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.

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Golden Triangle Tours: Best Way to Explore Culinary Delights and India’s Riches

Golden Triangle Tours is the name given to the most fascinating touring circuit of India. Unleashing the country's historic past, its heritage, colorful cultures and flavorsome cuisines, Golden Triangle Tour packages takes one to a whirlwind ride of Delhi, Agra and Jaipur. The path to the touring circuit is resplendent with fortresses, spectacular palaces, historic monuments, UNESCO applauded World Heritage Sites and culture capitals. Encompassing Golden Triangle cities brings a visual treat to the eyes of history, art and architecture lovers, but it is also an opportunity for food frantic to taste real flavor of India.

Gourmets Feast Upon Delhi Cuisine: The capital city of India, Delhi is also a hub of political and cultural activities. A fabulous metropolis Delhi is also a significant center of education and technology; also its historical heritage is very impressive, but the real charm of the city is in its cuisine. Delhi is a potpourri of cultures, it has a mini-India in itself and has welcomed people of various cities, states, color and creed with open arms and thus the variety in its cuisine and flavor in its food is one to die for. From tangy Chaat (kind of spicy snack) to delicious curries and lip-smacking Mughlai there is an abundance of choice of food. Eating joints, low- budget restaurants, road side vendors to elite restaurants and more authentic Delhi cuisine means best of Indian food. From Punjabi style cooked South Indian food to Chinese Tadka-Mar-ke and of course famous Kebabs and Tandoori food, Delhi offers et al to satiate your taste-buds. One can even have best of authentic Continental and world cuisine in Delhi well-known as the Food-Capital of India.

Jaipur's Royal Grandeur: No Golden Triangle Tours are complete without experiencing royal charm which is well preserved till at the stunning palaces and fortes of Jaipur. On a sightseeing tour across famous royal capital of Rajasthan one experiences a royal saga unfolding at hilltop Amer Fort, honeycomb shaped- Hawa Mahal and fascinating royal observatory- Jantar Mantar. Mesmerizing sight of City Palace further add to the charisma of Rajasthan ideally known as the princely state of India. Explore its bazaars to pick interesting hand-made curios; silver jewelry, colorful puppets, hand-printed fabrics and more the vibrant bazaars of Jaipur will indeed sweep you off your feet with their elegance and simplicity. Further a mesmerizing performing art scene is a must for all those touring the fabled touring circuit.

Agra: What appears to be a painter's fantasy coming alive is actually a living specimen of Mughal artistic excellence. Agra is where the ultimate emblem of love- Taj Mahal is located which made city world-renovated. Also, Agra is well-known for other UNESCO World Heritage Sites such as Agra Fort and Fatehpur Sikri. On Golden Triangle Tours in India the sights of these UNESCO riches are a must visit for they give a sneak peep into the country's architectural heritage and also brings closer to its legendary history of mighty Knights and their dynasties.

In a nutshell Golden Triangle Tours avails a quick introduction to the vast sub-continent of India.

Real Estate Agent Job Description

Real estate agents liaise between home owners and buyers to conduct the sale, purchase or rent of properties. They work for brokers and play a major role in assisting people buy or sell residential, commercial or industrial property. They keep and maintain an up-to-date account of property listing and other relevant housing information to stay abreast with properties available on the real estate market. They subscribe to several listing services to advertise and market properties up for sale. They also contact property and market properties up for sale. They also contact property owners to obtain information regarding a property.

As part of their responsibilities, estate agents present sales and purchase offers to clients for consideration. They advise them on property rates, legal requirements and general market trend. They also interview clients to determine their property preference or specification. Usually, they prepare a list of properties that best match the needs and requirements of clients. They visit and inspect properties in order to establish precise property value. They also proffer recommendations to clients on properties that best suit their budget and preference.

Most estate agents oversee the preparation of closing statements, purchase agreements, representation contracts and other necessary documents required for estate trade. They conduct negotiations between property sellers and buyers to establish price and other terms of sales. They also liaise with pest control operators, home inspectors etc. to ensure the terms and conditions stated in a purchase agreement are met prior to the closing of sales.

In fulfilling their role, real estate agents oversee the closing of property sales, they ensure payment is complete and appropriate documents signed. They maintain contact with clients to offer them real estate services/products and assist with the resolution of issues. They also provide consultation services to clients to recommend strategies for the speedy sale of property. They often conduct training programs for junior/trainee sales agents to enhance their sales skill. This job position requires at least a high school diploma, state license for practice and an aptitude for sales. Qualities needed for the job include persuasion, interpersonal skills and problem-solving skills.

Real Estate Agent Job Description Sample

Given below is a sample of the job description usually handed real estate agents by most employers:

  • Act as liaisons to conduct real estate trade between property buyers and sellers
  • Present sales offers to clients as well as bid on available properties
  • Carry out investigations to determine client credit status and ability to complete payment
  • Inspect properties to appraise its value and estimate the worth on the property market
  • Interact with clients to identify their requirements and proffer recommendations on properties that best suit their budgets
  • Assist home sellers in promoting their buildings on property listing services to attract clients for purchase
  • Prepare and deliver sales pitches to clients in order to secure real estate contract
  • Provide clients with a list of properties available for sale to assist them in making choice selection
  • Conduct price negotiations between property buyers and sellers to ensure a fair bargain for both parties
  • Provide clients with a tour of residential, industrial or commercial properties to showcase and explain property features
  • Carry out investigations to confirm clients have clear property titles
  • Provide appropriate reply to client’s enquiries concerning property appraisals, financing, maintenance etc.
  • Examine property premises to recommend maintenance measure required to improve the face value
  • Assist clients in evaluating mortgage options to obtain the best rate and terms
  • Attend conventions, conferences and seminars to improve existing job knowledge and expand personal network.

If you are a recruiter needing the best real estate agent to hire, you can use the sample job description above in making one for your company, for use in hiring and assigning duties to the successful candidates.

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