chapter 3: rational numbers 3.1 what is a rational number? pg 94-105

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

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Page 1: Chapter 3: Rational Numbers 3.1 What Is a Rational Number? Pg 94-105

Chapter 3:Rational Numbers

3.1 What Is a Rational Number?Pg 94-105

Page 2: 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=?

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

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=?

Page 4: Chapter 3: Rational Numbers 3.1 What Is a Rational Number? Pg 94-105

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 = ?

Page 5: Chapter 3: Rational Numbers 3.1 What Is a Rational Number? Pg 94-105

Quick Review of What You SHOULD Know

• 4 5 = = 0.8

• This would be called finding the quotient

• What are these quotients?a. ¾b. 6/2 c. -11/2

4

5

Page 6: Chapter 3: Rational Numbers 3.1 What Is a Rational Number? Pg 94-105

Quickly what are the different types of numbers we know?

?????

Integers

Whole

Natural

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?

Page 7: Chapter 3: Rational Numbers 3.1 What Is a Rational Number? Pg 94-105

But what about……?

• Where does 0.5 fit in?• Or what about ?

• Are these numbers? Do they fit in the sets we have?

3

4

Page 8: Chapter 3: Rational Numbers 3.1 What Is a Rational Number? Pg 94-105

• We need a new set to fit these numbers

• They are called rational numbers.

Page 9: Chapter 3: Rational Numbers 3.1 What Is a Rational Number? Pg 94-105

Rational Numbers

• Rigorous Definition:– A rational number is of the form m/n where m and

n are any integer and n ≠ 0

Page 10: Chapter 3: Rational Numbers 3.1 What Is a Rational Number? Pg 94-105

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.

Page 11: Chapter 3: Rational Numbers 3.1 What Is a Rational Number? Pg 94-105

Do all decimals work?

• 0.25? 0.5? Why?

• What about something like this?– 0.123456789123456789123456789…….

– 3.1415962535897……..

Page 12: Chapter 3: Rational Numbers 3.1 What Is a Rational Number? Pg 94-105

• 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…

Page 13: Chapter 3: Rational Numbers 3.1 What Is a Rational Number? Pg 94-105

IRRATIONAL!

Page 14: Chapter 3: Rational Numbers 3.1 What Is a Rational Number? Pg 94-105

• 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.

Page 15: Chapter 3: Rational Numbers 3.1 What Is a Rational Number? Pg 94-105

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

Page 16: Chapter 3: Rational Numbers 3.1 What Is a Rational Number? Pg 94-105

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

0 1 2 3 4 5-1-2-3-4-5

Page 17: Chapter 3: Rational Numbers 3.1 What Is a Rational Number? Pg 94-105

What do we do if they are fractions?

• How do we put numbers like or onto a number line?

4

5

2

3

0 1 2 3 4 5-1-2-3-4-5

Page 18: Chapter 3: Rational Numbers 3.1 What Is a Rational Number? Pg 94-105

• Easy. Turn them into decimals and place (to a reasonable estimation) onto the number line.4

5

2

3= -0.8 = 0.6

0 1 2 3 4 5-1-2-3-4-5

Page 19: Chapter 3: Rational Numbers 3.1 What Is a Rational Number? Pg 94-105

Ordering Rational #’s

• 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

0 1 2 3 4 5-1-2-3-4-5

Page 20: Chapter 3: Rational Numbers 3.1 What Is a Rational Number? Pg 94-105

• How do you write a rational number between two given numbers?

• How many can we find between -5 and 5?

0 1 2 3 4 5-1-2-3-4-5

Page 21: Chapter 3: Rational Numbers 3.1 What Is a Rational Number? Pg 94-105

Rational

Integer

Whole

Natural

Irrational

Everything is contained in the Real Numbers