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When we shop for groceries on a limited budget, for example, we might have to account for the taxes on certain goods that aren't exempt from taxes. Perhaps multiple each item by the number of mouths to feed, and then maybe replace one of each to account for someone with allergies.
Maybe you have three kids, and each eats two pieces of fruit each school day, three vegetables each day, and a pint of ice cream each weekend day, or some other blend of purchases that must be repeated frequently in order to survive.
That problem can be represented with an algebraic math equation.
When we want to purchase anything that is on sale or discounted a certain percent, we must employ simple algebra equations to fulfill our needs. When we learn any other science subject, we must first have a basic understanding of the principles of Algebra and Algebraic equations in order to understand those topics.
To understand algebra at its simplest form, certain concepts must first be assimilated and understood. In this quick math course, we are going to review the basics of algebra and most of the concepts that will be needed in later courses.
Let's begin with math in its simplest form, and evolve our course from that elementary example. Algebra has equations that are read from left to right. That will be important later because when two operators are equal in an equation, then the equation begins being read from the left.
Next is the order of operators: 1) Parentheses, 2) Multiplication and Division are equal, 3) Exponents, 4) then addition and subtraction come last.
So, for example, (4-(2-5*2)^2-3)/(-3) = -21 is obviously incorrect, since it's positive twenty one (+21). Let's find out why.
Don't want to wait? Learn it now
For example, we know that:
1 + 1 = 2. So therefore, if x = 1, then x + x = 2
because x is 1 and 1 + 1 = 2.
That's easy.
Let's try that again.
2 + 1 = 3
If a variable named y is equal to 1,
then 2 + y = 3
because we defined the variable y to equal 1.
Now what if we don't know one of the numbers, perhaps the 2. In that case, when we write the above equation, instead of a 2, we place a variable[D: a character representing a numeric value or number] in its place.
Let's try it again.
The variable p = 3
And the variable q is unknown
But we know the following equation is true:
p + p = q
Then q must equal 6, right?
Because p = 3,
Then p + p = 3 + 3 = 6
Therefore, q = 6.
1 + 1 = X Or we could say:
1 + x = 2
You can decide what character you use as a variable, but keep in mind the following:
If you draw or write a symbol not available on a keyboard, then when you want to type the equation and your brain is working already on making sure you copy it right from paper, then remembering that cool symbol you drew before is now another thing to keep track of and could result in errors down the line. Meaning, keep it simple or as simple as possible for the sake of ease of use or understanding.
Let me explain. While you are free to choose any character or symbol at your discretion[LR: discrete, discretionary, lat: cogitare, sp: crer], you are not the first person to learn Algebra. Many others have learned the hard way that if everyone uses different variables to represent the same thing, then when someone else looks at your version of the same equation, precious time will be wasted translating your variable choices to the ones they will have understood.
So, what people did with their fancy public school systems served a la suburbua was agree on certain variables being standards for certain things.
One day, I'll link to a comprehensive[D: All inclusive but not necessarily complete] spreadsheet of all industry standard variables so we can all enjoy that saved time on better moments, but for now, here's some guidelines.
The upper carat symbol ('^') is a standard for symbolizing a power or exponent of a number. For example, X^2 is X to the second power or X squared.
Another example is the lower case i, which is reserved in advanced mathematical theorems for the imaginary number. Rest assured, any mathematics dependent upon the imaginary number or required to prove another equation true follows these three important rules:
1) The imaginary number will never be useful in anybody's future,
2) The imaginary number will never have any positive affect on your life or anybody else's life that we know, and
3) The imaginary number-based equations are still theories and even if they result in equations that do not include the imaginary number in them and seem to be true by all accounts, they were still proven using a fictitious algorithm based upon an imagined number that doesn't exist, which means the equations are not reverse engineer verifiable.
Back to math that can help our daily lives. Other standard symbols include:
t for time,
v for velocity,
d for distance (also diameter),
n for number,
g for gravity,
f for force,
r for radius,
h for height,
l for length,
p for price,
two numbers next to each other, each surrounded by parentheses symbolizes the multiplication symbol even though it is omitted, so (4)(3) = 12.
That same equation can be written (4)*(3)=12, or (4)x(3)=12, or 4*3 = 12, or 4 x 3 = 12.
All of those equations are the same.
x, y, and z together are used to symbolize each axis of a three-dimensional plane,
a for acceleration (also alpha)
/ forward slash for dividing the first number into the second,
< and > are the less than and greater than symbols, respectively. These symbols should not be confused with the same symbols in the context of programming HTML tags or when used to symbolize flow of text.
There's plenty more, but as you can see, most of the variables we thought we would get to invent ourselves have already been standardized.
Let's continue learning the math.
The equation we were working on is simple:
If:
1 + 1 = X And because we know that 1 and another 1 gives us 2, then we can logically deduce that in order for the equation to be true, X must equal 2;
Otherwise, the equation would not be true and the equal sign would have to be replaced with a greater than or less than symbol for any other value of X other than 2.
1 + 1 < 3
1 + 1 > 1.5
So that is an introduction to Algebra. Next, let's solve: 1 + y = 2z
Algebra 100 Intro
Algebra is a scary word to some people, myself included, but it doesn't have to be. Really, it's just a fancy way of complicating the simple math we normally do anyway everyday. The equations that represent these daily transactions are often unknown or perhaps unrealized in our day-to-day activities, but they can provide useful new perspectives on how we interact in society.Uses of Algebra
Algebra is useful in many others ways too though. All the functions we perform on the daily can, in one way or another, be represented using Algebraic equations.When we shop for groceries on a limited budget, for example, we might have to account for the taxes on certain goods that aren't exempt from taxes. Perhaps multiple each item by the number of mouths to feed, and then maybe replace one of each to account for someone with allergies.
Maybe you have three kids, and each eats two pieces of fruit each school day, three vegetables each day, and a pint of ice cream each weekend day, or some other blend of purchases that must be repeated frequently in order to survive.
That problem can be represented with an algebraic math equation.
When we want to purchase anything that is on sale or discounted a certain percent, we must employ simple algebra equations to fulfill our needs. When we learn any other science subject, we must first have a basic understanding of the principles of Algebra and Algebraic equations in order to understand those topics.
To understand algebra at its simplest form, certain concepts must first be assimilated and understood. In this quick math course, we are going to review the basics of algebra and most of the concepts that will be needed in later courses.
Let's begin with math in its simplest form, and evolve our course from that elementary example. Algebra has equations that are read from left to right. That will be important later because when two operators are equal in an equation, then the equation begins being read from the left.
Next is the order of operators: 1) Parentheses, 2) Multiplication and Division are equal, 3) Exponents, 4) then addition and subtraction come last.
So, for example, (4-(2-5*2)^2-3)/(-3) = -21 is obviously incorrect, since it's positive twenty one (+21). Let's find out why.
Don't want to wait? Learn it now
For example, we know that:
1 + 1 = 2. So therefore, if x = 1, then x + x = 2
because x is 1 and 1 + 1 = 2.
That's easy.
Let's try that again.
2 + 1 = 3
If a variable named y is equal to 1,
then 2 + y = 3
because we defined the variable y to equal 1.
Now what if we don't know one of the numbers, perhaps the 2. In that case, when we write the above equation, instead of a 2, we place a variable[D: a character representing a numeric value or number] in its place.
Let's try it again.
The variable p = 3
And the variable q is unknown
But we know the following equation is true:
p + p = q
Then q must equal 6, right?
Because p = 3,
Then p + p = 3 + 3 = 6
Therefore, q = 6.
Variables
A variable is anything representing something else in mathematics or science. Computers, physics, engineering, and many more science topics all rely on variables. A variable acts as a symbol of a number we do not yet know for sure. So now, with a variable of X in place of the 2, the equation would be written as follows:1 + 1 = X Or we could say:
1 + x = 2
You can decide what character you use as a variable, but keep in mind the following:
If you draw or write a symbol not available on a keyboard, then when you want to type the equation and your brain is working already on making sure you copy it right from paper, then remembering that cool symbol you drew before is now another thing to keep track of and could result in errors down the line. Meaning, keep it simple or as simple as possible for the sake of ease of use or understanding.
Tangent
As equations get more complicated, small mistakes in the beginning could grow into big mistakes later. Avoiding complications will reduce errors.Variable Symbols
Also, using symbols such as a dollar sign ('$') or something you found on your new mobile device, perhaps whatever this symbol is: ¥, could already be used as a reserved symbol representing something else; for example, Ï€ = 3.14 approximately.Let me explain. While you are free to choose any character or symbol at your discretion[LR: discrete, discretionary, lat: cogitare, sp: crer], you are not the first person to learn Algebra. Many others have learned the hard way that if everyone uses different variables to represent the same thing, then when someone else looks at your version of the same equation, precious time will be wasted translating your variable choices to the ones they will have understood.
So, what people did with their fancy public school systems served a la suburbua was agree on certain variables being standards for certain things.
One day, I'll link to a comprehensive[D: All inclusive but not necessarily complete] spreadsheet of all industry standard variables so we can all enjoy that saved time on better moments, but for now, here's some guidelines.
Variable Guidelines
Typical math numerals are italicized letters, usually lower case, but sometimes upper case, such as if you choose X, because a lower case X could be confused with a multiplication symbol. So of course, to add to the confusion, lower case x is in fact the standard for multiplying any two numbers but also for teaching variables in Algebra classes. I don't specifically remember ever running across the equation: X x X = X^2, but you can see how using a variable that appears identical to the symbols that modify it can be confusing. The asterisk ('*') is also used as the standard for multiplying but specifically with computer programs and programmers, and has in some cases replaced the letter X on graphic user interfaces ('GUI').The upper carat symbol ('^') is a standard for symbolizing a power or exponent of a number. For example, X^2 is X to the second power or X squared.
Another example is the lower case i, which is reserved in advanced mathematical theorems for the imaginary number. Rest assured, any mathematics dependent upon the imaginary number or required to prove another equation true follows these three important rules:
1) The imaginary number will never be useful in anybody's future,
2) The imaginary number will never have any positive affect on your life or anybody else's life that we know, and
3) The imaginary number-based equations are still theories and even if they result in equations that do not include the imaginary number in them and seem to be true by all accounts, they were still proven using a fictitious algorithm based upon an imagined number that doesn't exist, which means the equations are not reverse engineer verifiable.
Back to math that can help our daily lives. Other standard symbols include:
t for time,
v for velocity,
d for distance (also diameter),
n for number,
g for gravity,
f for force,
r for radius,
h for height,
l for length,
p for price,
two numbers next to each other, each surrounded by parentheses symbolizes the multiplication symbol even though it is omitted, so (4)(3) = 12.
That same equation can be written (4)*(3)=12, or (4)x(3)=12, or 4*3 = 12, or 4 x 3 = 12.
All of those equations are the same.
x, y, and z together are used to symbolize each axis of a three-dimensional plane,
a for acceleration (also alpha)
/ forward slash for dividing the first number into the second,
< and > are the less than and greater than symbols, respectively. These symbols should not be confused with the same symbols in the context of programming HTML tags or when used to symbolize flow of text.
There's plenty more, but as you can see, most of the variables we thought we would get to invent ourselves have already been standardized.
Let's continue learning the math.
The equation we were working on is simple:
If:
1 + 1 = X And because we know that 1 and another 1 gives us 2, then we can logically deduce that in order for the equation to be true, X must equal 2;
Otherwise, the equation would not be true and the equal sign would have to be replaced with a greater than or less than symbol for any other value of X other than 2.
1 + 1 < 3
1 + 1 > 1.5
So that is an introduction to Algebra. Next, let's solve: 1 + y = 2z