Illustrating Fractions Concretely

In this tutorial, let's use apple to illustrate fractions more concretely. We could use the same fruit (banana) as before, but I was reminded of a very sad and actual experience in my few years of teaching Algebra to one of my Engineering classes.

In all of my examples in our lessons about fractions, I had used the same kind of fruit over and over again to illustrate fraction concretely in the class. My students were doing very well. They could easily answer all questions, and of course using the same fruit as in the example. However, when I had given them simple examination on fraction using another fruit, instead of banana, I used apple, there were some students who used to answer my questions very loudly, were not able to answer it.

The funny thing was, they told me "You give us banana before and now you're asking us about apple." So, to avoid the same result from occuring again, let's use another fruit this time to illustrate the same thing - fraction.

This time, we have an apple in the first picture above cut equally into six pieces as shown in the second picture.

Now, let's put all the six pieces together to form the whole apple again, and then removing one of them to give us picture like the one as shown in the third picture below.

In this picture, we can express two fractions: for the right part, we have 1/6 and for the left part, we have 5/6.

On the right side of each of the succeeding pictures,except for one of them which you need to send your answer by posting your comment below, is the summary of the corresponding fractional expressions as described briefly.






Left: 5/6

Right: 1/6






Left: 4/6 or 2/3

Right: 2/6 or 1/3






Left: 3/6 or 1/2

Right: 3/6 or 1/2






Left:?

Right:?





Left: 5/6

Right: 1/6





Left: 4/6 or 2/3

Right: 2/6 or 1/3





Left: 3/6 or 1/2

Right: 3/6 or 1/2







We will discuss more on this part, especially on the reduction of fraction into its lowest expression when we have finished discussing our tuturials on the four basic mathematical operations: addition, subtraction, division and multiplication.