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Properties

Properties

Commutative Property:

order for + and × does not matter a+b=b+a

order for – and ÷ does matter a×b=b×a

$5+3=3+5$

$8=8$

$2\times3=3\times2$

$6=6$

Associative Property:

grouping for + and × does not matter a+(b+c)=(a+b)+c

grouping for – and ÷ does matter a×(b×c)=(a×b)×c

$2+(3+4)=(2+3)+4$

$2+7=5+4$

$9=9$

$2\times(3\times4)=(2\times3)\times4$

$2\times12=6\times4$

$24=24$

Distributive Property:

a(b+c)=(a×b)+(a×c)

$3(5+2)=(3\times5)+(3\times2)$

$4x-8=4(x-2)$

Inverse Property:

addition → a+ (-a) = 0 additive inverse of 54=-54

multiplication → a ×\frac{1}{a}=1 multiplicative inverse of 7=\frac{1}{7}

# combined with inverse = identity

Identity Property:

addition → a+0=a

multiplication → a ×1=a