Recognizing rational and irrational expressions

The  exercise appears under the Algebra I Math Mission. This exercise explores some of the properties of rational and irrational numbers.

Types of Problems
There is one type of problem in this exercise:


 * 1) Determine which expressions are rational or irrational: This problem provides a list of expressions and some assumptions about the types of numbers involved. In each instance, the student is asked to classify each expression as rational, irrational, or "insufficient information to be determined".Rraie1.png

Strategies
Knowledge of many of the properties of numbers, such as the closure properties, are encouraged to ensure success on this exercise.
 * 1) Rationals are closed under the four basic arithmetic operations.
 * 2) Irrationals numbers are not closed under any of the four basic arithmetic operations.
 * 3) Generally, mixing rationals and irrationals is irrational. For example, a rational multiplied by or subtracted by an irrational is irrational.

Real-life applications

 * 1) Recognizing the effect of operations on the types of numbers increases the likelihood of being successful in some upper-division theory courses, such as Modern Algebra and Elementary Analysis.