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.

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.

Choosing Ringbearer Gifts Does Not Have to Be A Bear

The significance of wedding rings is best illustrated in people's fear of losing them. There are people who boast of having never removed their wedding ring since their wedding day, though this is sometimes due to changes to their weight since they said, "I do." But really, how important are wedding rings? Moreover, how many times have we heard of what a nightmare it is to lose your ring? We hear stories of people losing their rings in the labyrinth of pipes underneath the kitchen sink. Then, there was the movie "American Wedding," in which wacky Steve Stiffler accidentally feeds the bride's wedding ring to a dog. Clearly, wedding rings are very important. Consequently, even though the ringbearer is one of the shortest members of the bridal party, his is the task of the tallest order. So, when you choose ringbearer gifts, keep in mind the critical role that your ringbearer plays.

The Ringbearer
The use of ringbearers is fairly modern. They tend to be young brothers or nephews of the bride or groom, and usually range in age from 5 to 10. In weddings that are formal, the ringbearer, or pageboy, has one of two different functions. First, the ringbearer might carry the bridal party's rings on a huge white satin pillow. Boys will be boys, and almost anything could happen during his waddle down the aisle. Usually, the best man himself secures the rings, or thread is used to attach the rings onto the ringbearer's pillow.

Another function of the ringbearer is to carry the bride's train, if it is lengthy.

The Basics
Whether the ringbearer totes the rings or holds the train, make him feel special through your choice of ringbearer gifts. For example, consider what your ringbearer likes. Here are some ringbearer gifts that might ring well with him.

Ring Bearer Fun Box Gift: This is decorated to look like a Ringbearer's tuxedo. Inside it is fun games, cookies, and candies.

Ringbearer Baseball Cap: This will remind the boy that he was in the starting lineup of the wedding ceremony.

Space Magic Cookie Pot: This is a bouquet that is packed with cookies and candies. What kid says no to sweets?

Ringbearer Activity Tote Bag: This is a fabric bag with several gift items inside.

Personalized Gifts
Aside from the obvious height difference, kids and adults are not too different from each other. Like adults, kids want to feel special, too. Personalized ringbearer gifts help you do just that. Here are a few personalized ringbearer gifts to consider.

Personalized Baseball: This will make any little leaguer feel like a big leaguer. The ball is mounted on a walnut-finish stand.

Ringbearer T-shirt: This will let your mini lord of the rings remember the special day. How could he not with his name is printed on the shirt?

Personalized Silver Plated Yo-Yo: Give a new twist to the old toy! Each time your ringbearer uses this ringbearer gift, he will remember his walk down the aisle.

Being the ringbearer in a wedding can be daunting for any youngster. Help your ringbearer enjoy the task by giving him a well-thought out ringbearer gift. Carefully chosen ringbearer gifts will make your wedding day one that will always ring a bell in your little ringbearer's mind.

Furniture Store Marketing – When Everyone Is Your Customer, No One is Your Customer!

One of the biggest challenges home furnishing owners must overcome, in order to be successful in this new economy, is the dreaded I-offer-everything-for-everyone syndrome. On the surface this looks like a sure-fire way to get more customers, but it is already proven time and time again that it is not always the most successful way to prosper in your store.

If you are an independent home furnishing retailers, then chances are you have a limited budget and limited space to work with. So, if your store offers several contemporary collections, several ultra-modern collections and some eclectic pieces as well as some early American collections scattered through you store, do you really think that you have enough of any of those styles to satisfy the type of customers who are looking for a specific style? However, style is only one way to target your customer.

In fact, the most successful furniture retailers in my area focus on a couple of things to attract a specific type of customer:

  • Complete living room packages for under $ 2,000 or furnish your entitlement home for under $ 5,000.
  • Long-term low or no interest financing
  • Fast delivery within 3 days or less
  • Lower prices for packages

So, by narrowing down their advertising, they attract a customer that wants to purchase multiple pieces, which in turn, drives the average ticket sale and profits up. They then offer attractive financing terms which attracts customers with good credit and income, while enticing them to spend more money because the customer has longer to pay for it.

Most importantly, they save the customer money by buying more and can get it in their homes in a couple of days. There is also another twist to these retailers. They reward their salespeople handsomely for NOT selling the financing, but getting customers to pay off their balances in less than 90 days.

There is a common slogan in marketing statute, "There are riches in niches." Simply put, this slogan means determine who your most profitable, enjoyable and easy to attract customer is, and then specialize in getting more of those customers to come into your store and buy. You do this by creating a USP (Unique Selling Proposition) that compels your most profitable customer to come back into your business again and again.

What if you reviewed your business over the last couple of years and discovered the following trends about your customers and prospects:

  • Wives initially visited the store without their husbands.
  • Recently married
  • Had three kids
  • Lived within five miles of your store
  • Spent between $ 800 – $ 1500 on sofa, loveseat and tables.
  • Paid by Visa, MasterCard or Discover

Once you have this information, you can redesign your store and business to cater to more of the same types of customers that are currently spending good money in your store.

However, you can only use this information to your advantage if you take the time to find out who your customer is, what is important to them and what they really want.

It may come as a surprise to you, but your customers want more than just a sofa. If you are just selling a sofa, you are missing out on a ton of business. Here are a few of the keys I have discovered over the years:

  • Do not sell mattresses, sell relief from back pain.
  • Do not sell home theater seats, sell the entertainment experience.
  • Do not sell sofas or loveseats, sell comfort and warmth.
  • Do not sell furniture, sell status and prestige.
  • Do not sell interior design, sell ENVY and the WOW factor!

Once you know what your customers really want then, you could use that information to create a USP that attracts more of the same type of customers. For example:

  • "Do not hire expensive interior designers, use our 23 point design checklist and give your home a million dollar look for FREE!"
  • "Discover how to give your home an extreme $ 20,000 makeover, on an $ 8,000 budget."
  • "Your family and friends will say" Oh my gosh! Your home is simply amazing! "In 27 seconds flat … we guarantee it!"