Class Notes Variables And Expressions

Class Notes: Algebra: Variables and Expressions Course 1: Ch 1 L 6; Course 1 Ch 4 Vocabulary: Algebra- Math which uses letters of the alphabet (called variables) to represent numbers. Expressions Think of an expression as one side of a math problem. If the math problem is: 2 + 3 = 5. The math expression is: 2 + 3. 5 is not a math expression. Expressions can have: numbers, letters (variables), or numbers and letters (variables) Expressions must have at least one operation sign: addition, subtraction, multiplication, or division Expressions must not have an equals sign. Numerical expressionsNumerical expressions are expressions that contain only numbers and operation signs. NO variables (letters) are used. Algebraic expressionsAlgebraic expressions are expressions that must contain variables (letters of the alphabet) and operation signs. They can contain numbers too. VariablesUsually a letter of the alphabet, but it could be any symbol that is not a number. For instance, an empty box, a question mark, a blank underlined space. Variables are used in math for two reasons: 1. There is a mystery number. No one knows what the number is yet. We know it's a number, but we don't know which number. Your job is to find out the mystery number or "variable". 2. There is a number which we want to be able to change or switch frequently, so that we can see what the answer would be if that number were first one number and then another, and another number.

Class Notes: Variables and Expressions p. 2 In the above example of 2 + 3 = 5, we knew quite a few things. a. The + sign, told us it was an addition problem. b. The 2 and the 3, told us the exact two numbers (amounts) being added together. c. The = sign told us we know the answer for the question. What is 2 + 3 added together? The = sign says, "Keep reading, I'm going to tell you right after this symbol for equals '=' ." d. The 5 tells us that 5 is the exact same amount (or you could say, the answer, or our book likes to call the answer, the value) as 2 + 3. If I change that problem to this problem, 2 + ? = 5. Now all of a sudden, we don't know what one number is in advance. We have to figure out what is added to 2, to become 5. When we figure that out, we figure out what the ? is. The ? can only be one number, the number 3. The ? sign in that problem is called a variable. It is a symbol put in the place the number belongs. Once the number is figured out, we put the actual number in its place. We "solve for the variable". When the variable is defined (Example: x = 4) Sometimes you will be told what the variable (mystery number) is. Like this: x = 4. Then all you need do to solve an expression, or find the value of an expression, or find the answer is substitute the known mystery number for the variable. Like this: 7 + x They told us what the variable (or mystery number) is x = 4, so we rewrite the expression like this: 7 + 4. We took out the variable x, and in its place substituted the 4. Now, because we CAN, we solve the expression like this: 7 + 4 = 11. The expression 7 + x can NOT be solved any further, so we keep it just that way, UNTIL we are told or can figure out what the variable (mystery number) is. If all we are given is 7 + x we don't have enough information to solve the problem any further. So we keep it this way. If we are given an equation, 7 + x = 11; now we have enough information to figure out the one number x has to be. And we can solve for x. x = 4.

You can use anything you want to show a variable. You can use an empty box, a blank line, a question mark, anything at all. And you have probably seen empty boxes and blank lines used in first and second grade a lot. But, in math, the favorite choice to use for variables are letters of the alphabet. And the favorite letter to use in math and in algebra is x. That creates a problem. From now on, you have to be careful. Is the x a variable, or does it mean multiply? Other ways to show the multiplication operation Most mathematicians do not use × to show multiplication anymore. Instead they choose one of these methods for showing the multiplication operation. 1. A raised dot •, also called a dot operator, or a bullet operator. Like this: 2 • 3 = 6 or like this 2 • x = 6 2. A parenthesis around one or both of the numbers or variables. Like this 2(3) = 6 or (2)(3) = 6 or like this 2(a) = 6 or this (2)(a) = 6. 3. Or they leave out the parenthesis and just smush two or more things together. BUT not when ONLY numbers are involved. Like this 2a = 6, BUT NOT like this 23 = 6, because 23 is the number 23, NOT 2 × 3, and 23 does NOT = 6. IF mathematicians use this symbol × for multiplication, they usually write it like a lower case printed x. Then, if they need to use the variable x, they make the x cursive or italicize (slant) it. Expressions vs. equations Expressions are math problems that do NOT have an equals sign. Like this: 2 + 3 Equations are math problems that DO have an equals sign. Like this 2 + 3 = 5