Warm Up
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Transcript of Warm Up
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Warm Up
Simplify each square root
1. √8
2. √12
Monday, January 13th
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Week at a Glance
Monday: Rational and irrational numbers Tuesday: Simplifying Square Roots with numbers Wednesday: Simplifying Square roots with variables Thursday: Operations with square roots/reviewFriday: Quiz
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Warm Ups
10 points each day 1. Write down the question 2. Show work (if you can)
3. Correct answer
*Use your warm ups as a second study guide
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Useful Tools
1. Website: mskristaevans.wordpress.com Daily PowerPoints Important upcoming dates Test information-study guide
answers
2. Remind 101 Text: @27abTo: (470) 238-2447
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EOCT Practice One question a
day We will have a
winner each week-reward will be
given
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EOCT QUESTION 1
1. In the diagram, ABC ~ DEF. Find length DF. a. 14.4 b. 16.5 c. 18.8 d. 28.2
A
B
C D
E
F
16
11
2124
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Part I-Classifying
What is a number?How do you classify it?
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Natural Numbers
Natural numbers are the counting numbers: 1, 2, 3, …
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Whole Numbers
are the natural numbers and zero:
0, 1, 2, 3, …
WH0LE
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Integers
are whole numbers and their opposites:
–3, –2, –1, 0, 1, 2, 3, …
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Rational Numbers
Are all integers, fractions, terminating decimals, square roots of perfect
squares: -3, ½, 5, 8.74,
4
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Irrational Numbers
Can’t be expressed as a fraction or whole number. They include:
Square roots of non-perfect squares
Π, e, Non-terminating decimals
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After the game show…Keeping it straight!
Natural Numbers Integers Irrational Whole Numbers Rational Numbers
REAL NUMBERS
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Does yours match mine?!?
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Part II-PropertiesMultiplication
and Addition
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1. Commutative Property
Commutative Property of Addition--changing the order in which you add does not change the sum.
5 38 3 5 8a b b a
9 7 7 9
So, 5 33 5
2.1 6 6 2.1
More Examples:
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Commutative Property
Commutative Property of Multiplication--changing the order in which you multiply numbers doesn’t change the product.ab ba
122 24 212 24
86 6 87.53 37.5
So, 122 212More Examples:
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2. Associative Property
Associative Property of Addition--changing the way the numbers are grouped does not change the sum.
(a b) c a (b c)
(31) 6 103 (1 6)10
(2.5 4) 8 2.5 4 8
Add parenthesis to show Associative Property
6 2 9 6 (2 9)
23.5 8 7 23.5 8 7So,(31) 6 3 (1 6)
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Associative Property
Associative Property of Multiplication--changing the way the numbers are grouped does not change the product.
(ab)c a(bc)
(63)118
6(31)18
So,(63)16(31)
Add parenthesis to showAssociative Property
(792)2379223
5.1635.1(63)
7.3210 7.3210
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3. Identity Property
Identity Property of Addition--if you add zero to a number, you get the same number!
a 0 a
8 0 8
5 0 5
7.342 0 7.342
0 is called the identity of addition!!
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Identity Property
Identity Property of Multiplication--if you multiply a number by 1, you get the same number!
616 91 9
a1a
2.345612.3456
1 is called the identity of multiplication!!
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4. Inverse Property
Inverse Property of Multiplication--a number multiplied by its reciprocal equals 1.2
1
21
1
55 1
3 13
1
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Inverse Property
Additive Inverse Property--a number plus its opposite equals 0.
a ( a)0
9 ( 9) 0
9.3 9.3 0
5 ( 5) 0
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5. Distributive Property
A number outside parenthesis gets multiplied by every number inside parenthesis.
5(4 2)
20 1030
4(8 2)10(9 5)(109) (105)
(48) (42)
(54) (52)
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Identify the Property
54 453 0 3
(9 3.2) 5 9 (3.2 5)
9.819.8
Commutative Prop. Of Multiplication
Identity Prop. Of Addition
Associative Prop. Of Addition
Identity Prop. Of Multiplication
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Part III-Order of Operations
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When we say the word
OPERATION
What are we talking about?
What are some “Operations” in math?
How can we remember what order to do them in? Does it matter?
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Do you remember PEMDAS?!?!
P: “PHUNKY” stuff: Parentheses, Brackets, Braces, square Roots, and Absolute Value
E: ExponentsM/D: Multiplication/DivisionA/S: Addition/Subtraction
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Example #1
5 3 10 2 2
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Example 2
20 4 10 8