Download presentation

1
**Is it rational or irrational?**

2
**Rational or Irrational?**

Fill-in-the-blank: Rational or Irrational? 1) The sum of two rational numbers is ________. 2) The product of two rational numbers is ______. 3) The sum of a rational and an irrational is ____. 4) The product of a non-zero rational and an irrational is _____. 5) The product of two irrational numbers is _____.

3
**1) The sum of two rational numbers is rational.**

Example: Proof: Let and be two rational numbers. Then, , which is a rational number!

4
**2) The product of two rational numbers is rational.**

Example: Proof: Let and be two rational numbers. Then, , which is a rational number!

5
**3) The sum of a rational and an irrational is irrational.**

Example: Proof: Let x be irrational and r be rational. Assume x + r = t is rational. (So, t is rational.) Then, x = t – r. Since t and r are rational, their difference is rational. However, this contradicts the assumption that x is irrational. So, proof by contradiction, x + r is irrational.

6
**4) The product of a non-zero rational and an irrational is irrational.**

Example: Proof: Let x be irrational and be rational. Assume x is rational. Then, x So, x = , which by definition is a rational number. This contradicts the assumption that x is irrational. Proof by contradiction … x is irrational.

7
**5) The product of two irrational numbers is sometimes rational and sometimes irrational.**

Examples:

Similar presentations

OK

Chap 3 –A theorem is a statement that can be shown to be true –A proof is a sequence of statements to show that a theorem is true –Axioms: statements which.

Chap 3 –A theorem is a statement that can be shown to be true –A proof is a sequence of statements to show that a theorem is true –Axioms: statements which.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Upload and view ppt online student Download ppt on brain chip technology Stem and leaf display ppt on tv Diaphragm anatomy and physiology ppt on cells Ppt on critical thinking Ppt on hydrogen fuel cell vehicles gm Ppt on eisenmenger syndrome image Ppt on programmable logic array design Ppt on file system in unix/linux Ppt on resistance temperature detector calibration