Intro to operations (2)

In the previous page I mentioned some common operations. It may seems a lot, but the operations are really connected with each other:

  • They often work in pairs. Think of one operations "do" something to the number, then there will be another operation "undo" the work. For example, subtraction "undo" addition, so if you add 3 then subtract 3, essentially you did nothing. Those pairs are called "inverse operation" of each other.
    • Addition and Subtraction are inverse operations
    • Multiplication and Division are inverse operations
    • Power and Root are inverse operations
    • Exponential and Logarithm are inverse operations...
  • Some operations are more "compact" way of doing the other operations:
    • Multiplication is a compact way of doing addition, say to add 2 five times, you can either do addition: 2+2+2+2+2, or you can simply do 2*5. Now, which operations will you choose when you need to add 2 a hundred times?
    • Power is a compact way of doing multiplication, you can multiply 2 three times, 2*2*2, or you can use power (cube) 2^3
Operations has priority (like onion has layers), some has to be performed first, this rule is often called "PEMDAS", this is short for "Parenthesis, Exponent, Multiplication and Division, Addition and Subtraction". This means you always do what's in parenthesis first, then see if there is any exponent (power), then take care of multiplication and division (they have same priority), lastly Addition and Subtraction (they have same priority). 

Note when you solve for an equation with variables you will go backwards, because you can't add variable and number together, so you want to "unpack" them, just like peel the most out layer of an onion.

Something cool: In the future, your teacher may tell you "addition and subtraction are really the same thing, multiplication and division are the same thing". That is because subtract a number is same as add a negative number, and divide a number is the same as multiply by 1 over that number.

Comments

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