Rational Numbers in Mathematics
Rational numbers are numbers that can be written as fractions. They are a fundamental concept in mathematics. Learn about the definition of rational numbers, how to express them in reduced form, simplify them under square roots, and practice skills with examples in this informative presentation.
Download Presentation
Please find below an Image/Link to download the presentation.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author.If you encounter any issues during the download, it is possible that the publisher has removed the file from their server.
You are allowed to download the files provided on this website for personal or commercial use, subject to the condition that they are used lawfully. All files are the property of their respective owners.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author.
E N D
Presentation Transcript
CHAPTER 5 Section 5.1 Rational Numbers FoM PPT Template1.jpg FoM PPT Template1.jpg Book cover image by iStock.com/McKevin Shaughnessy
Section 5.1 p. 198 A rational number is a number that can be written as a fraction. The word rational number comes from the term ratio. FoM PPT Template1.jpg FoM PPT Template1.jpg
Section 5.1 p. 198 Ratio A ratio is a comparison of two quantities by division. FoM PPT Template1.jpg FoM PPT Template1.jpg
Section 5.1 p. 198 Positive Rational Number A positive rational number is a ratio expressed as a fraction whose numerator is a whole number and whose denominator is a natural number. FoM PPT Template1.jpg FoM PPT Template1.jpg
Section 5.1 p. 198 Every whole number is a rational number. Improper fractions and mixed numbers are rational numbers. FoM PPT Template1.jpg FoM PPT Template1.jpg
Section 5.1 p. 198 Example 1 Express each of the following in reduced rational form. 3 5 35 91 a. 14 b. 8 c. 7 5 13 7= 5 14 1 43 5 13 FoM PPT Template1.jpg FoM PPT Template1.jpg
Section 5.1 p. 198 When a rational number is under a square root symbol, it can be simplified by taking the square root of the numerator over the square root of the denominator. m m n = n FoM PPT Template1.jpg FoM PPT Template1.jpg
Section 5.1 p. 198 Example 2 1 4 Simplify . 1 1 2 = 4 FoM PPT Template1.jpg FoM PPT Template1.jpg
Section 5.1 p. 198 Example 3 25 144 Simplify . 25 5 = 12 144 FoM PPT Template1.jpg FoM PPT Template1.jpg
Section 5.1 p. 199 Skill Check 1 Express each number in reduced rational form. 10 4 1. 2. 0 FoM PPT Template1.jpg FoM PPT Template1.jpg
Section 5.1 p. 199 Skill Check 1 Express each number in reduced rational form. 5 11 3. 6 4. 36 FoM PPT Template1.jpg FoM PPT Template1.jpg
Section 5.1 p. 199 Skill Check 1 Simplify the following. 100 9 4 5. 64 6. FoM PPT Template1.jpg FoM PPT Template1.jpg
Section 5.1 p. 199 Example 4 Simplify each expression to a reduced rational number. 3 5 9 ( ) ( ) 3 + 45 45 1 2 a. 3 + 1 27 10 3 37 = 37 ( ) 45 15 = 15 FoM PPT Template1.jpg FoM PPT Template1.jpg
Section 5.1 p. 199 Example 4 Simplify each expression to a reduced rational number. ( b. 3 4 5) 64 125 4 5 4 5 4 5 = FoM PPT Template1.jpg FoM PPT Template1.jpg
Section 5.1 p. 199 Example 5 61 44 15 11 6 5 Simplify to a reduced rational number. 61 44 15 11 6 5 61 44 25 22 = = 11 61 44 50 44 44= 1 = 4 FoM PPT Template1.jpg FoM PPT Template1.jpg
Section 5.1 p. 199 Example 6 64 121 5 Simplify 3 + and leave the 12 ( ) answer in rational form. 1 5 12 4 8 11 5 4 8 11 = + = 87 55 44 32 44 3 1 ( ) + = + 44 FoM PPT Template1.jpg FoM PPT Template1.jpg
Section 5.1 p. 200 Skill Check 2 Simplify each expression. Write each rational number in lowest terms. 5 2 3) 2 5 3 4 ( 2. 1. + FoM PPT Template1.jpg FoM PPT Template1.jpg
Section 5.1 p. 200 Skill Check 2 Simplify each expression. Write each rational number in lowest terms. 11 12 1 4 1 4+ 10 7 8 4. 3. 15 FoM PPT Template1.jpg FoM PPT Template1.jpg
Section 5.1 p. 200 The addition or multiplication of rational numbers always results in a rational number. This means that the set of rational numbers is closed under these operations. FoM PPT Template1.jpg FoM PPT Template1.jpg
Section 5.1 p. 200 The rational numbers are not closed under the operation of square root. A number that is not a rational number is called an irrational number. The square root of any number that is not a perfect square is an irrational number. FoM PPT Template1.jpg FoM PPT Template1.jpg
Section 5.1 p. 200 Example 7 Identify the following numbers as rational or irrational. a. 180 5 = 6 = 36 Rational FoM PPT Template1.jpg FoM PPT Template1.jpg
Section 5.1 p. 200 Example 7 Identify the following numbers as rational or irrational. b. 219 3 = 73 Irrational FoM PPT Template1.jpg FoM PPT Template1.jpg
Section 5.1 p. 200 Example 7 Identify the following numbers as rational or irrational. c. 4 12 75 4 2 5 = = = 25 25 Rational FoM PPT Template1.jpg FoM PPT Template1.jpg
Section 5.1 p. 200 Skill Check 3 Simplify each expression. Write each rational number in lowest terms. 3 5 14 1 3 ( ) 2. 1. 10 42 FoM PPT Template1.jpg FoM PPT Template1.jpg
