1st math test of 2025-26 properties of Algebra

9th grade

Addition/subtraction property of Equality

Two sides of the equation  remain equal if you add or subtract the same thing to both sides

Example:

x+6=15

  -6   -6

x=9

Multiplication/Division property of Equality

Two sides of the equation remain equal if you multiply or divide the same number to both sides 

Example:

4x=16

4     4

x=4

Zero property of multiplication (zero product property)

Other teams think about anything multiplied by 0 is 0 

Example:

5(0)=0

Identity property of addition

0 added to any number keeps the number the same 

Example:

0+15=15

Identity property of multiplication

1 multiplied by any number keeps the number the same 

Example:

5(1)=5

Inverse property of addition

A number added to its inverse equals 0 

Example:

5+(-5)=0

inverse property of multiplication

Multiply a number by its reciprocal equals 1 

Example:

5(⅕)=1

associative property

Changing the group does not affect the answer multiplication and division

Example:(4+7)+6=4+(7+6)

              

commutative property

Changing the order does not affect the answer multiplication and division

Example:

7+8=8+7

Distributive property

Multiply the outside term by everything in the inside 

Example:

4(x-2)=4x-8

Term

a single number, variable or number and variables together 

Example:

3x^2+5x-7

3 terms

constant

term with no variable

Example:

5 or 7

like terms

have same variables and same exponents

example:

5x and 3x

coefficient

the same number in front of the variable

example:

7x ( 7 is the coefficient)

Variable

a letter or symbol that represents an unknown

algebraic expression

 Consist of a number, A variable, or a combination of both with operations 

Addition

Some, more than, plus, total, increase by combined 

subtraction

Difference, less than , minus, decrease by, take away 

Multiplication

Times, product, multiply, twice/triple, of 

Division

quotient, divide by, ratio