From an outside perspective, math can look pretty scary.
How would you even start to understand something like this? Three words:
Order of Operations (OoO)
No matter how simple or complicated whatever question you're trying to solve is, every solution will, by necessity, follow the order of operations.
Order of operations dictates the priority of each operation in an equation. Regardless of the complexity of the question, you need to resolve each before moving on to the next.
PEMDAS is the mnemonic I learned to keep OoO straight in my head.
P - Parentheses
Any operations contained in-between parentheses MUST be computed before EVERYTHING else (the computations within must also necessarily follow OoO).
Example:
5 * (1 + 2)
If we ignore the parentheses and simply evaluate the expression from left to right, we'd end up with 5 * 1 + 2 = 7. Incorrect.
When we tackle what's within the parentheses first, the expression correctly evaluates like so:
(I am going to use -> as a proxy for saying "plug this in". This is NOT notation used anywhere else, but it's easier for me to type out here.)
5 * (1 + 2) = ?
(1 + 2) = 3 ->
5 * 3 = 15
A massive difference from such a simple mistake. Failure to simplify the contents of parentheses FIRST is likely the singularly most common mistake by those who are starting out. Be careful!
We can also have nested parentheses, like so: (5 + (5 * (5 * 2)))
Looks more complicated, but fret not, as we can use OoO to sort this mess out.
We tackle what's in the first set of parentheses: 5 + (5 * (5 * 2))
Then we realize there's another set of parentheses that takes priority, so we look at the contents contained within the second set: 5 * (5 * 2)
Yet again, we have a set of parenthesis in our equation, so we take a peek at what's inside: 5 * 2
Look at that! No more parentheses! Now we can solve this part, and plug it back into the second, and the second into the first.
(5 + (5 * (5 * 2))) = ?
5 * 2 = 10 ->
5 * (10) = 50 ->
5 + (50) = 55
We have our answer!
E - Exponentials
Exponents are written as much smaller numbers above and to the right of the chunk of the equation they're being applied to. The smaller, raised number represents a repeated multiplication of the base number.
Example:
If we raise 2 to the 3rd power, 2^3, it is the same as multiplying the base (2) by itself 3 times.
2^3 = 2 * 2 * 2 = 8
We can even have exponents apply to entire equations within parentheses like so:
(2 + (2 * 2))^2
This may start to look a bit complicated, but remember - parentheses first, THEN everything else.
First we find the innermost set of parentheses and work out from there to simplify the expression:
(2 + (2 * 2))^2 = ?
(2 * 2) = 4 ->
(2 + 4) = 6 ->
6^2 = 6 * 6 = 36
M/D - Multiplication/Division
The remaining categories are some basic mathematical operations. Multiplication and division are the SAME THING, just in different directions, so neither takes priority over the other. When there is only multiplication and division left, simply evaluate the expression from left to right*.
*(Technically, left to right isn't strictly necessary, but it's a good habit to get into due to how easy it is to lose track of what you've already done in a problem.)
Example:
2/2 + 4 * 3
Multiplication/Division first, so:
2/2 + 4 * 3 = ?
2/2 = 1 AND 4 * 3 = 12 ->
1 + 12 = 13
A/S - Addition/Subtraction
Like multiplication and division, addition and subtraction are the SAME THING, just in different directions, and can be handled in the same step. These should be tackled as the last operation in the current chunk you're trying to solve.
Example:
1 + 2*(4/2) - 3 = ?
4/2 = 2 ->
2 * (2) = 4 ->
1 + 4 - 3 = 2
Order of Operations informs every level of mathematics, no matter how complex the equation you're trying to solve might be, it will ALWAYS obey OoO. This is by FAR most important piece of information you need to be able to do mathematics, everything else is a matter of practice and exposure.
If you can lock OoO down, you can begin to learn any branch of mathematics you want. Just remember to break your problems down and solve them chunk by chunk!
