Download 1.3 Properties of Numbers

1.3 Properties of Numbers
8/24/16
Common Core State Standards
• Interpret complicated expressions by viewing one or more of their
parts as a single entity.
• Use the structure of an expression to identify ways to rewrite it.
New Terms
• Equivalent expressions
• Additive identity
• Multiplicative identity
• Multiplicative inverse
• Reflexive property
• Symmetric property
• Transitive property
• Substitution property
Equivalent expressions
• The expression 4k + 8k and 12k are called equivalent
expressions because they represent the same number.
• IE
2 x + 5x and 7x
Additive identity
• The sum of any number and 0 is equal to the number.
Thus, 0 is called the additive identity.
• IE 4 + 0 = 4
• 99 + 0 = 99
Multiplicative identity
• The solution of the equation is 1. Since the product of
any any number and 1 is equal to the number 1.
• IE 8 • n = 8 ,
4 • x = 4
Multiplicative inverse
• Two numbers whose product is 1. Zero has no
reciprocal because any number times 0 is 0.
• IE
•
1 • 2 = 1
2
1
1
Reflexive property
• Any quantity is equal to itself.
• IE
5 = 5
4 + 7 = 4 + 7
11 = 11
Symmetric property
• If one quantity equals a second quantity, then the
second quantity equals the first.
• IE
If 8 = 2 + 6 then 2 + 6 = 8
Transitive property
• If one quantity equals a second quantity and the
second quantity equals a third quantity the the first
quantity equals the third quantity.
• IE If 6 + 9 = 3 + 12 and 3 + 12 = 15 then
• 6 + 9 = 15
Substitution property
• A quantity may be substituted for its equal in any
expression.
• IE If n = 11 then 4n = 4 • 11
4(11) = 4 • 11
44 = 44
Commutative and Associative Property
• Commutative Property of Addition
The order in which you add
or multiply does not change
their sum or product.
•
a + b = b + a
•2 + 3 = 3 + 2
• Commutative Property of
Multiplication
• a• b = b• a
•4• 6 = 6• 4
Associative Property of Addition and
Multiplication
• When you group 3 or
more numbers when
adding or multiplying,
does not change their
sum or product.
( a + b) + c = a + (b + c)
(a • b) • c = a • (b • c)
Evaluate the expression then name a property
in the process.
• 7( 16 ÷ 42 )
• 7(16 ÷ 16) Substitution
• 7(1)Multiplicative
Identity
•= 7
• 2[5 – ( 15 ÷ 3)]
• 2(5 – 5) Substitution
• 2(0) Mult. Prop. of Zero
•= 0
Evaluate each expression and name a
property in any step
• 16 + 8 + 14 + 12
• Ticket Out the Door
2•4•5•3