Proportions and Ratios!

OK, to recap what we did today:
1) We use proportions in daily life. Recipes, speed (miles/hour, feet/second), and prices ($3.50/6 pack) are three examples.


2) There are two main ways to solve them. The real world way and the math way.
     i) Real World: Figure out what "one" is (how much per person, how long it takes to go one mile, the cost per can of soda, etc.) then multiply by the total we want (times the number of people we're serving, times the number of miles we went, times the number of cans we need).
     ii) Math: Set up two fractions equal to each other and multiply

      3        x
     ---  =  -----
      5       15

Multiply by 15 to get the x by itself.

     15      3
     --- *  ---  =  x
      1      5

         45
        -----  =  x
          5

          9   =   x

Sometimes the x is in the denominator. If it is, flip both fractions first.

       12       20
     -----  =  -----
       7        x

Flip:

       7         x
     -----  =  -----
      12        20

Then multiply:
 20      7          
---- * -----  =  x
 1       12

 140
-----  =  x
 12

Make sure to reduce!

  35
-----  =  x
  3