Download Chapter 3: Rational Numbers

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

4
5=
= 0.8
5
• This would be called finding the quotient
• What are these quotients?
a. ¾
b. 6/2
c. -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?
3
• Or what about
?
4
• 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. 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 0
1
2
3
4
5
What do we do if they are fractions?
4
• How do we put numbers like
or
5
onto a number line?
-5 -4 -3 -2 -1 0
1
2
3
2
3
4
5
• Easy. Turn them into decimals and place (to a
reasonable estimation) onto the number line.
4
2
= 0. 6
= -0.8
5
3
-5 -4 -3 -2 -1 0
1
2
3
4
5
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
-5 -4 -3 -2 -1 0
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 0
1
2
3
4
5
Rational
Irrational
Integer
Whole
Natural