Math- Ch. 1 Sections 1,2,4,5,6 & Ch. 2 Sections 1,2,3,4,7

Front 1

additive inverse

Back 1

for any number (a), the sum of a and 0 is a.
a+0=0+a=0

Front 2

multiplicative identity

Back 2

for any number (a), the product of a and 1 is a.
a*1=1*a=a

Front 3

multiplicative property of zero

Back 3

for any number (a), the product of a and 0 is 0.
a*0=0*a=0

Front 4

multiplicative inverse (reciprocals)

Back 4

for any number (a/b), where a=0 and b=0, there is exactly one number (b/a) such that the product of a/b and b/a is 1.
a/b*b/a=1

Front 5

what is zero's reciprocal?

Back 5

zero has no reciprocal because any number times zero is zero.

Front 6

reflexive property

Back 6

any quantity is equal to itself.
a=a

Front 7

symmetric property

Back 7

if one equals a secound quantity, then the second quantity equals the first.
if a=b then b=a

Front 8

transitive property

Back 8

if one quantity equals a second quantity and the second equals the third, then the first equals the third.
if a=b, and b=c, then a=c

Front 9

subsituation property

Back 9

a quantity may be substituated for its equal in any expression.
if a=b, then a may be replaced by b in any expression

Front 10

distributive property

Back 10

for any numbers (a,b,c)
a(b+c)= ab+ac
a(b-c)= ab-ac

Front 11

commutative property

Back 11

the order in which you add or multiply numbers doesnt change the sum or product.
a+b=b+a
a*b=b*a

Front 12

associative property

Back 12

the way you group 3 or more numbers when adding or multiplying doesnt change the sum or product.
a+b)+c=a+(b+c)
(ab)c=a(bc)