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.

Food and Food Health

We all have passed through a phase, or are still in one where the mind still walks the streets of dilemma as to whether the salad in the afternoon can make up for the double cheese hamburger of last night. Whatever the calories gained through the chocolate pudding can be balanced through the oatmeal in breakfast.

A few years back, there was a stigma about having the perfect thin or muscular (as one prefers), flat-stomached body. There was this misconception that slim and trim is the way to look beautiful. But fortunately, this stigma and misapprehension is slowly and somehow being eliminated from the society. Today, every type of body is beautiful, whether it is a flat-stomach or a fat belly. But that does not give any of us the right to overlook the fact about eating healthy.

Eating healthy does not mean gulping down only chunks of vegetables and salads. Eating healthy does not mean being on a "diet". Eating healthy means providing the body every kind of nutrients to function properly. And it includes the Broccoli Soup one cringes to as well as the delicious classic double crust cheese-filled pepperoni pizza, everyone craves for.

REQUIREMENTS OF THE BODY

We all love eating, mainly the junk type, but sometimes realization hits us and we tend to understand that salads and vegetables and fruits are really important part of a diet. Every type of nutrient is needed to keep the body functions in its right place. Vitamins, proteins, minerals, carbohydrates, fats, roughage and water, these are the nutrients we need almost on a daily basis. I will not waste time by telling what these are and how each of them are important because this is something we all have learnt in six-grade science subject. But I do would like to mention some of the dishes that are delicious, healthy and contain all of the above nutrients in the right amount.

THE FINGER-LICKING CLASSIC CHICKEN SALTIMBOCCA

It is a delicious chicken preparation, which is roled up with prosciutto and mozzarella cheese and drenched in a tasty white wine pan sauce. It is a mouth-watering dish with the goodness of protein (found in chicken), fats (cheese) and the palatable white wine sauce. It can easily be garnished with vegetables, providing the wholesome richness of vitamins and minerals.

THE DELICIOUS UN-CHEESY POTATO BROCOLLI SOUP

The name may seem to have no part of it seem delicious- 'un-cheesy', the dreaded 'broccoli' and 'potato', but the taste seems to be contradictory It's not-so appealing name. It is a preparation which will fill the tastebuds with an explosion of flavor and its richness makes it almost hard to resist. The dish is a mixture of health and taste.

THE OH-SO YUMMY APPLE CINNAMON BREAKFAST BARS

This is the perfect preparation for all those fuzzy kids who refuse to eat any fruits. This flavorful dish is full of protein and fiber and a favorite among the children and adults alike.

THE IMPORTANCE OF FOOD HEALTH IN OUR LIFE

There is absolutely no need to state what importance food holds in the existence of an individual. As stated above, it does not matter if one is slim or fat, what matters is where the individual is eating healthy. Excess of nothing is good, especially not food. But we need to understand the right amount and the right kind of nutrients for our body needs, to stay healthy and to keep our loved ones healthy as well.

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.

How To Search Google For Country Specific Results

Running an international online business with the capability to service people from any country means that you want your site to perform well not only in local country specific results but also global results. You may not realize this but doing a standard Google search and leaving the "full web" option selected does not necessarily give you your website's true location in the Google global results. It gives you the global results given your location.

For example, the results of doing a full web search in my home city of Brisbane Australia will be different to a full web search from Toronto Canada.

Google gives results based on your location even when you are not stipulating a local result. You can click your local country only result button and get sites that are from your home country, usually determined by the domain name extension, for example .com.au for Australia, .ca for Canada, etc. or the IP address of your web hosting server, or you can click the web option and get global Internet results that vary depending on your computer's location in the world (based on the IP address of the computer you are using to access the Internet).

Think Global

If your business can service the world then you really can not ignore the American marketplace, or if you are in the USA do not forget about Europe, Asia and the rest. Since you need to know how well your site is performing in Google global search results and unfortunately simply ticking the "the web" option in Google when searching can be misleading because your ranking will be different if it was someone in a different country doing the exact same search.

What you want to know is when someone in the UK does a Google search for one of your terms, how high is your website up in the search results? With this little trick you can figure it out.

The Code

All you need to do is add & gl = uk to the URL at the end of the Google search query.

For example:

http://www.google.com/search?hl=en&q=sample+query&meta= & gl = uk

This tells Google to spit out the results for the query based on UK servers.

I can not guarantee 100% conclusively that this works as I expect it does, but it definitely does something and you should try it yourself and see if your site shows up in a different place in the results. The "gl" stands for G eographic L ocation and of course you can exchange the last letters to test different country results around the world.