Solving Equations by Multiplying and Dividing (1-11)

Solving Equations by Multiplying and Dividing

Vocabulary:

Multiplication Property of Equality - Multiplying both sides of an equation by the same number, the
                                                            statement is still true.
Division Property of Equality - Dividing both sides of an equation by the same nonzero number, the
                                                   statement is still true.

Examples:

x  = 20            Think of this as a fraction containing a variable. This is set up as a division problem.
7                      The only way to get the variable alone is to use the inverse operation of
                        division...multiply (Multiplication Property of Equality)
(7) x  = 20 (7) This will cancel out the 7 under the x, leaving x alone. Don't forget whatever you do 
      x  = 140     on one side of the = sign you must do on the other, so we multiply 20 by 7.  This gives
                         you 140. COOL TRICK: For some it is difficult to multiply 2 or 3 digit numbers. If
                         your numbers contain a 0, like 20, use Zero Property. With zero property you can
                         drop the 0, as in the case of 20 x 7. Multiply 2 x 7...14 now put the zero back on the
                         end of the number...14 is now 140.

240 = 4z          Any time we have a number next to a letter (variable) we will multiply. That is unless
240 = 4z          we are going to be using the inverse operation. For multiplication it is division
  4       4           (Division Property of Equality). It is important that we use the integer next to the
60 = z              variable, since our objective it to get the variable alone. Placing the 4 under 4z
                        cancels out the 4's leaving the z (variable) alone. Once again, we can use 
                        Zero Property to make the division easier to work with. Just don't forget to put the zero
                        back when you are done.

Video Help:

https://www.khanacademy.org/math/algebra-basics/core-algebra-linear-equations-inequalities/core-algebra-solving-basic-equations/v/solving-one-step-equations-2

https://www.youtube.com/watch?v=6Buj_mPTW3o

https://www.youtube.com/watch?v=2eEgMLHyNpQ