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.

3 Innovative Ways To Attract Money To You

It’s no secret everyone yearns to have more money in their wallet or bank account. Developing a healthy relationship with money is essential if you want to have more of it.

Money is, after all, just another energy. Yet so much emphasis has been placed on it.

We are told as children that money doesn’t grow on trees.

We are pushed to ‘keep up with the Jones’ and over and over we are told ‘money is what makes the world go ’round.’

All of this gives money an inordinate amount of power.

If you have an unhealthy relationship with money, you will never create the abundance you wish you had. In order to change your financial world, you need to change your feelings and paradigm about money. You need to change the way you think, feel and act about money.

If you believe you will never have enough money, you will never have enough money. What you focus on the most gives you exactly what you focus on the most.

These fun and practical little tips will magnify your energy and get the Law of Attraction sending more prosperity your way.

  1. Learn to pick up coins from the ground: Ask my friends and family how many times I find coins on the ground and it will blow you away. I always pick them up, hold them to my heart (Thanking The Universe) and then put them in my pocket. Even if it’s just five cents, make sure you bend down and pick up the money! You’ll show the Universe that you are open to collecting abundance. When you feel like you’d be embarrassed or self-conscious about doing this, I want you to re-frame it so that you are looking after the money. You are a conscious custodian of cash making sure that money feels loved. This generates the energy of appreciation.
  2. Write Yourself A Check: Do you know the story about Jim Carrey? Jim Carrey was a struggling young comedian trying to make money in Hollywood. He was just about to give up his dream of becoming a professional actor and comedian when he was booed off the stage at an open mic session in an LA nightclub.Jim sat by himself at the top of Mulholand Drive contemplating his success or failure. He then pulled out his check book and wrote himself a big fat check for $10 million dollars and made a note on it: “for acting services rendered.”He then carried that check with him in his wallet everywhere he went from that day forward.By 1995, after the success of his blockbuster movies: Ace Ventura: Pet Detective, Dumb and Dumber, and The Mask, his contract price had risen to the price of $20 million dollars.Write yourself a check for a specific amount and place it in your purse or wallet.
  3. Learn to love your bills: Sounds crazy right? Hold on as I explain. When bills land in your e-mail inbox or your mail box make sure that you mentally send them love and say thank you to the Universe for the services you have received in exchange for the bill. Draw little hearts on them and use the bills as an affirmation that prosperity flows into your life in many forms in order for you to pay your bills on time. Whatever you do, don’t send the bills negative energy. Try and re-frame your perspective. Remember that more than 80% of the world’s population survive on less than $10 per day. There’s something to think about.

Developing a healthy relationship with money is critical if you are someone who wants to attract more of it. Continuing your unhealthy relationship is a choice and quite honestly a bit of a cop out. Even if you just want enough to survive and occasionally take a little vacation, adopting a healthy relationship with money is imperative to achieve that.

Health Conscious Cooking Schools

Cookery school is a relatively modern concept that proves to be an exciting holiday option. Though the classes revolve around culinary art, they do not offer graduate degrees and are not accredited institutions. They are usually restaurants, hotels or snack bars. Cooking school tours are perfect vacation options, as they help tourists to acquire a local experience and try their hands at cooking local dishes, while traveling and shopping. Health conscious cooking schools tours provide details regarding various cooking styles that help retain food value and nutrition.

Many people follow diet plans that may be self created, recommended or decided upon by their physicians. They are planned, keeping in mind the nutrition needs and food preferences. Health conscious cooking school tours revolve around cooking classes that are meant to teach people about the food options that safeguard the interests of health conscious people.

Established hoteliers and restaurants often make health conscious cooking school tours available. It is important to make reservations in advance, as these classes are not walk-ins. Most of these classes have a minimum number of attendees to enable the in- house chefs and nutritionists to concentrate and interact with all the participants, individually.

These classes teach the tourists to prepare easy, healthy and delicious meals. Such classes are available for amateurs and professionals, separately. This allows enthusiastic visitors to learn to prepare basic health conscious dishes, whereas professionals can opt for the gourmet preparations. In case these tours are a part of overseas vacations, rather than a weekend activity, people need to enquire about availability of English speaking staff. Tourists need to be attentive to their visa terms and should carry all relevant documents. Tourists may book a health conscious cooking school tour or ask travel agents to include such activities, as part of their vacation plan.

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.