Properties of Addition:
commutative property of addition
Also called order property of addition. This property means that addends can be added in
any order and the sum is always the same.
associative property of addition
The property that states that when adding three or more real numbers, the sum is always
the same regardless of their grouping. That is,
(a + b) + c = a + (b + c)
additive identity
The number zero is called the additive identity because the addition of zero does not
change the value of any number, that is,
x+0=0+x=x
for any given real number x.
additive inverse
The additive inverse of a number is the opposite of that number, that is, the additive
inverse of a number x is -x. The sum of a number and its additive inverse is always zero,
that is, x + (-x) = 0.
Properties of Multiplication:
associative property of multiplication
The property that states that when multiplying three or more real numbers, the product is
always the same regardless of their grouping. That is,
(a × b) × c = a × (b × c)
commutative property of multiplication
Also called order property of multiplication. This property means that factors can be
multiplied in any order and the product is always the same.
distributive property of multiplication over addition
The distributive property states that multiplying a sum by a number gives the same result as
multiplying each addend by the number and then adding the products together.
4 × (2 + 3) = 4 × 2 + 4 × 3
multiplicative identity
The number one is called the multiplicative identity because the multiplication of one does
not change the value of any number, that is,
x times 1 = 1 times x = x
for any given real number x.
multiplicative inverse
The reciprocal of a given number or expression
Name that Property! Answer Sheet
1. Commutative Property of Addition 2. Additive Identity 3.
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12+4+1=4+1+12 5+2=2+5 -­‐2+0=-­‐2 8+0=8 Additive Inverse -­‐4+4=0 1/8+-­‐1/8=0 Associative Property of Addition (2+3)+4=2+(3+4) (8+14)+5=8+(14) Associative Property of 9x (2x12)=(9x2)x12 Multiplication (3x2)x1=3x(2x1) Commutative Property of 3x4=4x3 Multiplication 3x2x4=2x3x4 Distributive Property of 8(x+2)=8x+16 Multiplication Over/Across 3x+6=3(x+2) Addition Multiplicative Inverse -­‐1/2 x (-­‐2)= 1 3x1/3= 1 Multiplicative Identity 1/5X1=1/5 -­‐3X1=-­‐3