Math and its Use in Everyday Activity

Math and its Use in Everyday Activity By, Malcom E. Gocken

1 Chapter 1: Basic Math A person uses basic math at least once every hour of every day. It consists of the most mundane activities of math, but comprises some of the most important functions of a human being’s day. The first all children learn quickly into their lives, known commonly as counting. You use counting to know things such as how many of something to buy at a store, as well as how much it costs. Counting is the base of all math, and is the base for most of the things you engage in every day. Though I will have to mention counting many times within this writing due to it being the base of 2 mathematics, it helps other math to perform usefully. One example is adding. Though adding can be almost exactly like counting, it helps you to count more quickly and more efficiently than actual number counting. Using adding helps you to combine large numbers together to form a new number that can be used for simple business extractions, trade, and knowing how much money you currently have. The opposite function of adding, subtracting, is used often in other functions of math, rationing in the military, and simple business exchanges. As it is simply the inverse function, it can be used in many similar ways. Subtracting is used in small stores for 3 how much change to return to a customer, estimate value, and to determine multiple lengths of time. You can use any of these three functions to determine age. Counting is the simplest but takes the longest and can involve multiple human errors. You can also tell the difference in your age to someone else’s by subtracting the lesser age from the greater age in the equation. You can even subtract the current year from the year you were born in to tell your own age or the age that you will turn this year. Another element of basic math is to be able to take measurements, whether they be in the Metric System or in the Imperial System. Those various units 4 are used to tell multiple measures of all objects, being both macroscopic and microscopic. They are used to compare data, to measure objects, and also to conduct scientific experiments. If I wished to measure the length or height of an object, I would simply measure them with some form of ruler. Once I have that measurement, I can find the perimeter of any square. For most other two-dimensional shapes, I have to gather two or more measurements. Another form of measurement is weight, which also has addition and subtraction able to be used to determine things such as the

5 difference between two animals weight, or what their combined weight would be. Now, there are obscure things that some may argue has no math involved in it whatsoever, but I believe that they are wrong. For something as simple as looking at a clock is a form of math, is it not? How do you tell time if you are unable to determine what the symbols on the clock represent? There are also the tick marks that are imbedded in the clocks in 60 different areas. You must be able to perform basic mathematics to count a clock’s ticks, as well as to estimate how much time you have to get ready before some important event. 6 A thermometer is another tool of measurement that you must be able to use. If you go out in the cold wearing a parka in blazing conditions, then either your thermometer is broken, there is something going on in your head that you should get checked, or you misread the thermometer. Telling what the thermometer has marked is just another of many ways to count, add, and subtract numbers.

7 Section 2: Elementary Math Now it’s time to jump into multiplication. Multiplication is another extremely common core function of math used for a huge variety of things. These things can range from the simplest questions of ‘How many apples should I buy if I want 5088 children to each have 23 apples?’ to questions as complex as it was to find the speed of light. The opposing function to multiplication is known as division. It undoes every aspect multiplication stands for, unraveling and twisting multiplication into its most basic digits. To give an example of its use, it can tell a business owner who 8 just got an order of 117,024 apples for 5088 children that each child will most likely receive 23 apples. Another interesting concept that division plays strongly into is the idea of fractions and chance. A fraction is a simple simplification of a number that usually is not part of a whole number, instead the number is usually an improper number. Fractions are used to express numbers that are not a completely whole object, such as ½ of an apple or 1/51354 of the known universe. Estimations and guessing go practically hand in hand. To estimate is to guess, and to guess is to estimate. Estimation is defined in mathematical 9 terms as rounding a number either up or down to make an un-precise number somewhat precise. Examples of this are the radical number pi, which is estimated to 3.14, even though it has shown to go on continuously in an infinitive path. You can use these four things to large advantages for a variety of professions, from a dancer to a professor of physics. For the example of the dancer, they can use fractions to determine the beat of the music. Music commonly states its beats in fractions, such as 4/4, 3/4, 2/4, and others. From a set of girders you can learn how much metal is inside of the girders by getting its area 10 mathematically. Knowing the area of an object can tell you how much of a substance there is, how much an empty or hollow substance can hold, and even what the material itself can fit inside of. Cooking measurements are read in degrees per Fahrenheit or Celsius, which can be converted from one to the other to tell another country of discoveries that could be important to the rest of human society. This can range from certain details of weather patterns to the heat conditions needed for animals in captivity, which is especially important to reptiles and amphibians.

11 Section 3: Junior-High Math Time multiplied by Speed is equal to Distance. This equation can tell how many miles you have to go if you already know how long it takes as well as the speed of your mode of transportation. You can also tell the time if you know how many miles you have to go (Distance) and the Speed of your mode of transportation. The equation changes depending on what you wish to find, as is common in all functions of mathematics. The volume of an object can be shown to be much less or much larger than one may believe. Knowing this can be useful for things like the game 12 industry, where you have to know how much circuitry and wiring you will be able to fit into a console or handheld or how much space you would need for all of the wiring. It can also be useful for any type of company that sells products in bottles, boxes, totes, and other delivery methods. Decimal numbers allow you to read gas pumps and hand out money without not knowing how a dollar breaks down into its decimal (coin) parts. If we were unable to tender money with this system, it’s possible that we could still be stuck with a system like ancient Rome had with giant iron bars and shillings or real value. 13 Exponents are used heavily in mathematics. It is utilized in things such as programming, computer analysis, and many other tech-based formats. They can also be used to solve of other numbers in problems that may need to be uprooted in equality statements, and is commonly used with cylindrical buildings and architecture with the function A=πr2. Knowing which numbers can only be reached by 1 and itself isn’t used very often, though it is still useful. Prime numbers are commonly used in cryptology and coding theory. In cryptology, they are used as two prime numbers for a “Public Key” that people can use to encrypt messages to the 14 cryptographer, and the cryptographer will have the prime factors, a “Secret Key,” of that number to decrypt the encrypted messages. Greatest Common Factors can be used to split things into rows or groups, determining how many people can be invited to a dance or party, and to split things into smaller sections. An example of these are arranging balloons in specific patterns, such as if you have 38 red, 24 blue, and 16 yellow, you can use GCF’s to determine how many you’d need in each row or column to make each have the exact same number of each color.

15 Place values are used all the time in everyday life with money. When you have $1.59, then you have a 9 in the hundredths place, a 5 in the tenths place, and a 1 in the ones place. It is also useful for when things are being grouped in tens, such as the measurements of the metric system. This includes liters, decimeters, centimeters, meters, etc. It is also used in the International Bureau of Weights and Measures, who measure such things as gas pumps to make sure that fairness is followed in all business dealings measured by weights and other measurements for value. 16 Venn Diagrams are commonly used in order to show two different sides to something as well as a middle ground between them. They can also be used as lists that group things according to specific characteristics, in this case they are usually composed of more than two circles and the middle shows something that has traits of all things in the lists. Rational numbers are used to find a wide variety of things when you know the total and wish to find a certain part of the whole. There are dozens of examples of this in real life, such as the cost of text messaging, scuba diving, duration of certain 17 activities, and many more. Rational numbers are by far one of the most diverse functions used in mathematics today.

18 Section 4: Algebra Triangulating distances can be extremely useful when you want to know the distance between one place and another. Many things use this method to tell where things are, such as forest fire lookout towers to locate spot fires. It was also used for large-scale land surveying until the rise of global navigation satellite systems. The distributive property can be used when shopping at a supermarket or the like and knowing what the sales tax is so that you can simply solve for the total price of all the groceries that you buy. It can also be used for when you wish to perform mental 19 calculations in your head quickly, such as 9 x 15. You can take 9 x 10 to reach 90 and then 9 x 5 to reach 45 and come with a different equation, 45+90, to reach the same answer to the equation: 115. A good brunt of problems in mathematics tend to be solved using systems of linear equations. When these problems are used in the involvement of real-life situations, they tend to be incredibly complex. That is one of the reasons that Linear Algebra is enthralled within its own branch of mathematics. However, I will give a simpler example of what it can be used for in real life. Take that you’re running a food stand and your manager wants to know how 20 many senior customers attend. To further simplify we’ll say that you were selling only one product for two different prices, an average and a senior discount. So let’s say that the food stand made about $436 in one day. You know that 230 people showed up in a single day, with everyone ordering only one item. You also know that the average price was $2.35 while the senior discount was $1.78. You could determine from that information exactly how many seniors appeared. Graphing is used in the real world to show data strands and how they interact with each other. They can also be used to indicate financial loss and gain. It 21 would seem that most graphs are used in order to indicate values and their places in any given system. That is also what the use of graphs in mathematics is, even though its use is a bit more shrouded. Quadratic Equations can determine parts of things that interact with you every day. They can determine the length of plane flights, the costs of manufacturing, how gravity acts upon an object, how certain forces interact with objects, the best price to put up for your supply and product demand, how much of something to manufacture, and more. Quadratic Equations are definitely an area of mathematics that will cause you to do better in life. 22 Radical Expressions are used in many functions of the everyday world. One of the things that they are commonly used in is electrical engineering. Another common place that radical expressions are used is in masonry and carpentry. The reason for this is the reliance on triangles that occurs in both masonry and carpentry, where triangles are used for nearly any type of building imaginable. Inequalities are a function of mathematics that would seem like they wouldn’t be used much. However, they are used to determine what margins of error can be allowed when trying to solve other

23 problems, as well as for when you need to make certain mechanical items. Determinants are used heavily in Linear Algebra and Matrices. They are used in matrices for such purpose as a way to display and analyze gathered data. Polynomial functions are used in many places of telling where certain things will be at during certain times. They can be used for numerous things, such as the stock market, water levels, demand for electricity, and even telling when a medical dosage is too high or too low. Polynomial functions are used commonly with Doctors of medicine and 24 pharmaceutical companies due to its value in how much medicine to give to a patient. Conic sections are most often used in conjunction in electrical systems. They are used in car lights in order to use high, bright beams of light and low, dim beams of light in the headlights. They are also used to allow you to watch satellite TV by means of a parabolic antenna.

25 Section 5: Geometry The Area of a Circle is used a lot in actual real world situations, you just have to know where to look. Civil Engineers use it for building structural support columns on bridges, sewer ways, and much more. It can also be used for finding an area of a swimming pool for your backyard, the size needed for a football stadium to fit both the field and fans, as well as even if you wanted to know what size pizza would be the best deal according to the entire area instead of its diameter. The Pythagorean Theorem is used mainly outdoors and in anything to do with triangles. You 26 will find yourself using it when surveying land, laying bricks, and in construction due to the nature of supports in a building. Surveying land often leads to mapping the same land, which also makes heavy use of the Pythagorean Theorem. The shapes of quadrilaterals surround us. Their shapes are used in nearly everything every day. They are used as kites, baking sheets, windows, blankets, and more. For so many of these it is also necessary to know how to do basic quadrilateral mathematics to find certain lengths and areas needed to fit things like windows into vacant spaces. 27 Angles are used in every part of the world today. Look to the side of your bed when you next get to it. What do you notice about your bed stand? The fact that it’s only held up by ninety-degree angles should be an obvious fact of its design, unless it’s one of those bed stands with little cat paws as its legs. Angles are used in the construction of buildings, in circles, and in any shape imaginable, both 3D and 2D. Triangles are used in building many structures. They are used in camping, in bridges, homes, curved domes, and even skyscrapers. A question then, would be why do architects prefer these shapes over others? They are thus chosen in the fact that their 28 two legs brace each other, and that a triangle’s shape is such that it will not change its dimensions without either a length being changed or a side snapping, unlike say a rectangle, which can contort into many different forms. Parallel lines aren’t used as much in human society as they are in nature. Though in some of these instances they are not truly ‘lines’ such as the banks of a river, which do never meet, but they have the potential to curve as well. Yet, they always curve in the same direction as the other bank. Another example of parallel lines are railroad tracks, which humans have used from the industrial era until now 29 for the transportation of people and heavy goods that nothing else can carry. We see circles being used around us every day. We see them being used to transport us from place to place. We see them being used to make something produce energy. We even see them being used to tell ourselves the amount of time in a day!

30 Section 6: Trigonometry Have you ever looked up to the stars, wondering what was there? Have you ever wondered if we could get there? Maybe we never could, but taking a human’s known lifespan and the various dangers of space travel, mathematics could give you a near-precise amount of time for how long it would take you to travel there. We can also tell the distance between two celestial bodies using those same principles. How important do you think that lighthouses are to society? If you’re familiar with the ocean, you’d realize that they are extremely important to us. 31 They have saved numerous humans from disasters against the sheer rocky surfaces that could have killed so many more than they did. All thanks to an understanding of how bright a beam of light needed to be for a boat to see it, how tall the lighthouse needed to be to be seen at the furthest point from shore, and where it should be built. All due to mathematical functions that saved lives. How tall is Mt. Everest? How do you know that? Someone didn’t hike step-by-step with a ruler, did they? No, no one did. We used triangulation of the mountain from sea level to determine its height. We do the same with any buildings that we 32 construct. If we didn’t have the capacity to use mathematics, we’d still be wondering at now casual mysteries like the height of Mt. Everest. It’s thanks to mathematics that we do not live in that dark world. Ocean tides are quite interesting, don’t you think? This is another speculation in nature where math will show its flowing cape of symbols. For, is it not true that waves are affected by the gravitational pull of the moon? If that is the case, then the equation of E=mc2 would seem to make an appearance. What about Sound Waves and Light Waves? Isn’t the understanding of mathematics what makes 33 our understanding of them possible in turn? Such as that a sound wave must have something to travel through. It cannot exist in something like a vacuum, like space. Light is also understood to be created by stars and replicated by us, as well as having a set speed that we have figured out, again all by the use of mathematics.