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.

Beachfront Vs Inland Real Estate Ownership In Miami

Miami real estate is one of the fast-selling and bought after pieces of real estate in the market nowdays since it is considered by many to be one of the best places to live or vacation in.

One of the reasons as to why a lot of people would like to invest on a real estate in Miami is because of all the other things that people will be getting when they do decide to purchase a real estate property in Miami. These Miami real estate owners know that they are not only getting the property, but they also get to benefit from all the other things that goes along with the property, such as the pristine beaches and the culture in Miami.

Owning a real estate property in Miami can be a real treat, especially for people who are very much into the whole Miami culture and lifestyle. However, there are a lot of real estate property types to choose from, ranging from condos to hotels. Although there are a variety of real estate properties in Miami, two of the more ideal property types that people can purchase are the beachfront and inland real estate properties. These two property types are very different from each other, although they both offer great real estate properties for potential buyers. In order to be able to decide which one bests suits your taste, you need to know what makes each of these properties unique.

One of the things that make the two property types so different is the aesthetic aspect that these property types offer its potential investors. Of the two, the beachfront real estate properties offer the better esthetic quality since the property is situated along the coastline along the coast of Miami.

These beachfront real estate properties is made more beautiful by the fact that the beaches that made Miami so bought after and popular is the backyard of such properties. All you need to do is look out your window and you can see the beaches that draw such diverse crowds into Miami.

Inland real estate properties, however, although are beautiful in their own right, still can not match the aesthetic beauty that the beaches add to the different beachfront real estate properties. It is one thing to have a beautiful house with nice amenities in a nice neighborhood, but it is another to have white sandy beaches very close to your home.

Another thing that differentiates these two property types is the level of their appeal or popularity with the different investors and potential buyers of the real estate properties. Beachfront real estate properties are moreought after than inland real estate properties since these beachfront properties are very close to the beaches, which is the major reason for its appeal. Inland properties may be closer to other structures, but people do not wish to live or vacation in Miami because of the malls and the stores in the city. People wish to come to Miami mostly for the beaches.

Although both real estate properties can be used by its owners to earn profit, especially if they do not intend to live in Miami permanently, beachfront properties are still the more popular choice for people who want to rent out condos or houses in Miami, especially for those people who are just vacationing. Vacationers go to Miami for the beaches, and if they are able to live near one, then the better it is for them.

Whatever real estate property you may choose to buy, it is important to remember that these types of properties, especially if they are bought after in the market, may cost you a lot of money if you plan on investing on Miami real estate. However, inland real estate properties tend to be more reasonably priced, as compared with beachfront property types. The high cost of owning a beachfront property is the price that any potential buyer have to pay in exchange for all the perks that goes along with the property.

Vanessa A. Doctor

http://miamirealestateinc.com

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