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.

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.

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.

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.