(as opposed to fake numbers?) REAL NUMBERS (as opposed to fake numbers?)

Warm UP Simplify the following expressions. 1. 2.

Essential Question How can I classify real numbers? Why is the sum or product of rational numbers rational? Why is the sum of a rational number and an irrational number irrational? Why is the product of a nonzero rational number and an irrational number irrational?

Vocabulary Words Real Number- a number which can be written as a decimal. Rational Numbers- a number expressible in the form a/b or –a/b (fractions) including integers. Irrational Numbers- a number not expressible in the form a/b or –a/b and the decimal form is non repeating and non terminating. Integers- the numbers …-3,-2, -1, 0, 1, 2, 3 …., if 1 is in the denominator can be written as a fraction. Whole Number- the numbers 0, 1, 2, 3, … . Natural Number- the numbers 1, 2, 3, … .

Two Kinds of Real Numbers Rational Numbers Irrational Numbers

Branching Real Numbers Rational Irrational Now let’s break these subsets down further!

Examples of Rational Numbers 16 1/2 3.56 -8 1.3333… - 3/4 Can you write 16 as a ratio? Now try writing -8 as a ratio!

Examples of Irrational Numbers Square roots of non-perfect “squares” Pi 17 What is the square root of 17? What is another non-perfect square?

Integers One of the subsets of rational numbers So what do integers branch off of?

What are integers? Integers are the whole numbers and their opposites. Examples of integers are 6 -12 186 -934 What do you notice about these integers?

Whole Numbers One of the subsets of rational numbers and integers So what do whole numbers branch off of?

Natural Numbers One of the subsets of rational numbers, integers and whole numbers So what do natural numbers branch off of?

Classify the following Numbers What subset(s) do the following numbers belong to? Remember they could belong to more than one! Whole, Integers, Rational, and Real

Classify the following Numbers (Con’t) 4 Natural, Whole, Integer, Rational, Real -9 Integer, Rational, Real Π Irrational, Real

Classify the following Numbers (Con’t) 3/4 or 0.75 Rational and Real 4 Natural, Whole, Integer, Rational, Real 15 Irrational, Real

Warm up Simplify 1. 2. 3.

The Big Picture!!!

Why is the sum or product of rational numbers rational? Find the sum of two rational numbers. or Find the product of two rational numbers.

Find the sum of the rational number and the irrational number. 1. 2. Why is the sum of a rational number and an irrational number irrational? Find the sum of the rational number and the irrational number. 1. 2.

Why is the product of a non zero rational number and an irrational number irrational? 1. 2.