LETTERS ARE NUMBERS?

What do you mean a letter is a number? That's nuts right?

Well, not completely. In algebra you have letters that have a job to take the place of numbers; these numbers are usually unknown or numbers that can change. Math folks call these letters variables because they can be different. When given an algebraic expression (remember that means numbers, operations and at least 1 variable) you may or may not be given a value to represent the variable. Starting off we will work with an expression and I will give you a value for the variable.

To work with expressions it is very very very important that you understand the expression you are reading. For example:
    a.) 3m  {This means 3 times the value of m}
    b.) x - 7 {This means the value of x minus 7, or take 7 away from the value of x}
    c.) 4p + 2 {This means 4 times the value of p and then add 2}

When a value is given for a variable you are going to use substitution. Just like when I was absent there was another teacher in my place which is why they call them substitute teachers. Also like the coach sending in a player to replace you during a game.

In example a.) 3m again means 3 times the value of m, if the value of m is 7, this means to multiply 3 times 7. Often students want to just replace the letter with the value and say the answer is 37.

In example b.) x - 7, if the value of x is 18, this means to subtract 18 - 7. Not as tricky because the operation sign is there to direct you correctly.

In example c.) 4p + 2, if the value of p is 3, this means to multiply 4 times 3 first and then add 2. It should be written like this 4(3) + 2 (remember parentheses is another symbol for multiplication). Multiply first and then add 2.


Substitution is not hard as long as you understand what the expression is and what it is asking you to do.