Dividing Fractions Problem - Why does order matter?

Question

Billy made 1/2 a quart of lemonade. Each glass holds 1/6 of a quart. How many glasses will Billy be able to fill?

Question: Why do I have to do 1/2 divided by 1/6? Why can't I do 1/6 divided by 1/2? Why does order matter in dividing fractions?

 

 

Answer 1

In this problem, you are asked to find how many glasses of 1/6 quart can be filled by a container of 1/2 quart, so you have to divide 1/2 quart by the number of quarts in one glass to get the number of glasses that can be filled.  That is

 

(1/2 quart) / (1/6 quart/glass) = 3 glasses

 

If you divide 1/6 by 1/2, you are calculating how many 1/2 quart containers can be filled by 1 glass of 1/6 quart, which is

 

(1/6 quart) / (1/2 quart/container) = 1/3 of a container of 1/2 quart

 

Those are two different calculations when you flip the order.

Answer 2

1/2 divided by 1/6 = (1/2)(6/1) = 3 glasses

1/6 divided by 1/2 = (1/6)(2/1) = 1/3 glass, which makes no sense.