Learn It Part 2

You now know the definitions for the different categories of rational numbers and irrational numbers. Consider the following questions:

  • What happens when we perform mathematical operations using rational numbers and irrational numbers?
  • How do rational numbers and irrational numbers relate to each other?
  • How are rational numbers and irrational numbers different?

Before you explore how to work with two rational numbers, or a rational number and an irrational number, watch this video for a quick review of adding and multiplying integers.

This video player plays a quick review video on finding the sum and product of integers.

> Text version for video: Quick Review: Finding the Sum and Product of Integers Opens a new window

If the sum or product of two integers is always an integer, is this also true for the entire rational set of numbers? In other words, is the sum or product of two rational numbers always rational?

Watch this video to learn the answer. Be sure to pause as you watch so you can allow yourself time to closely follow what is being said.

This video player plays a video on finding the sum and product of two rational numbers.

> Text version for video: Finding the Sum and Product of Two Rational Numbers Opens a new window

Now you know that the sum or product of rational numbers is always rational numbers. Now let’s explore the sum of a rational number and an irrational number, and the product of a rational number and an irrational number.

Be sure to pause as you watch so you can allow yourself time to closely follow what is being said.

This video player plays a video on finding the sum and product of rational and irrational numbers.

> Text version for video: Finding the Sum and Product of Rational and Irrational Numbers Opens a new window


Tip

A graphic organizer displaying the Real Number system. Two circles are shown. The circle on the left is the circle graphic organizer containing the Rational Numbers circle with the nested Integers circle, Whole Numbers circle and the Natural Numbers circle. The circle on the right is a graphic organizer labeled Irrational Numbers.