How can we help?

You can also find more resources in our Help Center.

Axiom or postulate

a statement that is assumed to be true

Reflexive Property

a=a

every real number equals itself

every real number equals itself

Symmetric property

if a=b then b=a

you can switch the sides of an equation

10=3x-5 or 3x-5=10

you can switch the sides of an equation

10=3x-5 or 3x-5=10

Transitive Property

if a=b and b=c then a=c

if 3y+22=m then m=3y+22

if 3y+22=m then m=3y+22

Addition property of equality

if a=b then a+c=b+c

you can add any real number to both sides of the equation 3x+=y then 3x+7=y+2

you can add any real number to both sides of the equation 3x+=y then 3x+7=y+2

Multiplication property of equality

if a=b the ac=bc

here you are multiplying both sides by c

you can multiply both sides of an equation by any real number

here you are multiplying both sides by c

you can multiply both sides of an equation by any real number

Closure Property

a+b and ab are unique real numbers

whenever you add or multiply 2 real numbers together you get a real number

7+5=12 always

whenever you add or multiply 2 real numbers together you get a real number

7+5=12 always

Commutative Property

a+b=b+a, ab=ba

you can change the order of numbers you are adding or multiplying

3+4=4+3

3(4)=4(3)

you can change the order of numbers you are adding or multiplying

3+4=4+3

3(4)=4(3)

Associative Property

(a+b)+c=a(b+c)

(ab)c=a(bc)

you can change the grouping of numbers that are being added or multiplied

4+(5+6)=(4+6)+5

(ab)c=a(bc)

you can change the grouping of numbers that are being added or multiplied

4+(5+6)=(4+6)+5

Identity Property

0+a=a

1(a)=a

adding 0 does not change the number neither does multiplying by 1

1(a)=a

adding 0 does not change the number neither does multiplying by 1

Inverse Property

a) opposites or additive inverses:

a+(-a)=0

any number plus its opposite equals 0

x+ (-x)= 0

b)reciprocals or multiplicative inverses:

any number times its reciprocal = 1

mx1

- =1

m

a+(-a)=0

any number plus its opposite equals 0

x+ (-x)= 0

b)reciprocals or multiplicative inverses:

any number times its reciprocal = 1

mx1

- =1

m

Distributive Property

2(x+5)=2x+10

you must take the most out that you can

12m+18=6(2m+3)

you must take the most out that you can

12m+18=6(2m+3)