Chapter ISG, Problem 7.4.7P

To determine

To justify the given statement.

Answer to Problem 7.4.7P

Never, average of a student’s homework score is an irrational number.

Explanation of Solution

Given information:

Category	Type of score
Midterm Exam	Whole number from 0 to 100
Final Exam	Whole number from 0 to 100
Quizzes	Rational number from 0 to 10
Homework	0, $\frac{1}{4},\frac{1}{2},\frac{3}{4},1$

Formula used: Number system theory.

Never, average of a student’s homework score is an irrational number.

Let’s take an example:

Student’s homework scores are:

  $1,\frac{1}{4},\frac{3}{4}$

Finding the average,

  $\frac{1+\frac{1}{4}+\frac{3}{4}}{2}$

Taking least common factor,

  $\frac{\frac{4+1+3}{4}}{2}$

After solving,

  = $\frac{(\frac{8}{4})}{2}$

So,

  $\frac{\frac{\frac{2}{1}}{2}}{1}$

Which is 1

Which is a rational number.