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.

How To Start A Restaurant Business

First of all you will need to think about the type of restaurant you want to open. Primarily, restaurants are grouped into three categories: quick service or fast food, midscale where you will get a good meal for a good price, and upscale with plenty of charm and fancy cuisine. This will also be dependent upon the type of food you want to serve, and the type of customers frequent the area.

One idea is to open an ethnic restaurant such as, Italian, Mexican, French, etc.. You can open an ethnic restaurant in any of the three categories, but before you choose take a look at the demographics of your area. You may want to take a demographic survey so you can get information on:

o The ages of the customers that will eat at your restaurant business.

o What types of ethnic groups live in the surrounding area.

o The occupations and income levels near your restaurant business.

o How many people will be interested in the type of food you will be serving.

o What are the needs, in terms of services or products, of the people in your area? Will you get enough business in the area you are planning to put your restaurant business?

A competitive analysis will show you what other restaurant business are in the area and what type of competition they will give you. You can do this by going to the restaurants as a customer, and checking out the menu to see how much they charge for their food and drink. This will help you decide how much to charge for your fare. To start your competitive survey, you should check the phone book and yellow pages in that area that have a restaurant business in the same category as yours.

The type and size of your restaurant business will determine the amount or size of the following:

o What you will need in the line of equipment.

o How many pieces of dishware, glassware, flatware, linens and napkins, you will need.

o Cooler, freezer, and storage size.

o How large your building will need to be.

o How many employees you should hire.

o How much parking you will need.

o What you will need in the line of advertising.

What will you call your restaurant business? The choice of a name should be one that reflects what you sell and will help you sell your goods. You will want all of your customers to be able to pronounce and spell the name to look it up in the phone book, or when writing a check. The name should be more creative than the competition, and represents the type of menu you are offering.

Make sure you are not stepping on someone else, check to see if the name you have chosen has been registered to someone else under a trademark. If it isn’t, make sure that you register the name with your county clerk. You should also check with the federal government to see that there are no trademarks registered through them with the name you have chosen. You can be sued for using an already registered name.

Top 50 Christmas Quotations

  1. "Let us remember that the Christmas heart is a giving heart, a wide open heart that thinks of others first. the healing medicine of love which has transformed all manner of hearts for almost two thousand years … Underneath all the bulging bundles is this beating Christmas heart. " - George Matthew Adams
  2. "The rooms were very still while the pages were softly turned and the winter sunshine crept in to touch the bright heads and serious faces with a Christmas greeting." - Louisa May Alcott
  3. "Christmas Eve was a night of song that wrapped itself about you like a shawl. But it warmed more than your body. - Bess Streeter Aldrich
  4. "The perfect Christmas tree? All Christmas trees are perfect!" - Charles N. Barnard
  5. "Gifts of time and love are certainly the basic ingredients of a truly merry Christmas." - Peg Bracken
  6. "The earth has grown old with its burden of care But at Christmas it always is young, The heart of the jewel burns lustrous and fair And its soul full of music breaks the air, When the song of angels is sung." - Phillips Brooks
  7. "I am not alone at all, I thought. I was never alone at all. And that, of course, is the message of Christmas. indifferent. For this is still the time God chooses. " - Taylor Caldwell
  8. "Remember, if Christmas is not found in your heart, you will not find it under a tree." - Charlotte Carpenter
  9. "Christmas is not a time nor a season, but a state of mind. To cherish peace and goodwill, to be plenteous in mercy, is to have the real spirit of Christmas." - Calvin Coolidge
  10. "Christmas, in its final essence, is for grown people who have forgotten what children know." Christmas is for whoever is old enough to have denied the unquenchable spirit of man. " - Margaret Cousins
  11. "Without we make Christmas an occasion to share our blessings, all the snow in Alaska will not make it 'white'." - Bing Crosby
  12. "Whatever else be lost among the years, Let us keep Christmas still a shining thing: Whatever doubts assail us, or what what fears, Let us hold close one day, remembering its poignant meaning for the hearts of men. faith again. " - Grace Noll Crowell
  13. "It is the personal thoughtfulness, the warm human awareness, the reaching out of the self to one's fellow man that makes giving worthy of the Christmas spirit." - Isabel Currier
  14. "Something about an old-fashioned Christmas is hard to forget." - Hugh Downs
  15. "They err who thinks Santa Claus comes down through the chimney; he really enters through the heart." - Mrs. Paul M. Ell
  16. "Christmas, my child, is love in action." - Dale Evans
  17. "Do give books – religious or otherwise – for Christmas. They're never fattening, seldom sinful, and permanently personal." - Lenore Hershey
  18. "My first copies of Treasure Island and Huckleberry Finn still have some blue-spruce needles scattered in the pages. They smell of Christmas still." - Charlton Heston
  19. "At Christmas, all roads lead home." - Marjorie Holmes
  20. "My idea of ​​Christmas, whether old-fashioned or modern, is very simple: loving others. - Bob Hope
  21. "The joy of brightening other lives, bearing each others' burdens, easing other's loads and supplanting empty hearts and lives with generous gifts becomes for us the magic of Christmas." - WC Jones
  22. "A Christmas candle is a lovely thing; It makes no noise at all, but softly gives itself away; While quite lonely, it grows small." - Eva K. Logue
  23. "Were I a philosopher, I should write a philosophy of toys, showing that nothing else in life need to be taken seriously, and that Christmas Day in the company of children is one of the few occasions on which men become absolutely alive." - Robert Lynd
  24. "Blessed is the season which engages the whole world in a conspiracy of love." - Hamilton Wright Mabi
  25. "The merry family gatherings – The old, the very young; The strangely lovely way they harmonize in carols sung. For Christmas is tradition time – Traditions that recall the precious memories down the years, The sameness of them all." - Helen Lowrie Marshall
  26. "There is no ideal Christmas; only the one Christmas you decide to make as a reflection of your values, desires, affections, traditions." - Bill McKibben
  27. "I wish we could put up some of the Christmas spirit in jars and open a jar of it every month." - Harlan Miller
  28. "Christmas is the keeping-place for memories of our innocence." - Joan Mills
  29. "Christmas is, of course, the time to be home – in heart as well as body." - Garry Moore
  30. "What is Christmas? It is tenderness for the past, courage for the present, hope for the future. - Agnes M. Pharo
  31. "Mankind is a great, an immense family … This is proved by what we feel in our hearts at Christmas." - Pope John XXIII
  32. "One of the most glorious messes in the world is the mess created in the living room on Christmas day. Do not clean it up too quickly." - Andy Rooney
  33. "Christmas – that magic blanket that wraps itself about us, that something so intimate that it is like a fragrance. day of remembrance – a day in which we think of everything we have ever loved. " - Augusta E. Rundel
  34. "Christmas is doing a little something extra for someone." - Charles Schulz
  35. "As long as we know in our hearts what Christmas bought to be, Christmas is." - Eric Sevareid
  36. "Christmas is the day that holds time together." - Alexander Smith
  37. "Christmas renews our youth by stirring our wonder. The capacity for wonder has been called our most pregnant human faculty, for in it are born our art, our science, our religion." - Ralph Sockman
  38. "Christmas … is not an eternal event at all, but a piece of one's home that one carries in one's heart." - Freya Stark
  39. "Christmas is a day of meaning and traditions, a special day spent in the warm circle of family and friends." - Margaret Thatcher
  40. "At Christmas play and make good cheer, For Christmas comes but once a year." - Thomas Tusser
  41. "What do you call people who are afraid of Santa Claus? Claustrophobic." - Unknown
  42. "Perhaps the best Yuletide decoration is being wrought in smiles." - Unknown
  43. "If there is no joyous way to give a festive gift, give love away." - Unknown
  44. "Until one dreams the spirit of Christmas, there is no Christmas. All else is outward display – so much tinsel and decorations. Firelight's glow. It's the warmth that comes to the hearts of men when the Christmas spirit returns again. " - Unknown
  45. "Many banks have a new kind of Christmas club in operation. The new club helps you save money to pay for last year's gifts." - Unknown
  46. "Are you willing to believe that love is the strongest thing in the world – stronger than hate, stronger than evil, stronger than death – and that the blessed life which began in Bethlehem nineteen hundred years ago is the image and brightness of the Eternal Love ? Then you can keep Christmas. " - Henry Van Dyke
  47. "Christmas is for children. But it is for grownups too. Even if it is a headache, a chore, and nightmare, it is a period of necessary defrosting of chill and hide-bound hearts." - Lenora Matttingly Weber
  48. "Like snowflakes, my Christmas memories gather and dance – each beautiful, unique and too soon gone." - Deborah Whipp
  49. "Somehow, not only for Christmas, But all the long year through, The joy that you give to others, Is the joy that comes back to you. your heart's possessing, Returns to you glad. " - John Greenleaf Whittier
  50. "Never worry about the size of your Christmas tree. In the eyes of children, they are all 30 feet tall." - Larry Wilde

Why Holiday Villas Are Popular in Most Holiday Destinations

Holiday villas with swimming pools are becoming a very popular form of holiday accommodation with holiday makers going on a family holiday. You are now able to stay in a villa in most countries in the world.

These holiday homes are especially popular in countries with a warm climate. There is nothing better than sitting outside your holiday villa by the side of the swimming pool with a cool drink.

When choosing a villa for your vacation you need to consider very carefully what sort of holiday that you want. The first thing to consider is what sort of climate that you are looking for. There are typically holiday villas in most climates but there is a much greater selection of villa in the countries that have a warmer climate. You must decide how hot you want it to be and what time of the year you want to go away on your villa holiday.

Having decided on the climate, you must then look to see which country can offer you that climate on your vacations. Some countries may require you to get a visa to spend your vacations there and other countries that you consider for a villa holiday may require certain vaccinations before you go there. Then check how long it will take you to fly to your chosen destination and also if there are flights available.

Once you have done this you can start thinking about what sort of villa accommodation that you are looking for. There are some superb villas available around the world and they vary in price to suite just about every budget.

For holiday makers looking for a relaxing holiday by the beach it is possible to find some stunning villas with swimming pools right by coast. For families looking for a villa in the mountains there are also plenty to choose from with some offering spectacular views over the local countryside.

Most holiday villas have swimming pools. You must check to see if you want a swimming pool with your holiday villa and what size the swimming pool is. Many holiday villas also have outside barbecue areas and outdoor seating areas. In some countries that have mosquitoes you will find that some of the holiday villas have mesh screens around them to keep the bugs out.

It is possible to find holiday villas to suite almost every budget. There are some small two bedroom holiday villas and also some huge holiday home with seven or eight bedrooms. Some families like to go on a villa holiday by themselves and others like to stay in a larger holiday villa and take friends with them.

Atypical villa will have bedrooms with en-suite bathrooms. Typically the master bedroom or suite will be much larger than the other bed rooms in the villa. It will also have the best bathroom in the villa. Typically it will have a walk in shower, large bath and his and hers washbasins and a toilet. Above the washbasins will be a large mirror and below there will be plenty of storage space.