Fractions
The concept of fractions can sometimes be confusing and if this confusion is not cleared up then the later processes involving fractions become very difficult to understand.
Often the concept of fractions is only partly understood in the early years of schooling which means that a child may be able to do very well in some questions on fractions and not be able to correctly answer other questions that seem to be of a similar level. This can lead to a lot of frustration.
An important fact that is sometimes overlooked is that there are parallel concepts of fractions and each of these has developmental stages.
The first stage is to understand that fractional parts must be equal. If a cake is cut into two parts and the parts are equal then the cake has been cut in half and each part is a half piece of the cake. This is the foundation of the concept that the size of the fraction is based on the number of equal parts that have been created by a division.
The application of the above concept is that if the cake is cut into two parts and one part is bigger than the other then the cake has not been divided in half. This is the foundation of the concept that dividing something into equal parts creates fractional parts.
The above step and its application lay the foundation for all the subsequent concepts regarding fractions. Although both concept and application seem similar they are actually very different in terms of skill levels required.
In fractions the concept is about the size of the part once it has been created and the application is about creating the equal part through division.
It can be immediately seen that the application of fractions is indelibly (or permanently) linked to dividing and the associated facts and skills of division. As such multiplication facts and the converse division facts are crucial for achieving mastery of fractions. If these facts are not known then even if a child understands fractions they will not be able to demonstrate their understanding adequately.
Therefore the importance of multiplication and division skills cannot be overstated.
The questions below illustrate the difference between concepts and application.
1. Ann was shown the picture below of 15 apples. What fraction of the apples is in the box? Simplify your answer.

2. Ann was asked to put 3/5 of 15 apples into a box. How many apples does she have to put in the box? 
The first question is relatively easy to answer and many students only require counting skills to get the answer  3 columns of apples out of 5 columns of apples and the answer is 3/5. However the parallel question (Question 2) requires the student to use division (15 divided by 5 = 3) and multiplication skills (3 multiplied by 3 = 9) in order to complete the task accurately. It is this application of fractions that causes the most frustration.
Knowing that there are two aspects to understanding fractions and acquiring the skills required to complete questions like Question 2 above will go a long way to helping students experience less friction with their fractions.