Chapter 3: Rational Numbers 3.1 What Is a Rational Number? Pg 94-105

Quick Review of What You SHOULD Know If we are looking for the SUM of two numbers, that means two numbers added together. Ex. The sum of 2 and 3 is? Aka. 2+3=?

Quick Review of What You SHOULD Know The DIFFERENCE between two numbers is one number subtracted by another number. Ex. What is the difference of 5 and 2? Aka. 5-2=?

Quick Review of What You SHOULD Know The PRODUCT of two numbers is one number multiplied by the other. Ex. The product of 12 and 5 is?. Aka. 12 x 5 = ?

Quick Review of What You SHOULD Know 4 5 = = 0.8 This would be called finding the quotient What are these quotients? ¾ 6/2 -11/2

Quickly what are the different types of numbers we know? Natural numbers: 1, 2, 3, 4, 5, 6, ….. Whole Numbers: 0, 1, 2, 3, 4, 5, 6, …… Integers: ……, -6, -5, -4, -3, -2, -1, 0, +1, +2, +3, +4, +5, +6, ... ????? Anything bigger? Integers Whole Natural

But what about……? Where does 0.5 fit in? Or what about ? Are these numbers? Do they fit in the sets we have?

We need a new set to fit these numbers They are called rational numbers.

Rational Numbers Rigorous Definition: A rational number is of the form m/n where m and n are any integer and n ≠ 0

What does that actually mean? Basically if you can write a number as a fraction, it is rational. SO! All integers are rational because we can write them like this. 2=2/1 , 439=439/1 , 7993857667=7993857667/1 And obviously all fractions are rational.

Do all decimals work? 0.25? 0.5? Why? What about something like this? 0.123456789123456789123456789……. 3.1415962535897……..

Not all decimals will be rational Not all decimals will be rational. They will be rational if they are not infinite, or they have a finite repeatable pattern. So if something is not rational it must then be…

IRRATIONAL!

So everything that isn’t rational is then irrational. The example I gave was Pi Part of your homework is to find two other irrational numbers.

How to write a rational number on a number line. First we need to review what a zero pair is. ZERO PAIR is two numbers that have the same value but opposite sign. Exs. -2, +2 -20.5, +20.5 -926, +926 Take any of these pairs and add them, you will get zero every time. Thus zero pair. Zero pairs have the same distance from zero

How to write a rational number on a number line. Let’s try placing these values onto a number line: 2, 3, -1, -4, 0.5, -0.75 -5 -4 -3 -2 -1 1 2 3 4 5

What do we do if they are fractions? How do we put numbers like or onto a number line? -5 -4 -3 -2 -1 1 2 3 4 5

Easy. Turn them into decimals and place (to a reasonable estimation) onto the number line. = -0.8 = 0. -5 -4 -3 -2 -1 1 2 3 4 5

Ordering Rational #’s -5 -4 -3 -2 -1 1 2 3 4 5 List in order from least to greatest. Same strategy; place them on a number line and list them off in order. -3/5, 1.1, 13/12, -0.5, 12/12 -5 -4 -3 -2 -1 1 2 3 4 5

How do you write a rational number between two given numbers? How many can we find between -5 and 5? -5 -4 -3 -2 -1 1 2 3 4 5

Everything is contained in the Real Numbers Rational Irrational Integer Whole Natural