Variables & Properties

Variables & Properties

Variables & PropertiesIdentities, Inverses, Commutative, Associative, DistributiveShared Learning TargetI will be able to ~ use the properties that we discuss to simplify and solve numerical and algebraic expressions.I will need to learn/recall ~ properties & order of operationsI will demonstrate my knowledge by ~ showing correct work and answers on my classwork, clicker questions, and homework.What is a math property?A shortcutThey teach about the character of numbersThey may be used to rearrange an expression or an equation to make the problem a little easier to work withThere are limits to the propertiesSome of them can only be used in certain cases.Additive identityWhat number can you add to anything and still get the same number as the answer?

Zero (0)

So the ADDITIVE IDENTITY PROPERTY tells usn + 0 = n

multiplicative identityWhat number can you multiply by anything and still get the same number as the answer?

ONE (1)

So the multiplicative IDENTITY PROPERTY tells usn 1 = n

Additive inverseWhat number can you add to a number and get zero for the answer?

The numbers opposite!

So the ADDITIVE Inverse PROPERTY tells usn + -n = 0The additive inverse undoes what you have.

multiplicative inverseWhich property is this an example?15 + (-15) = ?

Additive IdentityMultiplicative IdentityAdditive InverseMultiplicative Inverse12 of 26

Which property is this an example?257 + 0= ?

16 of 26Additive IdentityMultiplicative IdentityAdditive InverseMultiplicative Inverse

Which property is this an example?

21 of 26Additive IdentityMultiplicative IdentityAdditive InverseMultiplicative Inverse

Which property is this an example?

19 of 26Additive IdentityMultiplicative IdentityAdditive InverseMultiplicative Inverse

Commutative propertyOnly for ADDITION & MULTIPLICATION

n + s = s + nns = sn

What does this tell us?

Its okay to switch the order of the numbers when adding or multiplyingno combining the operations!Is this the commutative property?56 + 48 + 95 + 12 = 12 + 48 + 56 + 95

YesNo0 of 30

Is this the commutative property?A b c = b c a

YesNo0 of 30

Is this the commutative property?15 + 24 2 = 2 + 15 24

YesNo0 of 30

associative propertyOnly for ADDITION & MULTIPLICATION

a + (b + c) = (a + b) +ca(bc) = (ab)c

What does this tell us?

Its okay to change how the numbers are grouped in the parenthesisno combining the operations!Is this the associative property?500 + (12 + 480) = (500 + 12 + 480)

YesNo0 of 20

Countdown20Is this the associative property?56 + (48 + 95) + 12 = (56 + 48) + (95 + 12)

YesNo0 of 20

Countdown20Is this the associative property?(ab)c= a(bc)

YesNo0 of 20

Countdown20Is this the associative property?15 + 24 2 = (15 + 24) 2

YesNo0 of 20

Countdown20distributive propertyMay useADDITION & Subtraction

a(b + c) = ab + aca(b - c) = ab - ac

What does this tell us?

We can take the number outside the parenthesis and multiply it by each term (number or variable) inside the parenthesis.distributive propertyExampleADDITION

4(25 + 10) = 4(25) + 4(10)

4(35) = 100 + 40

140 = 140distributive propertyExample Subtraction

5(52 - 22) = 5(52) 5(22)

5(30) = 260 + 110

150 = 150distributive propertyExampleAlgebraicADDITION & Subtraction

5(b + 2) = 5b + 5(2)8(x - 6) = 8x 8(6)

5(b + 2) = 5b + 108(x - 6) = 8x 48

How are these expressions equal?We dont know what b or x areThats okayits supposed to be like that!

SummaryAdditive IdentityMultiplicative IdentityAdditive InverseMultiplicative InverseCommutative PropertyAssociative PropertyDistributive PropertyShared Learning TargetI will be able to ~ use the properties that we discuss to simplify and solve numerical and algebraic expressions.I will need to learn/recall ~ properties & order of operationsI will demonstrate my knowledge by ~ showing correct work and answers on my classwork, clicker questions, and homework.Do you feel that you have met the target of: use the properties that we discuss to simplify and solve numerical and algebraic expressions

Yes, I can see where the properties can/should be used.I understand what they say but need to see more examples.I remember their names.