Properties of Addition and Multiplication By Stephanie Lohr.
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Transcript of Properties of Addition and Multiplication By Stephanie Lohr.
Commutative Property
• Commutative Property of Addition--changing the order in which you add does not change the sum.
5 38 3 5 8
a b b a
9 7 7 9
So, 5 33 5
2.1 6 6 2.1
More Examples:
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:
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)
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
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!!
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!!
Zero Property (of Multiplication)
• Any number multiplied by 0 equals 0!
a0 0
90 0
8,823,4270 0
1,000,0000 0
Inverse Property
• Inverse Property of Multiplication--a number multiplied by its reciprocal equals 1.
21
21
1
55 1
3 13
1
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
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)
Identify the Property
54 453 0 340 0(9 3.2) 5 9 (3.2 5)
9.819.8
Commutative Prop. Of Multiplication
Identity Prop. Of Addition
Zero Property
Associative Prop. Of Addition
Identity Prop. Of Multiplication