alg 1 properties of real numbers

commutative

order doesn’t matter

commutative e.g.

4+y=y+4, 5x=x(5)

associative

grouping of values doesn’t matter

associative e.g.

(5+x)+y=5(x+y), (3*y)*x=3*(y*x)

identity

stays the same

identity e.g.

y+0=y, y*1=y

inverse

using opposites to cancel a value

inverse e.g.

y+(-y)=0, y*(1/y)=1

property of zero

multiplying by 0 always =0

property of zero e.g.

y*0=0

distributive

multiply a value to an expression inside a parenthesis

distributive e.g.

4(w+z)=4w+4z

reflexive

a number always equals itself

reflexive e.g.

y=y, 4=4

symmetric

if a=b, then b=a

symmetric e.g.

y=4, 4=y

transitive

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

transitive e.g.

y=4, 4=2*2, y=2*2

closure

addition, subtraction, multiplication, and division in a set always gives you a number in the same set