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First thing's first- math is a discipline of academia just like English and science and the like. One of the things about math is that a lot of people psych themselves out about it, or had a very negative experience with a teacher. As long as you approach it like a subject instead of a goliath, it should be a little easier to handle.
Let's start with the basics.
1. Arithmetic.
Before we can even touch statistics and calculus, we got to learn the four operations.
Addition and multiplication will give the same answers regardless of the order of the numbers being added or multiplied. Observe:
12 * 4 = 48.
4 * 12 = 48.
12 + 4 = 16.
4 + 12 = 16.
In the same fashion, we can make multiplication a lot easier on ourselves. You can break the two numbers into their factors(the numbers that, when multiplied, give the number) and get the same result. Observe:
12 * 4
12 can be broken down to 4 * 3.
4 can be broken down to 2 * 2.
So, you can make 16 * 3 and 24 * 2 look like 12 * 4- without changing its value. The process of taking factors manually is typically done through factor trees when it's just an ordinary number. Factoring terms that include variables will be included with algebra.
Keep in mind, though- division can not be switched around and retain its value.
6/3 = 2.
3/6 = 1/2.
However, you can break the numbers into its factors for easier division.
3 * 2/ 3 = 2.
Subtraction is only able to switch around like addition if you change it to adding a negative number.
4 - 3 = 1.
3 - 4 = -1.
4 + -3 = 1.
-3 + 4 = 1.
Don't forget PEMDAS: Parenthesis, Exponents, Multiplication and Division, and Addition and Subtraction.
1.2. Negative Numbers and Rules
Negative numbers are simply numbers to the left of zero. Zero is greater than any negative number. When it comes to negative numbers, the smaller the magnitude(absolute value), the larger the number. Now, how does that work?
It's sort of like driving. If you need to drive ten miles north, then driving south simply makes the distance even greater. Even where you started off is better than where you end up by driving south.
Negative numbers still exist, but they are simply in the wrong direction.
When you multiply a negative number with a positive number, it becomes negative. It may not make sense initially, but remember that multiplication is like speed-adding. You're just adding a negative number so many times over itself.
When you multiply a negative number with another negative number, the negatives cancel.
1.3 Exponents, Logarithms, and Rules
Now, if multiplying is like speed adding, putting things to a power is like speed multiplying.
The number being put to an exponent is called the base. It will be referenced in the rules this way.
Exponents, like anything else in math, have rules.
Anything to a zero power is one. (There's a lot of nerd debate as to whether or not zero to a zero power can be one, but it's very rare anyway. In calculus, there will be infinity to the zero power, which doesn't exist because infinity doesn't exist.)
Anything to the first power is the original number.
When you multiply like bases, you add their exponents.
When you divide like bases, you subtract their exponents.
When you put a base with an exponent to a power, you multiply the exponents.
Logarithms are the inverse of exponents- it looks for the exponent needed to make the number using a pre-determined base. The two normal logarithms have a base of 10 and a base of e. The latter is referred to as the natural logarithm and is represented by ln, whereas the former is a standard logarithm and is represented by log.
Note: If you have a logarithm with any other base, you have to specify. For example, if you wanted to use a logarithm with a base of two, you'd write log(subscript 2).
Logarithms have rules too!
log(subscript b) (b) = 1.
log(subscript b) (1) = 0.
a log(subscript b) (c) = log(subscript b) (c ^ a)
log(subscript b) (a) - log(subscript b) (c) = log (subscript b) (a / c)
log(subscript b) (a) + log(subscript b) (c) = log (subscript b) (a * c)
You see how I used letters to represent numbers? Those are called variables.
That's all I got for arithmetic. I'll write another post for algebra, since that will be considerably more extensive.
So, do you like it? Make critique and ask questions below. ^^
Let's start with the basics.
1. Arithmetic.
Before we can even touch statistics and calculus, we got to learn the four operations.
Addition and multiplication will give the same answers regardless of the order of the numbers being added or multiplied. Observe:
12 * 4 = 48.
4 * 12 = 48.
12 + 4 = 16.
4 + 12 = 16.
In the same fashion, we can make multiplication a lot easier on ourselves. You can break the two numbers into their factors(the numbers that, when multiplied, give the number) and get the same result. Observe:
12 * 4
12 can be broken down to 4 * 3.
4 can be broken down to 2 * 2.
So, you can make 16 * 3 and 24 * 2 look like 12 * 4- without changing its value. The process of taking factors manually is typically done through factor trees when it's just an ordinary number. Factoring terms that include variables will be included with algebra.
Keep in mind, though- division can not be switched around and retain its value.
6/3 = 2.
3/6 = 1/2.
However, you can break the numbers into its factors for easier division.
3 * 2/ 3 = 2.
Subtraction is only able to switch around like addition if you change it to adding a negative number.
4 - 3 = 1.
3 - 4 = -1.
4 + -3 = 1.
-3 + 4 = 1.
Don't forget PEMDAS: Parenthesis, Exponents, Multiplication and Division, and Addition and Subtraction.
1.2. Negative Numbers and Rules
Negative numbers are simply numbers to the left of zero. Zero is greater than any negative number. When it comes to negative numbers, the smaller the magnitude(absolute value), the larger the number. Now, how does that work?
It's sort of like driving. If you need to drive ten miles north, then driving south simply makes the distance even greater. Even where you started off is better than where you end up by driving south.
Negative numbers still exist, but they are simply in the wrong direction.
When you multiply a negative number with a positive number, it becomes negative. It may not make sense initially, but remember that multiplication is like speed-adding. You're just adding a negative number so many times over itself.
When you multiply a negative number with another negative number, the negatives cancel.
1.3 Exponents, Logarithms, and Rules
Now, if multiplying is like speed adding, putting things to a power is like speed multiplying.
The number being put to an exponent is called the base. It will be referenced in the rules this way.
Exponents, like anything else in math, have rules.
Anything to a zero power is one. (There's a lot of nerd debate as to whether or not zero to a zero power can be one, but it's very rare anyway. In calculus, there will be infinity to the zero power, which doesn't exist because infinity doesn't exist.)
Anything to the first power is the original number.
When you multiply like bases, you add their exponents.
When you divide like bases, you subtract their exponents.
When you put a base with an exponent to a power, you multiply the exponents.
Logarithms are the inverse of exponents- it looks for the exponent needed to make the number using a pre-determined base. The two normal logarithms have a base of 10 and a base of e. The latter is referred to as the natural logarithm and is represented by ln, whereas the former is a standard logarithm and is represented by log.
Note: If you have a logarithm with any other base, you have to specify. For example, if you wanted to use a logarithm with a base of two, you'd write log(subscript 2).
Logarithms have rules too!
log(subscript b) (b) = 1.
log(subscript b) (1) = 0.
a log(subscript b) (c) = log(subscript b) (c ^ a)
log(subscript b) (a) - log(subscript b) (c) = log (subscript b) (a / c)
log(subscript b) (a) + log(subscript b) (c) = log (subscript b) (a * c)
You see how I used letters to represent numbers? Those are called variables.
That's all I got for arithmetic. I'll write another post for algebra, since that will be considerably more extensive.
So, do you like it? Make critique and ask questions below. ^^
Oh, we definitely do that here. Lots of specific questions. I just thought it was really out of the blue to have such a random post.
