Algebra

algebra is a part of math where letters are used to represent unknown numbers

these letters are known as variables

we still use the order of operations (a.k.a. B.E.D.M.A.S.) in algebra

it will also serve you well to have a firm understanding of Negatives before beginning algebra

and remember that when you have an equation and are solving for an unknown variable 

what you do to one side of the equation you must do the same to the other side

(just like when you do something to the top of a fraction you must do the same to the bottom)

let's look at an example...

x + 10 = 18                                 ( you may note right away that x = 8 )

to solve this equation isolate the variable x by subtracting 10 from each side of the  = 

          x + 10 = 18

    x + 10 - 10 = 18 - 10

                   x =  8

another example...    5y - 3y = 16

                                            2y = 16                 this can be seen as a      2y = 16

                                      2y ÷ 2 = 16 ÷ 2             division either way       2       2

                                                         y = 8                                                   y = 8

a more complicated example...

                                                2 a + 3 = 7

                                                3

                                          2 a + 3 - 3 = 7 - 3

                                          3      

                                             2 a = 4                and now we multiply each side by the reciprocal

                                                       3                          of the fraction attached to the unknown variable

                                    3 x  2 a = 4 x 3

                                    2     3              2

                                              a = 12

                                                                   2

                                                          a =  6

You may already be familiar with solving for an unknown number through finding N with proportional reasoning.

                                                                            Example:         N    =     6

                                                                                                   20         40

you may also be asked to simplify an equation... put your matching variables (likeables) together

(remember: what you do to one side you must do to the other)

example...                9a + 2b - c - 12 = 3 ( 2a - b - c ) + 4b - 5

                                 9a + 2b - c - 12 = 6a - 3b - 3c + 4b - 5

                                 9a + 2b - c - 12 = 6a + b - 3c - 5

            9a - 6a + 2b - b - c + 3c -12 + 12 = 6a - 6a + b - b - 3c + 3c - 5 + 12

                                                3a + b + 2c = 7

It should be noted that simplifying can occur with both algebraic expressions and algebraic equations. The difference between the two is that expressions do not have an equal sign and equations do have an equal sign. Both follow the rules of simplification in algebra where you but likeables together (remember to take into account the sign in front of each term)

One part of algebra is to 'plug in' numerical values for your variables.  You may already be familiar with through finding the area of squares, rectangles, parallelograms by 'plugging in' numbers representing height and width. (A = H x W)

Or with by 'plugging in' the numbers for base and height to solve for the area of any triangle.

                                                                                                                    (A = b x h ÷ 2)

In each case you 'plug in' the value of each letter with a number and then continue to solve the equation.

more to come...

like:  y = mx + b

         finding slope

         FOIL

         factoring polynomials

         Word problems