Randomness in intervals and sets of numbers

We will create a question asking the students for the sum of two random fractions. First, we need to write the algorithm of the question.

The random command allows us to retrieve a random number in a given interval. We need four random numbers: two numerators and two denominators; that we will call a, b, c, and d (the name of the variables is essential). Let us write the code.

Now we have four random numbers between 1 and 9 (both included). We will also compute the sum of the fractions they define and store the result in a variable.

Once we have defined the algorithm, we write the solution in the Correct answer tab. Now it is not a number; it is a variable called sol. In order to write a variable anywhere outside CalcMe , we must precede the name of the variable with the pound sign #. Therefore, we will write #sol in the correct answer field.

Finally, once we have checked the question's behaviour in the Preview tab, we write the statement of the problem. Recall that our numerators and denominators were stored in variables called num1, num2, den1, and den2. In the same way, as in the Correct answer section, we have to write the name of the variables preceded by the pound sign #. Fractions can be written with MathType

Sum of two random irreducible fractions

Notice that the algorithm could generate some unwanted statements we have suggested above as

Where both fractions have the same denominator. We can avoid this situation with a simple change in our algorithm. We just have to exclude the first denominator value from the set of the second denominator possible values. Here we can see how the code will look like.

Furthermore, the initial algorithm could generate even more undesirable statements, as we can see in the following example.

In this case, the fractions that appeared in the statement are not simplified, and they can even be expressed in integer form. To prevent this situation, the values whose greatest common divisor with its numerator is different from 1 will be excluded from the set of possible denominator values. Here we can see how the code will look like.

We will create a question asking the students to round to the tenth ones and truncate some random numbers to the hundredth ones. We will choose the embedded answers (Cloze) question type. Let's write the algorithm of the question.

The random command allows us to retrieve a random number in a given interval. Actually, we can add an option, so just the interval numbers with a given step will be considered, as we will see below.

We need five numbers with three decimal digits each. Since it could result in a little bit tedious to write so many times that command, we will avoid it by defining a global function r():=random([0..10..0.001]). Let us write the code.

For now, we have five real random numbers between zero and ten with three decimal digits. We also have to round them to the tenth ones and truncate them to the hundredth ones.

As we have written the algorithm, we can obtain some unwanted numbers which are already rounded at the tenth one or truncated at the hundredth one, as we can see in the example below.

To avoid this kind of situation, we can prevent numbers ended with 0 or 00 from being generated in the following way.

This way, we will only obtain appropriate numbers with three decimal digits, as we can see below.