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.

Adirondack All Weather Furniture – Choosing the Right Wood Type

Few people are aware of the fact that the idea for quality Adirondack all weather furniture began with a quest to find the perfect chair for relaxing on lazy summer evenings. This is why comfort is one of the very first things anyone thinks of when imagining an Adirondack chair or lounger. Aside from comfort, the other feature that most comes to mind when thinking about Adirondack all weather furniture is durability … why else would they call it all-weather !?

Because the original Adirondack chairs were originally designed for outdoor use at some lake cottage or similar retreat-the furniture had to be durable and was made from woods such as:

1. Cypress

2. Pine

3. Cedar

The use of cypress for construction purposes dates all the way back to ancient Egypt when the wood was a material for the construction of caskets for the first pharaohs. Today, cypress is a very common wood and used to make outdoor furniture like swings and various deck accessories. Cypress is also commonly used to make doors and windows as well because it has a conservative within the wood grain that helps it naturally repel insects and resist rot and decay which is why it is a popular choice when crafting quality-made Adirondack chairs and patio furniture .

Pine is another common wood used to make quality Adirondack all weather chairs and other seasonal outdoor furniture. Because of its abundance and reliably quick growth cycle, pine tends to be cheaper wood and is used extensively in the construction of many outdoor furniture pieces, including tables, benches, swings, chairs, and loungers. Pine tends to have a relatively low oil content and bids to that dry out easily, making it susceptible to cracking. However, when properly maintained, pine can be used to make premium Adirondack all weather furniture.

Cedar is a great wood when thinking about quality Adirondack outdoor furniture. Having a reddish brown color, cedar wood tend to be somewhat knotty and is actually a softwood. Cedar is naturally insect repellant and tend to have a very distinct aroma which can be managed with a sealer. However, quality Adirondack all weather furniture made from cedar is both beautiful and very durable making it an excellent choice when buying patio or deck chairs, tables, or accessories.

Does Body Jewelry Make You Take Extra Risks?

Body jewelry is usually associated with body piercing. There are lots of styles available ranging from cute and sexy to exotic and tribal. The places that can be pierced and the type of jewelry worn are naturally endless. It seems that when a person moves beyond a traditional or conservative earlobe piercing that other people tend to think that this non-traditional self expression is a sign of rebellion. However, is the presence of body jewelry an indication that the person is willing to take extra risks?

That is a question that parents of teens battle with as their kids approach them for permission to get a piercing. They fear that piercing such as a belly piercing, nose piercing or tongue piercing may be an indication that their teen is rebelling against their own parental values.

This is true in some cases; however, many teens simply say that the desire to wear different types of body jewelry is merely a form of personal preference and expression. Not a rebellion against their parents, just a sign that they want to have their own look even if they will keep their parents value system.

What risks youth may encounter in their quest to wear body jewelry is trying to do the piercing by themselves with a needle and a prayer. This is often not the best road to travel. The risks for infection are far greater than the risks of not gaining permission from your parents. Many teens see self piercing as the only alternative when their parents "just do not get it."

Does this mean that parents should open the gates and permit their kids to wear any type of body jewelry that they desire? Will this lead their kids to continue that push into getting permission for other behavior such as under-age drinking, smoking, or drugs? In other words, is body piercing the "gateway drug" for a rebel youth?

Probably not. But that is what many parent fear when their teens ask them about body jewelry. Youth often believe that nothing bad can happen to them. They are young, resilient and can handle anything including the risks of a self-piercing. As a parent you have the ability to less some of the risks that youth will consider. Most experts would agree that by educating yourself about body piercing and by understanding your child's motives and desires for this trend, a solution can be formed that will keep harmony in the house and enhance the relationship with your teen.

Furniture Store Marketing – Generate Tons of Customers by Partnering With Other Furniture Stores

Partnering with other home furnishing stores is a joint venture strategy that most home furnishing store owners have probably never even considered. It is probably because this joint venture strategy will require you to be really confident and comfortable in your own business.

Otherwise it would seem like you are risking losing your customers to another furniture store, but that is not true. The key to this strategy is partnering with other furniture store companies that do not sell the same types of products that you sell. Now, just to be clear about this strategy; you will not be switching lists with other home furnishing stores, you will be creating a in store coupon or referral program to use this strategy.

Partnering with other home furnishing stores allows you to gain access to customers who you certainly know are in the market for home furnishings. For example, if there is a store in your area which sells picture frames, fake plants and other various home supplies, ask them to allow you to have a podium stand or counter display stand filled with coupons as a bonus for shopping at their store.

In return you could have the normal mailing to your customers or also allow them to have a floor display on your showroom floor. There are many ways to manage these types of joint ventures, so be flexible and ask your potential partners about their specific needs and wants.

Examples can include stores that sell:

Washers & Dryers

Television & Electronics

Windows

Custom Closets