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.

Furniture Store Marketing – When Everyone Is Your Customer, No One is Your Customer!

One of the biggest challenges home furnishing owners must overcome, in order to be successful in this new economy, is the dreaded I-offer-everything-for-everyone syndrome. On the surface this looks like a sure-fire way to get more customers, but it is already proven time and time again that it is not always the most successful way to prosper in your store.

If you are an independent home furnishing retailers, then chances are you have a limited budget and limited space to work with. So, if your store offers several contemporary collections, several ultra-modern collections and some eclectic pieces as well as some early American collections scattered through you store, do you really think that you have enough of any of those styles to satisfy the type of customers who are looking for a specific style? However, style is only one way to target your customer.

In fact, the most successful furniture retailers in my area focus on a couple of things to attract a specific type of customer:

  • Complete living room packages for under $ 2,000 or furnish your entitlement home for under $ 5,000.
  • Long-term low or no interest financing
  • Fast delivery within 3 days or less
  • Lower prices for packages

So, by narrowing down their advertising, they attract a customer that wants to purchase multiple pieces, which in turn, drives the average ticket sale and profits up. They then offer attractive financing terms which attracts customers with good credit and income, while enticing them to spend more money because the customer has longer to pay for it.

Most importantly, they save the customer money by buying more and can get it in their homes in a couple of days. There is also another twist to these retailers. They reward their salespeople handsomely for NOT selling the financing, but getting customers to pay off their balances in less than 90 days.

There is a common slogan in marketing statute, "There are riches in niches." Simply put, this slogan means determine who your most profitable, enjoyable and easy to attract customer is, and then specialize in getting more of those customers to come into your store and buy. You do this by creating a USP (Unique Selling Proposition) that compels your most profitable customer to come back into your business again and again.

What if you reviewed your business over the last couple of years and discovered the following trends about your customers and prospects:

  • Wives initially visited the store without their husbands.
  • Recently married
  • Had three kids
  • Lived within five miles of your store
  • Spent between $ 800 – $ 1500 on sofa, loveseat and tables.
  • Paid by Visa, MasterCard or Discover

Once you have this information, you can redesign your store and business to cater to more of the same types of customers that are currently spending good money in your store.

However, you can only use this information to your advantage if you take the time to find out who your customer is, what is important to them and what they really want.

It may come as a surprise to you, but your customers want more than just a sofa. If you are just selling a sofa, you are missing out on a ton of business. Here are a few of the keys I have discovered over the years:

  • Do not sell mattresses, sell relief from back pain.
  • Do not sell home theater seats, sell the entertainment experience.
  • Do not sell sofas or loveseats, sell comfort and warmth.
  • Do not sell furniture, sell status and prestige.
  • Do not sell interior design, sell ENVY and the WOW factor!

Once you know what your customers really want then, you could use that information to create a USP that attracts more of the same type of customers. For example:

  • "Do not hire expensive interior designers, use our 23 point design checklist and give your home a million dollar look for FREE!"
  • "Discover how to give your home an extreme $ 20,000 makeover, on an $ 8,000 budget."
  • "Your family and friends will say" Oh my gosh! Your home is simply amazing! "In 27 seconds flat … we guarantee it!"

Life Insurance 101, An Explanation of Various Types of Life Insurance

TERM LIFE INSURANCE – Life insurance for a set number or years. You can choose from 5 to 30 year terms. No cash value, if you die during the term you collect the death benefit. The policy dies after the selected term has ended and you receive nothing unless you have a, return of premium rider or you convert the policy to some form of permanent insurance.

RETURN OF PREMIUM TERM INSURANCE (ROP) – A term insurance policy that returns all or a portion of premiums paid at the end of the term if the death benefit has not been paid.

SIMPLIFIED TERM INSURANCE – Term insurance which uses a simple application. Underwriting is done electronically. No underwriting requirements by the applicant unless red flags arise out of the electronic underwriting process. Policy is usually issued much quicker than regular term. There is a limit of death benefit for this type of policy ($350,000 or less) depending on the insurance carrier. This type of policy is generally more expensive because of additional risk by the insurance carrier. Less underwriting =more risk.

CRITICAL ILLNESS INSURANCE – Applied for as a stand-alone policy or as a rider to another life insurance policy. Pay immediate benefit for a covered illness even if death does not occur.

ACCIDENTAL DEATH INSURANCE – Pays benefit in event of a covered sudden accidental death. Applied for as a stand-alone policy or as a rider to another form of life insurance.

MORTGAGE PROTECTION INSURANCE OR DECREASING TERM INSURANCE – Term insurance that pays the balance of your mortgage should death occur. The amount of death benefit decreases to match the amount owed on mortgage. The insurance is set up to end at the same time your mortgage is set to end.

UNIVERSAL LIFE INSURANCE (non variable) – Flexible premiums. Can be a permanent insurance as long as premiums are paid and policy is funded properly. Investment policy in which risk lies with insurance company.

Has a minimum guaranteed interest rate which differs by company. This policy has the ability to gain contract value. The death benefit can be set to level (death benefit stays the same throughout) or increasing (death benefit increases as contract value rises). You may obtain loans or make withdraws but you must be careful, if the policy is not funded, it will collapse.

VARIABLE UNIVERSAL LIFE INSURANCE – Agent must have securities license to sell. Very similar to non-variable universal life. The difference is that the policy owner assumes investment risk. There is no guaranteed interest rate. Policy can collapse if investment does not do well and policy is not funded properly.

WHOLE LIFE INSURANCE – Simply put, you pay the premium and the policy will last your whole life. You usually have an option to borrow against the policy, amount depends on the value of the policy. This type of policy is usually much more expensive than the universal life policy.

GRADED BENEFITS WHOLE LIFE – Partial or no benefits paid until a named or tiered waiting period has passed. If you die before the waiting period has passed, you usually will receive the return of your premium payments with some sort of interest.

FINAL EXPENSE WHOLE LIFE INSURANCE – This type of whole life insurance is aimed at burial and funeral expenses and other final expenses. Usually, no medical exam required and death benefit is limited to $50,000 or less.

SINGLE PREMIUM WHOLE LIFE – This whole life policy is paid for by a single lump sum payment. In return the beneficiary receives a larger death benefit than the payment.

THINGS TO CONSIDER: You may be interested in mixing and matching different types of policies. For example; There is a need for 500k immediately. As time goes on, the kids have graduated college and are out of the house, the house is almost or totally paid off. Now the need is less. In this example you may want to purchase a 330k universal life and a 20 year 200k term. This plan will save you money and still protect your family for life.

Or, you may want to mix term, critical illness, accident, universal life, or whole life in various ways depending on your needs.

RIDERS:

Waiver of Premium Rider – pays life insurance premium if you become disabled and can’t work. There is usually a waiting period and rider usually expires at age 60 or 65.

Critical Illness Rider – Rider is explained above.

Return of Premium Rider – Rider is explained above.

Guaranteed Insurability Rider – this rider allows you to purchase an additional amount of life insurance at a later date without having to prove insurability again or take another medical exam.

Term Conversion Rider – allows you to convert a term insurance policy into a permanent policy without proving insurability again.

Accelerated Benefit Rider – this rider is only for permanent life insurance policies. This rider is usually included automatically for free. It allows you to collect a portion of your policy’s death benefit if you become terminally ill with a short life expectancy, usually one year. The portion paid out is subtracted from you policy’s death benefit.

Accidental Death Benefit Rider – This rider pays in addition to the death benefit if you die from an accident.

Child protection Rider – Usually used to pay final expenses if the unthinkable happens. Often, at a nominal cost and purchased in units of $1,000.

UNDERWRITING: requirements depend on insurance carrier, type of policy, amount of death benefit, age, build chart, gender, medical history, medications, family history, motor vehicle report, and other factors.

An application is always required, although, non-medical policies usually have a simple application.

Requirements could be: Paramed (certified medical processor or nurse comes to your place of choosing, takes you through a medical questionnaire, measures your height and weight, takes blood and urine sample, possibly EKG either resting or non-resting), Medical information from your physician or hospital, Medical exam, etc.

HEALTH CLASSES – Typical health classes would be, Preferred Best, Preferred, Select Standard, Standard, and then different nicotine classes such as, preferred nicotine, select nicotine, and standard nicotine.

It is possible to be rated less than standard depending on health and underwriting factors.

You must qualify for a health class. This is chosen by the underwriter after the underwriting process is complete. The agent can only quote you the different health classes but this can change with the underwriting process.

Internet Marketing – The Basic Step of SEO in “Off Page Optimization”

SEO or Search Engine Optimization it the most important thing in Internet Marketing. It is the way of website optimization, sometimes how to be search engine friendly, so our site can appear on the first page of search results on the search engines, and so we can get free traffic from search engines.

SEO has 2 important phases:

  1. Optimization on the site itself (On-page Optimization)
  2. Optimization beyond the site (Off-page Optimization)

This time I will describe what is "off-page optimization".

What is Off-Page Optimization?

In a simple word Off-Page Optimization is the activities we do on our site with the goal of creating robots that search engines rate sites our site is famous among other sites. This is also known as "Link Popularity"

How famous our site among the other sites (with a particular target keyword) will be a consideration in determining search engine positioning of our site in search engine result.

Based on the experience of internet marketers who have been successful, Off-Page Optimization is very important now, even that says Off-Page Optimization is much more important than the On-Page Optimization. But I think both of them are important to get a high ranking on search engines.

The main components of the Of-Page Optimization, or to determine how famous our site is through the quality back links. So if you want the robot is considered as a famous site we need to have a lot of quality back links.

Back Link have 2 types:

1. One direction or One Way Back Link, where other site link to our site, but our site does not link back to the site. This is usually our sites have information that is considered interesting and he recommended to the visitor of their site.

2. Two-way (mutual link). Also known as "Link Exchange" or exchange links. Note that One Way Back Link has a wine better on search engine than two-way link.

Which link back is good for the Off-Page Optimization?

Many webmasters make the mistake and has wrong mind with Back Link. They tried to find link partners as much as possible without examining the positions, topic and status of the site which will be invited to become their Link-Partner.

To avoid this the following steps are necessary to find a quality Back Link:

1. When searching for potential link partners, select the same site, or at least close to the topic or topics related to our site.

2. Search site potential link partners with high-rank page.

3. When we do Link Exchange see where they will put the link. Usually they have a special page for Link Partner, see the page rank of the special page, either they have a high page rank or not. This is very important.

Note: Page Rank of each page of your site in one domain can be different. Although the main page has a high Page Rank, the other Page Rank can be lower or even zero. Or the Page Rank of the main page is lower but the other pages inside is higher. This can be caused by the On-Page Optimization and Link Back obtained by the page.

Conclusion:

– Do not exchange links with the other sites with different theme. – Do not link sites that has Page Rank 0 – When you want to Link Exchange, do not accept the link of our site is putting in the page with Page-Rank 0

4. Calculate how many link partners were there! Do not try to link the sites that have links Partner or save more than 50 links on one page!

Note: Value of Page Rank will be divided evenly with all of the existing link partners. More number of link partners that are stored in one page, the smaller Rank value will receive by each link partner.

5. Look at Anchor Text used for our site at the site of link partners, is already in line with our target keyword? Anchor Text must be the keyword of our target.

Many Webmasters are looking for Link Partner as much as possible without considering the above. Actually we do not need to find thousands of links to sites we create are considered by a robot, just looking for 30-60 quality links that are eligible that have been described above.

The Main points of the Off-Page Optimization:

1. Try the link + description of our website are there in the other sites, this is called the Back Links.

2. There are two kinds of Back Links: One Way Back Links (one-way link) and Link Exchange (exchange link).

3. For Link Exchange, search for related theme site.

4. Search potential site link partners that has high Page-Rank. Download Google toolbar http://toolbar.google.com to know the Page Rank of a site. When is found contact them to exchange links.

5. If they agree, check where the link is placed, see the Page Rank page, do not accept a link placed on the page Rank 0.

6. Calculate how many links that are posted on there, do not link to a site that has a link partner of more than 50 links in one page.

7. Always use the Anchor Text, the site's main keywords should be used the description of the link on the site of link partner.

Note: Although we have done all the above correctly, free traffic from search engines will not come immediately, but takes time. Give time 5 months to 1 year to see the results. While waiting for the results we can make another site. Remember, SEO is the most important thing in Internet Marketing .