The basic ideas of naming fractions and equivalent fractions developed on the other page of this lesson can be extended to include some concepts that we might not normally consider. Before, we stated that the numerator of a fraction described the parts under consideration compared to the total number of parts, described by the denominator. We can expand this definition a bit to include situations involving more than one whole unit, or, in this case, egg carton. Suppose we try this; put three egg cartons together and divide the whole amount into four equal parts:
Take a look at each of the parts. How much of an egg carton is in each part? The answer is interesting...
Thus, three cartons divided into four parts makes each part 3/4 of a carton. This is known as the division concept of a fraction, or the division model for fractions. It is extremely useful in problem solving. For example, if you wanted to share 5 candy bars between 8 friends equally, each would get 5/8 of a candy bar!
There is another interesting idea we can portray with the egg carton model. Suppose I divide an egg carton into sixths, and then put 5 eggs into the carton...
Two-and-one-half of the parts out of six are filled in. That gives us a fraction of 21/2/6. This seems unusual, but it is a perfectly good fraction name, and is meaningful. It can be readily seen that it is equivalent to 5/12. These kinds of fractions are called complex fractions.
One last idea concerning egg carton models. We have seen that a 12-egg carton can be divided into halves, thirds, fourths, sixths and twelfths. But there are other kinds of egg cartons; some have six egg spaces, some have 18 egg spaces, and some 24 or more. These cartons can serve as models for fractions with denominators besides 2, 3, 4, 6, or 12, and we can visualize any size carton we want to in order to suit our purposes
I'll leave you with a question: What size egg carton model could you use to model fractions like 3/8? How about 4/10 or 5/9? Can you think of other fractions to try to model?