p R28-31, B 18-21, G 17-22
Variables and Expressions You Tube link for following video. Thank you Mrs. Griffin at www.nutshellmath.com
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.
Numerical expressions
Numerical expressions are expressions that contain only numbers and operation signs. NO variables (letters) are used.
Algebraic expressions
Algebraic expressions are expressions that contain variables and operation signs. They can contain numbers too.
Variables
Variables are used in math for two reasons:
1. There is a mystery number. Noone 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, so that we can see what the answer would be if that number were this number or that number.
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
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 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. • 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
Do you understand everything? If not, what do you still have questions about? Ask (and answer!) in the comments section.
