# algebra properties

## 15 terms

for all a, a+0=0+a=a For example, 10+0=0+10=10

### mult id prop

for all b, b1=1b=b. For example, 21=12=2

### mult prop of 0

for all a, a0=0a=0. For example, 120=012=0

### mult inverse prop

for every nonzero number a/b, where a, b does not equal 0, there is exactly one number b/a such that a/bb/a=1. For example, 1/44/1=1

### reflexive prop of =

for any number a, a=a. For example, if 8=8 and 6+2=6+2 and 3+5=3+5 then we know that they are all equal to themselves.

### sym prop of =

for any numbers a and b, if a=b then b=a. For example, if 8=6+2 then 6+2=8.

### transitive prop of =

for any numbers a, b, and c, if a=b and b=c, then a=c. For example, if a is shorter than b, and b is shorter than c, then a is shorter than c.

### sub prop of =

if a=b, then a may be replaced by b in any expression.

### distributive prop

for any numbers a, b, and c, a(b+c)a=ba+ca;
a(b-c)=ab-ac and (b-c) a=ba-ca. For example,
7(10+2)
710+72
70+14
84

### commutative prop

for any numbers a and b, a+b=b+a and ab=ba. For example, 4+5=5+4

### associative prop

for any numbers a, b, and c,
(a+b)+c=a+(b+c) and (ab)c=a(bc) For example, (1+2)+3=1+(2+3).

### like terms

two or more terms with the same variable, variables have the same exponent, sane or different coefficents.

### coefficent

the number multiplying the variables. For example, in 3x 3 is the answer.

### commute

to go back and forth, mut are change

to "hang out"