Download 3. Rational number

Warm Up
• State whether the number is
rational or irrational:
1. ¾
2. ∏
3. 4
4. e
o
MCC9-12.N.RN.3:
Explain why the sum or product
of rational numbers is rational;
Unit 4: Extending the
Number System
Section 2: Rational and irrational
Numbers
Essential Question
• How can you determine if a subset of
real numbers is closed under a given
operation? How can you show that
the set of polynomials is closed
under addition?
o
MCC9-12.N.RN.3:
Explain why the sum or product
of rational numbers is rational;
Standards in this section
text book pages 452-453
• MCC9-12.N.RN.3: Explain why the
sum or product of rational numbers
is rational; that the sum of a rational
number and an irrational number is
irrational; and that the product of a
nonzero rational number and an
irrational number is irrational.
o
MCC9-12.N.RN.3: Explain why the sum or product of
rational numbers is rational; that the sum of a rational number and
an irrational number is irrational; and that the product of a nonzero
rational number and an irrational number is irrational.
Vocabulary Unit 4 section 2:
1. Real number : the set of all numbers that can be
expressed as a decimal or that are on the number line. Real
numbers have certain properties and different
classifications, including natural, whole, integers, rational
and irrational.
2. Irrational number- real numbers that cannot be
represented as terminating or repeating decimals. Example
∏, e, √2
3. Rational number: A number expressible in the form a/b or
– a/b for some fraction a/b. The rational numbers include
the integers.
4. Natural numbers: 1,2,3,4,...
5. Whole numbers. The numbers 0, 1, 2, 3, ….
6.Integers: …,-3,-2,-1,0,1,2,3,…
REAL NUMBERS
(as opposed to fake numbers?)
o
MCC9-12.N.RN.3: Explain why the sum or product of rational numbers is rational;
that the sum of a rational number and an irrational number is irrational; and that the
product of a nonzero rational number and an irrational number is irrational.
Two Kinds of Real Numbers
• Rational Numbers
• Irrational Numbers
o
MCC9-12.N.RN.3: Explain why the sum or product of rational numbers is rational;
that the sum of a rational number and an irrational number is irrational; and that the
product of a nonzero rational number and an irrational number is irrational.
Rational Numbers
• A rational number is a real
number that can be written
as a ratio of two integers.
• A rational number written in
decimal form is terminating
or repeating.
o
MCC9-12.N.RN.3: Explain why the sum or product of rational numbers is rational;
that the sum of a rational number and an irrational number is irrational; and that the
product of a nonzero rational number and an irrational number is irrational.
Examples of Rational
Numbers
•16
•1/2
•3.56
o
•-8
•1.3333…
•- 3/4
MCC9-12.N.RN.3: Explain why the sum or product of rational numbers is rational;
that the sum of a rational number and an irrational number is irrational; and that the
product of a nonzero rational number and an irrational number is irrational.
Irrational Numbers
• An irrational number is a
number that cannot be
written as a ratio of two
integers.
• Irrational numbers written as
decimals are non-terminating
and non-repeating.
o
MCC9-12.N.RN.3: Explain why the sum or product of rational numbers is rational;
that the sum of a rational number and an irrational number is irrational; and that the
product of a nonzero rational number and an irrational number is irrational.
Examples of Irrational
Numbers
• Square roots of
non-perfect
“squares”
• Pi
17
o
MCC9-12.N.RN.3: Explain why the sum or product of rational numbers is rational;
that the sum of a rational number and an irrational number is irrational; and that the
product of a nonzero rational number and an irrational number is irrational.
Integers
One of the subsets of rational
numbers
o
MCC9-12.N.RN.3: Explain why the sum or product of rational numbers is rational;
that the sum of a rational number and an irrational number is irrational; and that the
product of a nonzero rational number and an irrational number is irrational.
What are integers?
• Integers are the whole numbers and their
opposites.
• Examples of integers are
6
-12
0
186
-934
o
MCC9-12.N.RN.3: Explain why the sum or product of rational numbers is rational;
that the sum of a rational number and an irrational number is irrational; and that the
product of a nonzero rational number and an irrational number is irrational.
• Integers are rational numbers
because they can be written as
fraction with 1 as the denominator.
o
MCC9-12.N.RN.3: Explain why the sum or product of rational numbers is rational;
that the sum of a rational number and an irrational number is irrational; and that the
product of a nonzero rational number and an irrational number is irrational.
Closure
When you multiply two rational
numbers you get a rational number
Example:
4x½=2
This rational numbers are closed under
multiplication
o
MCC9-12.N.RN.3:
Explain why the sum or product
of rational numbers is rational;
How can you check if a set
of numbers is closed under
a certain operation?
• If a set of numbers is closed under
an operation then you can perform
that operation on two of those
numbers and get a number in the set
o
MCC9-12.N.RN.3:
Explain why the sum or product
of rational numbers is rational;
Example
Is the set {-1,0,1} closed under
multiplication?
o
MCC9-12.N.RN.3:
Explain why the sum or product
of rational numbers is rational;
Is the set of irrational
numbers closed under
multiplication?
Try multiplying the square root of 2 by
the square root of 2.
o
MCC9-12.N.RN.3:
Explain why the sum or product
of rational numbers is rational;
Homework
• Section 4-3 worksheet
• Text book p 453 # 1 – 15
• Coach book: Pages 168 # 1-11
o
MCC9-12.N.RN.3:
Explain why the sum or product
of rational numbers is rational;