The Real Number System
Presentation
•
Mathematics
•
6th - 12th Grade
•
Medium
Emily Finley
Used 10+ times
FREE Resource
16 Slides • 27 Questions
1
The Real Number System
Classifying Numbers and Their Properties
2
Irrational Numbers
are decimals that never end... think Pi
are non-perfect square roots
ARE ALSO REAL NUMBERS
CANNOT BE RATIONAL NUMBERS.
3
Multiple Select
Check all of the IRRATIONAL numbers.
4.13254981321985164...
4
π
73
2.57
4
Rational Numbers
can be written as a fraction (1/2)
are decimals that have a repeating pattern (1.32323232...)
are decimals that terminate (2.75)
are ALL numbers that aren't irrational (like 3 or -57).
ARE ALSO REAL NUMBERS
CANNOT BE IRRATIONAL.
5
Multiple Select
Select all of the RATIONAL numbers.
161
π
36
1.333333...
2.51354832156...
6
Rational Numbers are broken down into 3 subsets:
Integers
Whole Numbers
Natural Numbers
7
Integers
are counting numbers on a number line. This includes negative numbers.
do not include decimals or fractions.
ARE ALSO RATIONAL NUMBERS AND REAL NUMBERS.
8
Every number on the number line is an integer.
9
Multiple Choice
1.78 is an integer.
True
False
10
Multiple Choice
-123 is an integer.
True
False
11
Whole Numbers
Include POSITIVE integers
includes ZERO
DO NOT include negative integers
do not include decimals or fractions
ARE ALSO INTEGERS, RATIONAL NUMBERS, AND REAL NUMBERS.
12
Whole numbers start at 0 and include every positive integer on the number line.
13
Multiple Choice
45 is a whole number.
True
False
14
Multiple Choice
-2 is a whole number.
True
False
15
Multiple Choice
0 is a whole number.
True
False
16
Multiple Choice
π−π is a whole number.
True
False
17
Natural Numbers
include the integers on a number line STARTING AT 1.
DO NOT include 0.
DO NOT include negative numbers.
DO NOT include fractions and decimals
ARE ALSO WHOLE NUMBERS, INTEGERS, RATIONAL NUMBERS, AND REAL NUMBERS.
18
Natural numbers start at 1 and include every positive integer on the number line.
19
Multiple Choice
0 is a natural number.
True
False
20
Multiple Choice
56 is a natural number.
True
False
21
Multiple Choice
436 is a natural number.
True
False
22
23
Multiple Select
Select ALL SETS to which
−35 belongs. It is also REAL.Irrational
Rational
Integer
Whole Number
Natural Number
24
Multiple Select
Select ALL SETS to which
25 belongs. It is also REAL.Irrational
Rational
Integer
Whole Number
Natural Number
25
Multiple Select
Select ALL SETS to which
0.333333333... belongs. It is also REAL.Irrational
Rational
Integer
Whole Number
Natural Number
26
Multiple Select
Select ALL SETS to which
2−2 belongs. It is also REAL.Irrational
Rational
Integer
Whole Number
Natural Number
27
Multiple Select
Select ALL SETS to which
31 belongs. It is also REAL.Irrational
Rational
Integer
Whole Number
Natural Number
28
Multiple Select
Select ALL SETS to which
2 75 belongs. It is also REAL.Irrational
Rational
Integer
Whole Number
Natural Number
29
Multiple Select
Select ALL SETS to which
−0.78 belongs. It is also REAL.Irrational
Rational
Integer
Whole Number
Natural Number
30
Multiple Select
Select ALL SETS to which
164 belongs. It is also REAL.Irrational
Rational
Integer
Whole Number
Natural Number
31
Multiple Select
Select ALL SETS to which
735 belongs. It is also REAL.Irrational
Rational
Integer
Whole Number
Natural Number
32
Commutative Property
order of values does not matter
7+8=8+7
(9*4)+6=6+(9*4)
5*4=4*5
33
Multiple Choice
Which equation represents the Commutative Property?
5+0=5
3(x+1)=3x+3
2+(7⋅4)=(7⋅4)+2
34
Associative Property
The grouping of values does not matter! Move parentheses.
(a+b)+c=a+(b+c)
(5+1)+3=5+(1+3)
35
Multiple Choice
Which equation represents the associative property?
(5x+2y)+6=5x+(2y+6)
2+0=2
7+(−7)=0
36
Identity Property
Stays the same!!
a+0=a
b*1=b
4(1)=4
3+0=3
37
Multiple Choice
Which equation represents the identity property?
17⋅0=0
2+3=3+2
5⋅51=1
4+0=4
38
Inverse Property
uses the opposite to "cancel" a value!
a+(-a)=0
3*(1/3)=1
39
Multiple Choice
Which equation represents the inverse property?
(2⋅4)⋅7=2⋅(4⋅7)
5⋅1=5
7⋅71=1
2(4x+3)=8x+6
40
Distributive Property
Multiply a value to an expression inside parentheses.
a(b+c)=ab+ac
2(x+6)=2x+12
41
Multiple Choice
Which equation represents the Distributive Property?
3+(6⋅4)=(6⋅4)+3
x(2y+7)=2xy+7x
xy=yx
42
Poll
After this lesson, I feel confident on classifying numbers.
I'm ready for the quiz!
I feel okay about it.
I could use a little more help.
I'm completely lost still.
43
Poll
After this lesson, I feel confident on naming the number properties.
I'm ready for the quiz!
I feel okay about it.
I could use a little more help.
I'm completely lost still.
The Real Number System
Classifying Numbers and Their Properties
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