot, you can do that, and that draws a lot of people to this style of garden. But, no matter what container you are using, you need to make sure that there is proper drainage. There are a few different ways that you can create drainage, you can do a layer of rocks at the bottom so that there is room to drain where the roots won’t grow, or you can go ahead and put holes in the containers. You also need to make sure that the containers that you are using are going to be big enough, you need to have containers that are big enough for the size of the roots that are going to grow, otherwise the plant will die off or you will stunt the growth.

Have the Correct Soil and Light Conditions for What You’re Growing

The other factor that is really important with what you are growing and your container garden is having the correct soil and lighting conditions. With soil, you will find that you may need to have different soils for different plants, so one container may have a different pH than the other soil that is out there. Also, check the light conditions so that you know if the plants that you are growing have enough light. Different plants need different amounts of light, so it will depend on what you are growing in your container garden and how much light that they need. Generally, it is best to give them light that is less harsh, like morning light instead of afternoon light that can actually burn the leaves or harm the plants. Make sure that you have the right soil and light conditions so that your plants can flourish in it and grow to what you want.

Have a successful container garden with all the tools that you need, there are all kinds of little things that you need to do, but knowing these tips and tricks will make it a lot easier to handle. There are all kinds of little tips and tricks that will give you an extremely easy to grow container garden. See what works the best for you and use these container garden ideas to get a great looking container garden that is going to look amazing and be extremely functional, you’ll love it.

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.