Unit 2 Comparing and Ordering Rational Numbers

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

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

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

The Set of Real Numbers

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

Next Step... Whole Numbers

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

Rational Numbers

Rational Numbers The set of Rational Numbers now includes the ratios of integers, also called fractions. Hence the word Rational. The only exception is that the denominator cannot equal “0” Examples: 1/2 = 0.5 or 1/3 = 0.333... 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 Here is what they look like on the number line. -3 -2 -1 -1/3 1 2 -2 1/4 -1 1/3 1/2 1 3/4

Irrational Numbers If we now add to our list the set of Irrational Numbers - we have now have all of the Real Numbers. √2 = 1.41421 and Pi... are irrational. Irrational decimal neither end nor repeat.

Real Numbers 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

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

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

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

Key Words Integers are positive and negative whole numbers and zero. 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. Irrational Numbers have decimals that don’t repeat or stop. They cannot be written as a ratio of 2 integers

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

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

Show You Know Put the following rational numbers in ascending order… 0.3 -0.6 -3/4 11/5 -1 0.75 -21/4 21/4 -1/2 0.35 1/5 3/8 5/6 2/3 2/7

Show You Know Answers -1 -3/4 -0.6 0.3 11/5 -21/4 -1/2 0.35 0.75 21/4 -1 -3/4 -0.6 0.3 11/5 -21/4 -1/2 0.35 0.75 21/4 1/5 2/7 3/8 2/3 5/6

Show You Know Put the following rational numbers in descending order… -21/4 1.3 -7/8 -11/5 -1.3 .33 -23/5 -1/2 0.335 -0.56 -1/5 -3/8 -5/6 -2/3 -2/7

Show You Know Answers 1.3 -7/8 -11/5 -1.3 -21/4 1.3 -7/8 -11/5 -1.3 -21/4 0.335 .33 -1/2 -0.56 -23/5 -1/5 -2/7 -3/8 -2/3 -5/6

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