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Mathematics is a very important subject in people’s lives to the extent that one can not totally live without it. It does not just teach us to know how to solve mathematical problems in class but to generally be great problem solvers of problems in life. Most of the time when we are given hard mathematical problems, we usually analyze them first, by looking at each problem from all perspectives and noting down every detail. We then work out the likely solution and test it. This is exactly what happens in one’s life when faced with a problem, the problem is analyzed by looking at it from all perspectives, details sorted out and right decisions regarding its solution are made. These problems keep occurring over and over in peoples’ lives and therefore math always comes in handy. Basing on these, this term paper is going to look at a very important branch of mathematics that is applied in one’s every day life, Algebra.
Algebra is simply defined as a form of mathematics that deals with equations and symbols. Decimals, whole numbers, percentages and fractions seem to be everywhere in our lives. They are needed when dealing with money, taking accurate measurements, in understanding probability, following results of sports, lotteries or election polls and in doing many other things in life. All these fall under arithmetic, dealing with numbers. You will meet numbers almost everywhere you go. Algebra is different in that it is not obviously seen by many although they encounter it in one way or the other. There are many people who will claim that they have lived comfortably without using it, or there are those who might have studied it when young but have not seen its practical benefits and therefore will see no value in it. This might be true to some extent because the Algebra value is not as obvious as that of other disciplines like Arithmetic, but in reality its usefulness is always around us (Usiskin, 1995).
To understand this hidden value of arithmetic we will have to find answers to some frequently asked questions. Questions like; why is it taken to be so important as to make it a requirement for entry in almost every college? Why is it made to be compulsory in schools even when not all students will pursue it in future? And some of the answers are that, without algebra knowledge; one will miss out on jobs or on programs that can land him a job; one loses control of his life and therefore has to rely on others for assistance; one is likely to make unwise financial decisions and; one will not be able to understand many ideas that are taught in the other disciplines. Just as lack of knowledge limits one from doing many things, it is the same with lack of algebra, which limits one’s capabilities and therefore one can not do without it (Usiskin, 1995).
Algebra can be taken to be a language of generalization in that it provides one with a language of describing something that is done over and over, it describes patterns and most patterns are formulas and as it is known, formulas state quantities in terms of others. These formulas are met in all walks of life. For example changing temperature from Fahrenheit to Celsius needs a formula; F=C+3. If one is looking for a place to stay and would like to know the dimensions of the room to live in, he will use the formula for area. This also applies in tailoring in determining the amount of material needed for a particular cloth. There is also the formula for perimeter that helps one in determining the amount of fencing needed for a field, or the length of ribbon to tie a package. There are also formulas used in sports, for instance in baseball when calculating earned-run average or rating a quarterback in football, or in basketball, you can determine the probability of a player making two free throws in a row. When dealing with money matters like discounts, sales tax, income tax, you will need a formula. Some people get along without these formulas but are prone to being fooled by others (Usiskin, 1995).
Algebra enables one to answer questions that are similar at one time. For instance if one wants to borrow money, and as it is known, borrowed money must be paid back on a monthly basis, of course with an interest that is usually given a yearly rate. One will therefore want to know how much he will pay monthly, something that is not easy to calculate without a formula. With a formula this is easy even if one is given strange figures. Such kinds of formulas can also help one in determining miles per gallon that a car gets and therefore helps one to know exactly the amount of fuel that he will need for a particular journey (Usiskin, 1995).
Algebra as a language that relates quantities is also very important in one’s daily life. Here questions touching on the aspects of one’s health as he grows old, or changes in weight, or changes his diet or takes a different type of medicine? How much it will cost in producing a piece of clothing if the factory decides to make more or if it uses a different material? How will changing one’s spending habits affect his budget? How does the population affect energy use in the world? And many more questions. These types of questions form the foundation of functions, which are described using long tables or graphs by those who lack algebraic knowledge. Algebra gives a shorter and easier to interpret description; it also gives more information that might be missing in the other descriptions. These functions are the ones that form the basis for calculus, which requires knowledge of algebra to use (Usiskin, 1995).
Algebra can be used as a language that solves specific types of numerical problems. This helps one to know the amount of a particular food he or she can eat and comfortably stay within a particular diet. How much one can spend and still remain within the budget. Existence of a formula that relates two quantities helps a person to get one quantity if given the other and this uses algebra (Usiskin, 1995).
Some important Algebraic Topics and their Applications
There are important topics in algebra that are used almost in everyone’s daily life. These are; Linear equations- these arise from anything that undergoes a constant rate of change. They generally have the formula T=Ax +By. Such formulas help in determining total cost of items provided each item costs the same. For example determining the total calories or minerals consumed, getting total cost on household bills like electricity and other energy costs, the cost that one meets in renting a car, and when making a long-distance call. Algebra can help in indicating the initial and additional cost of a phone bill from a long-distance call per minute (Usiskin, 1995).
Quadratics: this is where the paths followed by objects are described. Many objects in our daily life follow given paths that can be described by quadratics, these include planets, comets, stars, moons, meteors, rockets and even bullets, baseballs, basketballs and many objects that can be thrown. These are applied in activities that employ the throwing or propelling of objects. For instance in armed services, in physics, space science, in hobbies and in sports (Usiskin, 1995).
Logarithms: is another important topic of algebra. This comes in handy when dealing with scales that cover quantities whose magnitudes are vast and different, like the earthquake’s Richter scale, the Ph scale used in chemistry, in astronomy there is the star magnitude scale and many more statistical scales. Ideas from Permutations and Combinations are used in determining the odds in winning any game of chance; lotteries, card games and many others (Usiskin, 1995).
As it has been shown, algebra is indeed a very vital discipline in one’s daily life. The universe and all that is contained in it function according to the principles of mathematics which are more precisely explained through algebraic equations. Software developers, scientists, engineers and mathematicians all need algebra knowledge. The technologically advanced world of today finds it more important than ever before. Though people do not tackle algebraic problems directly, many of them solve algebraic problems without realizing daily in their homes, schools or places of work and those who do not use it in their daily life still benefit from those who use it. For instance in the transport sector where many people are affected, the use of algebra to calculate the amount of fuel and its cost ensures that enough fuel is filled in a certain vehicle for a specific journey to avoid inconveniences along the way. In the making of many food products, algebra is used to calculate the amount of calories in the particular food for the benefit of the consumer. These therefore show that no one can absolutely deny that algebra plays a big role in his/her daily living.