Download Math Properties Commutative Property of Addition and Multiplication

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Math Properties
Commutative Property of Addition and Multiplication
“Sometimes order matters: You do not put on your socks after your shoes. But
sometimes order doesn’t matter: You could put on your shoes before your belt”
(Math On Call, 1998).
Commutative Property of Addition
Changing the order of addends does not change the sum.
a+b=b+a
Ex1) 24 + 16 = 40
and
16 + 24 = 40
24 + 16 = 16 + 24
Ex2)
25 + 147 +75 = 25 + 75 + 147
172 + 75
= 100 + 147
247
=
247
Commutative Property of Multiplication
Changing the order of factors does not change the product.
axb=bxa
3(4) = 12
4(3) = 12
4(3) = 3(4)
Ex1) 5●63●2 = 5●2●63
315●2 = 10●63
630
=
630
Ex2) 6(3)(4) = 4(6)(3)
18(4) = 24(3)
72 = 72
Associative Property of Addition and Multiplication
“You associate with friends in groups. The associative properties are all about the
ways you can group addends and factors” (Math on Call, 1998)
Associative Property of Addition
Changing the grouping of addends does not change the sum.
(a + b) + c = a + (b + c)
NOTE that the order of the addends stays the same,
you just group them differently.
Ex) (15 +98) + 2 = 15 + (98 +2)
113 + 2 = 15 + 100
115 = 115
Associative Property of Multiplication
Changing the grouping of factors does not change the product.
(a ● b) ● c = a ● (b ● c)
NOTE that the order of the factors stays the same, you just group them differently.
Ex)
2 ● (25●4) = (2●25) ● 4
2 ● 100
= 50 ● 4
200
= 200
Zero Property of Multiplication
Zero Property of Multiplication
Any number multiplied by zero is ZERO.
a●0=0
Ex1) 6 ● 0 = 0
Ex2) 0 ● 3 = 0
Identity Properties
Identity elements are numbers that combine with other numbers without changing them.
The Identity Property of Addition
Ex: 5 + 0 = 5
0+5=5
Any number added to Zero is itself.
a + 0 = a and 0 + a = a
.
The Identity Property Multiplication
Any number multiplied by one is itself.
It is like looking into a mirror
Ex: 5 ● 1 = 5
1●5=5
a ● 1 = a and 1 ● a = a
Inverse Properties
Additive Inverse/ Inverse Property of Addition
Any number added to its opposite is zero.
a + -a = 0 and 2 + -2 = 0
Multiplicative Inverse/Inverse
Property of Multiplication
Any number multiplied by its multiplicative inverse (reciprocal) is one
𝟑
𝟒
𝟒
𝟏𝟐
𝟑
𝟏𝟐
· =
=𝟏
The Distributive Property
When you distribute things, you hand them out. With the distributive property, you can
distribute (or hand out) the multiplier to each addend in the group. Remember, no number
should feel left out.
The Distributive Property
You can multiply each term inside a set of parentheses
by a factor outside the parentheses.
a(b + c) = a●b + a●c
Example: 6(3 + 2) = 6●3 + 6●2
18 + 12
a(b – c ) = a●b – a●c
Example: 8(x – 4) = 8●x – 8●4
8x - 32