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Math Laws
Properties of Addition, Multiplication, and Equalities
Warm-Up
44 36 32
3 4 2
5 6 2
2 25 3
4 9.5
Warm-Up
44 36 32 44 68 112
3 4 2 3(6) 18
5 6 2 5 (8) 3
2 25 3 2(75) 150
4 9.5 38
What’s the Deal?• In these lessons we will use the
commutative, associative, and distributive properties of addition and multiplication.
• We will use the reflexive, symmetric, transitive, and substitution properties of equality.
• We will be reminded of the additive inverse and identity
properties.
Properties of Addition and Multiplication
• Commutative
• Associative
Examples:
• 4+3=3+4
71*25 = 25*71
• (6+7)+9=6+(7+9)
(8*10)*73=8*(10*73)
Nicknames
• CommutativeProperty
• Associative Property
• Order Property
• Grouping Property
Complete each step and name the property used
24+(27+56) =
(27 +__) + 56 =
27 + (24 + __ ) =
27 + __ = ____
• Given
• Commutative Property
• Associative Property
• Addition
Identity Properties
• 208 = 208
What number can we add to 208 to get the same answer? (208)
208+0 = 208
Identity Property of Addition
• 98 = 98
What number can we multiply by 98 to get the same answer? (98)
98*1 = 98
Identity Property of Multiplication
What is the opposite?
• 15x – 8y + 7
• Two Ways:– Change all signs or,– Multiply all terms by -1
One way:
-1(15x-8y+7) =
-15x + 8y – 7
OR
+15x – 8y +7
-15x +8y -7
I MUST GET PAID!
• Nora has two part-time jobs. She gets paid $8 per hour at the retail store and $12 per hour typing term papers for college students. How much will she be able to deposit into her piggy bank after working 7 hours at the store and 5 hours of typing?
• Copyright DDAHLBERG
Pg. 86:
12; 15-21; 43, 44
Distributive Property&
Properties of Equality
Transitive Property of Equality
• a = a
• Looks pretty straightforward.
Symmetric Property of Equality
• If b = a, then a = b
• If n = 99, then 99 = ____.
Transitive Property of Equality
• If a = b, and a=c, then a = c
• If x = 42, and n=(42), then x = ____.
• Hint: any time you see trans- in part of a word, the meaning usually involves “across”.
Substitution Property of Equality
• If b = a, then a = b
• If x = (44-2), and n=(40+2), then x = __.42
Distributive Property of Multiplication
• 35(20 + 9) means 35 x everything in the parentheses.
35*20 + 35 *9 =
700 + 315 =1015
• 755 * 45 = (700 + 50 + 5)•45(700•45)+ (50•45)+ (5•45)
Try Some
• 9 (5+y)=45 + 9y
• 14(x-5)=14x - 70
• 3(n+2)=3n + 6
• 3p(r+2)=3pr+3p2
Write these using the Distributive Property
• rs+rq
• 4bk + sk
• 9xy – 21xyz
• 10fg – 2kg• Start by finding the factors that
are common to both terms. • The first one shows r is
common to both.
• r(s+q)
• k(4b + s)
• 3xy(3 – 7z)
• 2g(5f – 2k)
assignment
• Pg 86: 24-31; 33-37; 45, 47 all
