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.

Top 11 Reasons to Use Social Media in Business

Over the past few years, to say social media has exploded would be an understatement. Members of social media sites have discovered it's the easiest way to find, learn about, and share information that directly influences their purchasing decisions. It is this reason alone that every business should be on multiple social media sites in an effort to reach as many people as possible.

Below are the top 11 reasons to use social media in business:

  1. Build relationships – personal and professional; connect with all types of people – past and present coworkers, current clients, prospects, vendors, competitors, and marketing professionals to build your network
  2. Share your blog posts; share interesting and useful articles, other blogs, webinars, podcasts, presentations, and poll / survey results with your fan base
  3. Gather valuable information – research similar products / services, competitors, prospects, marketing tips, blog ideas, create your own poll / survey – the amount of information available is endless
  4. Join a social network of like-minded individuals or start a new interest group where you can further brand your product / service, build relationships, and share ideas and information
  5. Stay current with the latest trends – write a blog or join a discussion on a trending topic; become aware of new social media sites that might fit the needs of your business
  6. Land a great new job – using your new connections on various social media sites, you can get the inside scoop on companies that are hiring, as well as resume and interview tips
  7. Discover a new passion in life, become a volunteer, or start a fundraising event
  8. Get found by prospects by using inbound marketing tactics – spread the word about your product / service through social media sites; to form a complete marketing plan, combine this with outbound techniques (interruptive marketing)
  9. Build business reputation and brand – constantly add value to all your posts and become a trustworthy leader in your industry; to quote Bob Burg, "All things being equal, people will do business with and refer business to those people they know, like, and trust."
  10. Build a marketing department inexpensively – for start-ups, employing inbound marketing tactics is a cheap way to start marketing your product / service; most social media sites are free to join, while others have a minimal monthly or annual fee
  11. Help increase conversion rates – use social media and inbound marketing to steer more organic traffic to your website and convert more leads into sales; the average conversion rate is 2.3%, but varies by industries according to ClickZ, Marketing News & Expert Advice, http://www.clickz.com/clickz/column/1691779/benchmarking-average-conversion-rate .

I recommend choosing a useful of sites to manage and start getting your feet wet. Not every social media site available will be right for you or your business and it would overwhelming to try them all. For example, consistently maintaining a blog, Facebook, LinkedIn, and Google+ pages, a YouTube channel, as well as a Twitter account might be a great place to start. Depending on the type of business, a Pinterest, Tumblr, or Flickr account might or may not be worthwhile, but obviously they are great certain brands.

If you need help getting started, there are countless different types of resources. I have used the An Hour a Day book series on Facebook Marketing, Twitter Marketing, and Social Media Marketing. They address each entity in a step-by-step fashion that is very user-friendly. I also find Hubspot to be extremely helpful. They are continuously publishing user guides that contain valuable information, tips, and tricks. Lastly, when creating your profile on the various social media sites that best fit your marketing plan, it's a good idea to connect with other marketers to check out what they are doing to boost business.

Do you have a tip or trick to share with newcomers to social media? Share it with us; you are more than welcome to post questions and / or comments here!

Garner Compliments Wearing Rose Gold Jewelry, the Latest Jewelry Trend

Rose gold jewelry, this is appearing since the past 2 to 3 years. This is a blush color metal and has gained prominence during spring and summer. This trend as gold fixtures is bought even as a gift. Today, this precious metal is widely used and women, you must have at least one in your collection.

Adding rose jewelry into your collection means find the pieces of jewelry that look good and go well in combination with your yellow gold and silver jewelry. The gold jewelry looks nice, regardless of the style or metal. Having a personalized rose ring stack is fun. These minimalist competing bands are now available as motifs and in varying thicknesses that it can be a statement ring that is less expensive yet appears dazzling with gemstone studded. The color braided gold band makes it very special.

How it is Made

First, Rose gold appeared in Russia as copper infused metal was incorporated in the jewelry designs by Carl Faberge, the well-known jeweler.

Rose actually is not available directly from the nature. As already known, the pure gold is in same color and the jewelry color changes only owed to the mixing of alloys or other metals. The metal mixing ratios change the gold color.

The metal receives its colors on mixing copper alloys with pure gold and silver is also added in small amount. The mix having more copper means the jewelry shows redder and the one with less copper comes in pink color.

The typical 18k modern-day rose looks featuring gold to 75%, silver 4% and copper to 21%. The fact is that as the content of silver reaches to 5% or closed, you will notice gold appearing more of pink in color.

The beauty of rose jewelry is that it offers a comprehensive look and the jewelry looks simple, yet stylish garnering compliments from your neighbors, love, coworkers, friends and relatives.

Rose Jewelry prominence

Copper is an alloy. Owing to the high copper content only the rose gold jewelry emerges and as the fact is that copper with age gets darker and over time less rosy. The jewelry appears vintage inspired, but certainly is a style statement.

Today, the market has rose jewelry in lots and there are designers trying to bring different styles using this hue of gold. The purple gemstones fit in soft pink makes the rose look stunning and reflect your skin glow.

The necklace pendants in rose gold also look amazing. Rose gold was used in the Victorian era in the pendants and today is a bohemian style. If you are a person loving antique jewelry, turn the gold into some jewelry piece of your taste. Even if a rose jewelry is broken, you can wear it as a brooch or a stickpin, it will shine. The rose gold jewelry is recognized as personalized jewelry offering a feminine touch and charm. Use it for your Zodiac sign and use it as charm pieces in your jewelry, in the necklace or ring, it is sure to look beautiful.

Why Healthy Food For Diet?

People already know that they need healthy food for diet. The problem is, not many of them really understand the meaning of it. Most of them are more interested in the diet itself than more the healthy food. Well, we need to get it right because there will be no result for our diet without we eat the right kind of healthy food.

Before we talk about the kind of food, we need to understand the meaning of diet. Diet is a way of controlling the amount of food and the kind of food entering our body in order to get a healthy body. So there are two things that we need to keep in mind, the amount and the kind of food. Actually by eating the right kind of foods, we do not need to worry to much about the amount.

Why? Because by choosing the right kind of food that can actually burn fat and help us gain muscle, and avoiding the kind of food that only encourage our body to store fat, we do not need to worry anymore either we should eat more or less. The more we eat, the more we burn fat and gain muscle.

For an optimum health, we also need foods that contain carbohydrates, protein, vitamins, minerals, and fat. We need all those nutrients so that our body can perform an optimum metabolism. So if you are following a diet or weight loss plan that recommend you not to eat one of them, you better STOP NOW.

We can actually find these foods anywhere. Lean meats and steaks, raw fruit, raw nuts, vegetables, olive oil are sources of healthy food. The key is choose raw or less processed foods.