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.

Culinary Arts Education – Degrees For a Job in the Hospitality Industry

There are many people that dream of a career in the hospitality industry and the most popular job is, of course, the head chef. To attain this role within a quality restaurant you will need to go through a culinary arts education course that will prepare you for working as a professional chef. These courses include the actual hands on preparation of food as well as the theories and lessons you will need to work in the industry. The courses run for anywhere from three to five years and even longer in you choose to complete a double degree.

There are many schools offering culinary education including everything from local community colleges through to world class cooking schools such as Le Cordon Bleu. Most of these schools offer professional degrees in culinary arts and will provide you with an opportunity to get a great job in the industry. However, it is more than likely you will need to get experience as an assistant, or sous chef, before you will be promoted or offered a job as a head chef. Like most other graduates you will need to make your way up the industry until you reach the top.

It is important to compare the different culinary arts education courses that are offered. Consider that some of the courses will not offer a formal degree so it is a good idea to put plenty of research into your decision. Create a short list of schools as it is a good idea to apply to more than one school in case you are not accepted by your first choice.

Clothes Dryer

There are two types of clothes dryers one is gas the other is electric. The gas dryer is half gas and half electric, the gas is used for lighting a flame to create the heat to dry the clothes, the electric is used to operate the motor, timer, ignitor, coil kit and thermostats.

The gas dryer has more working parts than the electric dryer, when there are more working parts there is a greater chance of something breaking, the gas dryer does break down more frequently than the electric dryer.

The electric dryer use 220 volts to operate the heater element only, all the other parts use 110volts. Both gas and electric dryer have some basic parts: motor, timer, belt, thermostats, and thermal fuse.

These are the functions of each part.

The motor turns the belt that is on the basket, the timer sends the desired voltage to each part for the desired time that it is set on, the thermostat maintains the desired temperature and the thermal fuse shuts down the dryer if the thermostat fails.

A common problem with both gas and electric is clothes taking a very long time to dry, lint building up in the exhaust vent hose is sometimes the reason. The best way to check if the exhaust is partially blocked is to turn on the dryer. Then go outside to where the vent is, put your hand close to the vent, if there is little or no hot air coming out out, your vent hose is blocked. There should be a strong flow of hot air coming out. Sometimes birds build their nest at the vent opening because of the warm air they find coming out of it. Also if the vent comes out near the ground it sometimes get covered by snow.

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.