1. PROPERTIES

2. ADDITIVE IDENTITY PROPERTY
BOOK DEFINITION:FOR ANY NUMBER A, A + 0 = A
OWN DEFINITION:
THIS PROPERTY SAYS THAT WHEN YOU ADD 0 TO ANY NUMBER IT EQUALS THAT NUMBER
EXAMPLE:
6 + 0 = 6

3. ADDITIVE INVERSE PROPERTY
BOOK DEFINITION:FOR ANY NUMBER A, A + -A = 0
OWN DEFINITION:
THIS PROPERTY SAYS THAT WHEN YOU ADD A NUMBER AND ITS OPPOSITE THE ANSWER IS EQUAL TO 0.
EXAMPLE:
= 0

4. MULTIPLICATIVE IDENTITY PROPERTY
BOOK DEFINITION: FOR ANY NUMBER A, A*1 = A
OWN DEFINITION:
THIS PROPERTY SAYS THAT WHEN YOU MULTIPLY ANY NUMBER TIMES 1 IT EQUALS THAT NUMBER
EXAMPLE:
6 ( 1 ) = 6

5. MULTIPLICATIVE PROPERTY OF ZERO
BOOK DEFINITION:FOR ANY NUMBER A, A 0 = 0
OWN DEFINITION:
THIS PROPERTY SAYS THAT WHEN YOU MULTIPLY 0 TIMES ANY NUMBER IT EQUALS ZERO.
EXAMPLE:
= 0

6. MULTIPLICATIVE INVERSE PROPERTY
BOOK DEFINITION: FOR ANY NUMBER A,
A(1/A) = 1
OWN DEFINITION:
THIS PROPERTY SAYS THAT WHEN YOU MULTIPLY ANY NUMBER TIMES ITS RECIPROCAL IT EQUALS 1.
EXAMPLE:

7. MULTIPLICATIVE PROPERTY OF -1
BOOK DEFINITION:
FOR ANY NUMBER A,
A(-1) = -A
OWN DEFINITION:
IF YOU MULTIPLY A NUMBER BY -1 IT EQUALS THE OPPOSITE OF THE NUMBER.
EXAMPLE:
4(-1) = (-1) = 2

8. REFLEXIVE PROPERTY BOOK DEFINITION: FOR ANY NUMBER A, A = A.
OWN DEFINITION:
THIS PROPERTY SAYS THAT A NUMBER IS EQUAL TO ITSELF.
EXAMPLE:
6= 6
2 + 4 = 2 + 4

9. SYMMETRIC PROPERTY BOOK DEFINITION:
FOR ANY NUMBERS A AND B, IF A = B, THEN B = A.
OWN DEFINITION:
IF, THEN FORM AND HAS TWO EQUAL SIGNS.
EXAMPLE:
IF 6 = , THEN = 6.

10. TRANSITIVE PROPERTY BOOK DEFINITION: IF A = B AND B = C, THEN A = C.
OWN DEFINITION:
IF, AND THEN FORM
3 EQUAL SIGNS
EXAMPLE:
IF 6 = AND = THEN 6 =

11. SUBSTITUTION PROPERTY
BOOK DEFINITION:
IF A = B THEN A MAY BE REPLACED BY B.
OWN DEFINITION:
ANY TIME YOU ADD, SUBTRACT, MULTIPLY OR DIVIDE TWO NUMBERS AND REPLACE WITH THE ANSWER YOU HAVE DONE SUBSTITUTION.
EXAMPLE:
(4 + 2 ) + 5 = 6 + 5

12. FOR ANY NUMBERS A AND B, A + B = B + A OR AB = BA.
COMMUTATIVE PROPERTY
BOOK DEFINITION:
FOR ANY NUMBERS A AND B, A + B = B + A OR AB = BA.
OWN DEFINITION:
YOU CAN CHANGE THE ORDER WHEN ADDING OR MULTIPLYING TWO NUMBERS AND THE ANSWER WILL BE THE SAME.
EXAMPLES:
6 + 7 = OR (5) = 5(4)

13. REGROUPS AND ALLOWS YOU TO MOVE THE GROUPING SYMBOLS.
ASSOCIATIVE PROPERTY
BOOK DEFINITION:
FOR ANY NUMBERS A,B, AND C , A + ( B + C) = ( A + B ) + C OR A(BC) = (AB)C
OWN DEFINITON:
REGROUPS AND ALLOWS YOU TO MOVE THE GROUPING SYMBOLS.
EXAMPLES:
4 + (3 + 5) = (4 + 3) + 5
0R 4(3·5) = (4· 3)5

14. DISTRIBUTIVE PROPERTY
BOOK DEFINITION:
FOR ANY NUMBERS A, B AND C, A(B+C) = AB + AC
OWN DEFINITION:
MULTIPLY EVERYTHING INSIDE THE ( ) BY WHAT IS OUTSIDE THE ( ).
EXAMPLE:
4 ( ) = 4(9) + 4(3)