Egg Carton Fractions and Basic Operations
Division with fractions often causes great difficulty, especially if we don't understand just what division with fractions (or any kind of numbers, for that matter) is all about. If we think about of division as a grouping process (see lesson 2 - division), then it's not so hard to understand. When we see 8 ÷ 2, we can think "How many groups of two are in eight?". The same is true with fractions. The problem 1 and 1/2 divided by 1/4 becomes "How many 1/4's are in 1 and 1/2?". That's easy to show with egg-carton models...
Here's another example, 3/4 ÷ 1/5. We just need to make sure our egg carton can be divided into five parts as well as four parts...
Sometimes, the number we are dividing by is bigger than the number we are dividing into. The model works for that, too. Here's a look at 1/3 ÷ 5/6.
As you can see, division with fractions can be an intuitive process. If we remain faithful to the meaning of the division operation and use a model, any kind of problem can be solved.