PROPERTIES

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

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: 6 + -6 = 0

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

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: 6 0 = 0

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:

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) = -4 -2(-1) = 2

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

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 = 2 3, THEN 2 3 = 6.

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 = 4 + 2 AND 4 + 2 = 3 2 THEN 6 = 3 2.

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

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 = 7 + 6 OR 4(5) = 5(4)

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

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 ( 9 + 3 ) = 4(9) + 4(3)