Unit 2 Comparing and Ordering Rational Numbers Ma

Unit 2 Comparing and Ordering Rational Numbers

Ma & Pa Kettle do math This is why we study math… n So you don’t make this mistake! n You. Tube Video n

Real Numbers n Are all numbers on the number line. n This includes (but is not limited to) positive and negative integers. . . n rational numbers, square roots, cube roots , π (pi), etc.

Venn Diagram n Venn diagrams are diagrams that graphically show possible relationships between a collection of sets (groups of things). n Now, let’s look at a Venn diagram of the set of Real Numbers

The Set of Real Numbers

Natural Numbers n n n Rational Numbers are a “sub-set” of the Real Numbers. The set of Rational numbers can be divided into 4 more categories. Our first group is the set of Natural numbers which are also called the counting numbers {1, 2, 3, . . . }.

Natural Numbers n 1 Here is what they look like on the number line. 2 3 4 5 6

Next Step. . . Whole Numbers

Whole Numbers n n n 0 Whole numbers {0, 1, 2, 3, . . . }. This set includes “ 0” Here is what they look like on the number line. 1 2 3 4 5

Now. . . Integers

Integers now include all the Whole Numbers and their negatives {. . . -3, -2, -1, 0, 1, 2, 3, . . . }. n Here is what they look like on the number line. -3 -2 -1 0 1 2

Rational Numbers

Rational Numbers n The set of Rational Numbers now includes the ratios of integers, also called fractions. n Hence the word Rational. n The only exception is that the denominator cannot equal “ 0” n Examples: 1/2 = 0. 5 or 1/3 = 0. 333. . . n Rational decimal end or repeat.

Rational Numbers § The term, Rational Number, refers to any number that can be written as a fraction where the denominator does not equal “ 0”. § This includes: § § § fractions that are reduced, fractions that can be reduced, mixed numbers, improper fractions, and even integers and whole numbers. An integer, like 4, can be written as a fraction by putting the number 1 under it.

Rational Numbers n -3 Here is what they look like on the number line. -2 1/4 -2 -1 1/3 -1 -1/3 0 1/2 1 1 3/4 2

Irrational Numbers If we now add to our list the set of Irrational Numbers - we have now have all of the Real Numbers. n √ 2 = 1. 41421 and Pi. . . are irrational. n Irrational decimal neither end nor repeat. n

Real Numbers n Real numbers are all the numbers on the continuous number line with no gaps. Every decimal expansion is a real number. Real numbers may be rational or irrational 0

Classwork Now that you have an understanding of the Real Number system… n Complete the blank Venn diagram given to you. n Label each set of numbers and give a short example for each. n

Classwork n Next let’s make a note of the Key Words using Cornell Notes. Name Defintion

Key Words n Real numbers are all the numbers on the continuous number line with no gaps. n Natural Numbers are the counting numbers - not including zero. n Whole Numbers are the counting numbers including zero.

Key Words n Integers are positive and negative whole numbers and zero. n Rational Numbers are simply numbers that can be written as fractions or ratios (this is where the term rational comes from). Decimals repeat or stop. n Irrational Numbers have decimals that don’t repeat or stop. They cannot be written as a ratio of 2 integers

Unit 2 - Review n How can you compare rational numbers that are in different formats. . . such as fraction or decimal format? n Put them all into the same format… you may have to convert some of them! n How do you convert fractions into decimals? n By simply dividing the numerator by the denominator.

More Key Words n Ascending Order - in numerical order from lowest to highest. n Example: 5, 6, 7, 8 n Descending Order - in numerical order from highest to lowest. n Example: 9, 8, 7, 6

Show You Know n Put the following rational numbers in ascending order… n 0. 3 -0. 6 -3/4 11/5 -1 n 0. 75 -21/4 -1/2 0. 35 n 1/5 3/8 5/6 2/3 2/7

Show You Know n Answers n -1 -3/4 -0. 6 0. 3 11/5 n -21/4 -1/2 0. 35 0. 75 21/4 n 1/5 2/7 3/8 2/3 5/6

Show You Know n Put the following rational numbers in descending order… n -21/4 1. 3 -7/8 -11/5 n . 33 -23/5 -1/2 0. 335 -0. 56 n -1/5 -3/8 -5/6 -2/3 -2/7 -1. 3

Show You Know n Answers n 1. 3 -7/8 -11/5 -1. 3 -21/4 n 0. 335 . 33 -1/2 -0. 56 -23/5 n -1/5 -2/7 -3/8 -2/3 -5/6

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