Using the capabilities of the Computer Algebra System (CAS) behind Grasple it is possible to create exercises that allow your students to practice with mixed numbers. However, mixed numbers are not interpreted as such in the CAS by default, so they need special attention. Below we explain all ins-and-outs of the support of mixed numbers within the platform.

A mixed number is defined as a number consisting of an integer and a fraction. So the mixed number 2 1/2 represents two and a half, or 3/2. However, in the default mode, the CAS system behind Grasple will interpret the expression 2 1/2 as 2 x 1/2, so two times a half, which is equivalent to 1.

In order to make sure the CAS interprets 2 1/2 as a mixed number (and thus equal to 5/2) you can use the Read Expression With Mixed Numbers parameter type. This parameter type takes an expression and assumes that constructs such as 2 1/2 represent mixed numbers, instead of a multiplication.

For more information about parameters, check What are the possibilities of parameters in an exercise and How do I create a parameterised exercise.

Important: in the default mode the CAS does not interpret expressions as mixed numbers. If you want to interpret an answer from a student as a mixed number you need to explicitly read it as such. See the Using mixed fractions in exercises below for how this can be done.

By default the CAS will always visualise expressions with improper fractions instead of mixed numbers. If you want to display an expression with mixed numbers you can use the Write Expression With Mixed Numbers parameter type. This parameter takes an expression and will visualise this expression with mixed numbers instead of improper fractions.

So how can these parameter types be used to generate an exercise which allows students to rewrite improper fractions to mixed numbers? Let's see!

As a start, we define some parameters to generate an improper fraction. For this we use two range-parameters which will give us some random integers. We also define the improper fraction we want to rewrite:

After this, we can also calculate both the whole number and the numerator we expect to see in our simplified mixed number:

Note that we have added a condition for the num parameter to be unequal to zero, as we want to make sure we actually have a fraction in our mixed number.

As a last step we define the exact mixed number we expect using the Read Expression With Mixed Numbers parameter type:

With these parameters defined we can define our actual question:

All that is left to do is the definition of the answer model. We want to define the following rules:

As a first step in our definition, we need to make that the answer of the student is read with mixed numbers. This is important, as by default the CAS will not recognise mixed numbers.

To do this, we define an answer parameter of the Read Expression with Mixed Numbers type. As the expression we simply give the expression which is entered by the student, which is in the form of student.answerX, where X is the number of question in the exercise.

In our case we only have a single question, so the expression is student.answer1. We can defined this parameter by clicking the edit answers and specific feedback button in the Math/Equation tab of the exercise:

We can define the answer parameter as follows:

Based on this parameter we can express our answer rules relatively straight-forward:

It is important to note here that the left-hand-side of the answer rules have our previously defined answer parameter selected. This ensures that the expression given by the student is parsed and evaluated as a mixed number instead of a multiplication.

As a last step we need to make sure that we provide students with valuable feedback in the scenario in which they only gave incorrect answers. A regular question will show the correct answer to the student in this scenario, but because of the way in which the answer rules are defined this does not happen in this case. Because of this it is important to also provide feedback in the Detailed solution field:

And we are done!

In the creation of the exercises with mixed numbers there are two important things to keep in mind:

Hopefully this support allows you to create meaningful exercises for your students. As always, if you have any questions please reach out to us via the chat icon in the bottom right.