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When the grouping of terms changes, the sum stays the same.
(2+x)+1=2+(x+1)
a(bc)= (ab)c
Associative Postulate of Multiplication
3+6=6+3
a+b=b+a
ab = ba
Commutative Property of Multiplication
commutative property of multiplication
If the order of factors changes, the product stays the same.
the opposite of a number
5+(-5)=0
The additive identity is 0. a + 0 = 0 + a = a
Multiplicative Identity
A * 1 = A
(1)(99)=99
Multiplicative Identity
Distributive Property of Multiplication over Addition
a(b + c) = ab + ac
3(4x-5y)=12x - 15y
Distributive Property of Multiplication over Subtraction
Distributive Property of Multiplication over Subtraction
a(b - c) = ab - ac
multiplicative inverse
reciprocal of a number
IF a=b THEN a+c=b+c
For all real numbers x, y, and z, if x = y, then x + z = y + z.
if a=b, then ac=bc
Multiplication Property of Equality
Multiplication Property of Equality
For all real numbers x, y, and z, if x = y, then xz = yz.
Division Property of Equality
For all real numbers x, y, and z, if x = y, and z ≠ 0, then x/z = y/z. You can divide each side of an equation by the same non-zero number and not change its truth value.
5x=30 then x=6
Division Property of Equality
6+8=8+6
-12+20+13=-12+13+20
9(a+b)=9(b+a)
12+(6∙8)=(6∙8)+12
3+(5∙2)=3+(2∙5)
Commutative of Multiplication
d(ef)=d(fe)
Commutative of Multiplication
(a+b)+c=a+(b+c)
6+(0+7)=(6+0)+7
2+(7+8)=(2+7)+8
(de)f=d(ef)
Associative of Multiplication
(7∙5)6=7(5∙6)
Associative of Multiplication
2∙(7∙8)=(2∙7)∙8
Associative of Multiplication
3+0=3
11+R=11
6(0+2)=6(2)