Attention Getting Question:
Have you ever decomposed fractions?
Fractions help us determine the number of equal parts that make up a whole. Fractions are also useful when creating fair portions. In order to make fair portions, we can use fraction decomposition. When something decomposes, it separates into smaller parts. Decomposing fractions is how we break down fractions into multiple parts that, when added, make the original fraction. Fractions do not have to decompose into equal parts, but can break down into any size fraction as long as they add together to make the original fraction.
Imagine it is your birthday party and, of course, the cake is the best part. There are eleven of your closest friends there celebrating with you and they are ready to eat. If half of the cake has already been cut, and you have six friends that still need a piece of cake, what fraction of the remaining cake does each of your friends get when the cake is cut into equal parts?
We can use decomposition of fractions to determine the size of each equal part. Since there are twelve people at your party, the cake is split into twelve pieces. Because half of the cake has already been cut, six-twelfths of the cake remains. Since there are six friends left that need a piece and six-twelfths of the cake remains, we can give each one of your friends one-twelfth of the cake. All of the cut pieces will add together to make the original fraction of six-twelfths of the cake.
Remember, decomposing fractions is not just adding together equal fractions to make the original fraction. We can make fractions of any size as long as the fractions add together to be the original fraction.
Imagine that somewhere in Florida there is a train that transports toys to children in North Carolina. One-tenth of the train is the engine that drives the train. This means that nine-tenths of the train can be used for delivering different kinds of toys for the children. Using decomposition of fractions, we can show what parts of the train are used to store the multiple types of toys. One way we can fill the train with toys is to use three-tenths of the train for dolls, four-tenths of the train for toy cars, and two-tenths of the train for bouncy balls. All of these fractions add together to make the nine-tenths of the train. Another way we can fill the train is to use one-tenth for dolls, two-tenths for toy cars, one-tenth for bouncy balls, two-tenths for crayons, and three-tenths for toy airplanes. Again, all of the fractions of the train that we filled with toys will add together to make the nine-tenths of the train.
To recap, decomposing is the process of breaking anything down into smaller parts and decomposing fractions is how we split up a fraction into multiple parts that add together to make the original fraction. As you can see, it is easy to decompose fractions into multiple fractions that will add together to make the original fraction.