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.

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.

Making Money – Get Paid to Refer

Sounds simple, making money by getting paid to refer, but is it really possible to make money by just referring people. Well the simple answer is yes you can. I came across this about 18 months ago and have been slowly but steadily seeing my earnings from it grow.

We all actually play a part in this chain. I'll give you an example:

Not so long ago I was spending a lot of time on Twitter and Facebook seeing what my buddies were up to, when one of them stated that they managed all their social profiles as well as all their email addresses in one easy desktop application called Digsby. I thought that was a pretty smart idea so I downloaded the free software and now use Digsby for handling all my social networking accounts.

Now even though I did not have to pay for Digsby my buddy who referred me was able to make money by referring me, so he was 'paid to refer', and there are 1000's of really useful software tools like that you can get paid from forseeing. Also there is a digital information warehouse that you can join for free, make money get paid to refer any of the 10'000's of the products and services that you refer of their. People can download whatever they buy straight way and you get paid money for referring them straight away too.

I know people who make 1000's a month getting paid to refer, and the ones that do not are the ones who think they are there to sell, selling does not work it's as simple as finding a group of people really eager for a solution say one on "how to train Labrador puppies" and then referring the to a digital product at ClickBank to solve their problems, it's a win win situation.

The best place to learn how to 'make money money paid to refer' is from the someone who does it every day, well the people who do it every day are called affiliate marketers.

Affiliate marketers get paid a commission on everything they refer and it does not stop with digital downloadable products either, you can take a look at company's like Commission Junction, Linkshare or even Amazon just to name a few, and make money getting paid to refer tangible goods of all kinds, it really just depends on what your into.

Golden Triangle Tours: Best Way to Explore Culinary Delights and India’s Riches

Golden Triangle Tours is the name given to the most fascinating touring circuit of India. Unleashing the country's historic past, its heritage, colorful cultures and flavorsome cuisines, Golden Triangle Tour packages takes one to a whirlwind ride of Delhi, Agra and Jaipur. The path to the touring circuit is resplendent with fortresses, spectacular palaces, historic monuments, UNESCO applauded World Heritage Sites and culture capitals. Encompassing Golden Triangle cities brings a visual treat to the eyes of history, art and architecture lovers, but it is also an opportunity for food frantic to taste real flavor of India.

Gourmets Feast Upon Delhi Cuisine: The capital city of India, Delhi is also a hub of political and cultural activities. A fabulous metropolis Delhi is also a significant center of education and technology; also its historical heritage is very impressive, but the real charm of the city is in its cuisine. Delhi is a potpourri of cultures, it has a mini-India in itself and has welcomed people of various cities, states, color and creed with open arms and thus the variety in its cuisine and flavor in its food is one to die for. From tangy Chaat (kind of spicy snack) to delicious curries and lip-smacking Mughlai there is an abundance of choice of food. Eating joints, low- budget restaurants, road side vendors to elite restaurants and more authentic Delhi cuisine means best of Indian food. From Punjabi style cooked South Indian food to Chinese Tadka-Mar-ke and of course famous Kebabs and Tandoori food, Delhi offers et al to satiate your taste-buds. One can even have best of authentic Continental and world cuisine in Delhi well-known as the Food-Capital of India.

Jaipur's Royal Grandeur: No Golden Triangle Tours are complete without experiencing royal charm which is well preserved till at the stunning palaces and fortes of Jaipur. On a sightseeing tour across famous royal capital of Rajasthan one experiences a royal saga unfolding at hilltop Amer Fort, honeycomb shaped- Hawa Mahal and fascinating royal observatory- Jantar Mantar. Mesmerizing sight of City Palace further add to the charisma of Rajasthan ideally known as the princely state of India. Explore its bazaars to pick interesting hand-made curios; silver jewelry, colorful puppets, hand-printed fabrics and more the vibrant bazaars of Jaipur will indeed sweep you off your feet with their elegance and simplicity. Further a mesmerizing performing art scene is a must for all those touring the fabled touring circuit.

Agra: What appears to be a painter's fantasy coming alive is actually a living specimen of Mughal artistic excellence. Agra is where the ultimate emblem of love- Taj Mahal is located which made city world-renovated. Also, Agra is well-known for other UNESCO World Heritage Sites such as Agra Fort and Fatehpur Sikri. On Golden Triangle Tours in India the sights of these UNESCO riches are a must visit for they give a sneak peep into the country's architectural heritage and also brings closer to its legendary history of mighty Knights and their dynasties.

In a nutshell Golden Triangle Tours avails a quick introduction to the vast sub-continent of India.