Problem The concept of unit conversion is relatively simple to demonstrate. Lets use the following example. 475 apples have been colledted. It takes 3 apples to make one pie. As many pies as possible need to be made. The pies need to be wrapped and boxed after they are made. 8 pies fit in one box. So the question is, how many boxes are need for the given amount of apples?
Solution
number of boxes = 475 apples *
1 pie
3 apples
*
1 box
8 pies
= 19.79 boxes, or rounding up, 20 boxes
Think about it this way, 3 apples make one pie, and there are 475 apples. So how many pies can be made? To find the answer, 475 (the number of apples) is divided by 3 (the number of apples per pie), or 158.33 pies can be made. So if there are 158.33 pies, and 8 pies fit in one box, how many boxes are needed? Again, divide 158.33 (the number of pies) by 8 (8 pies per box) and you get 19.79 boxes, rounding up to an even number is 20 boxes.
Well, in the above equation, instead of dividing by 3 and 8, we are multiplying by 1/3 and 1/8, so that the units can be cancelled out nicely. Multiplying by 1/3 is the same as dividing by 3.
Units cancel out in fractions the same way that numbers do. If there is a unit in the numerator, and the same unit is in the denominator, they cancel out.
