Real number system Standard: MFANSQ2 – Students will conceptualize positive and negative numbers including decimals and fractions.

The Real Number System The Real Number System is divided into two categories: Rational and Irrational Rational Numbers: numbers such as ½ and -3/1 that can be written as a ratio of two integers. Irrational Numbers: real numbers such as √2 or , that are not rational.

The Real Number System Rational Numbers: Includes integers, whole numbers, natural numbers, and numbers written as the ratio of two integers. Integers: {… -3, -2, -1, 0, 1, 2, 3,…} Whole Numbers: {0, 1, 2, 3, …} Natural Numbers: {1, 2, 3, …}

The Real Number System Real Numbers Rational Numbers Irrational Numbers 1/2 -2 3 2 3 2/3 3 4 -5 2 15% -0.7 1.456

The Real Number System Real Numbers Rational Numbers Irrational Numbers 1/2 Integers 2/3 -2 3 2 3 4 -5 2 -0.7 3 15% 1.456

The Real Number System Real Numbers Rational Numbers Irrational Numbers 1/2 Integers 2/3 -2 Whole 3 2 3 4 -5 2 3 -0.7 15% 1.456

The Real Number System Real Numbers Rational Numbers Irrational Numbers 1/2 Integers 2/3 -2 Whole 3 2 Natural 3 4 3 -5 2 -0.7 15% 1.456

Properties of Real Numbers

What does zero mean? Zero = nothing Zero is not positive or negative Zero does not have an opposite number

Graphing Numbers on a Line Graph the following on a number line and compare. -3 and 2 -4 and -7 5 and -6

Finding the Absolute Value of a Number The absolute value of a number is its distance from zero. The notation for absolute value is |a|. Using the number line, find the absolute value of each. |5| |-8|

Finding the Opposite of a Number The opposite of a number is the same distance from zero (both numbers have the same absolute value). Using the number line, find the opposite of the following: Opposite of 2: Opposite of -11:

Extension What does -|-4|=?? Compare -|-4| and 4 using <, >, or =.

Real Numbers in the Real World What number would represent the following situations? A hawk descends at 150 miles per hour when striking its prey. A skier wins a downhill race by skiing at 126 miles per hour.

Classwork/Homework