0 +1 +2+3 +4 +5 +6
-6 -5 -4 -3 -2 -1
NUMBER LINE
+2+3 = +5
ADD MOVE RIGHT
+2 -3 = -1
MOVE LEFT SUBSTRACT
-3 +2 = -1
-3 - 3 = -6
NOTE
1) SIGN OF 2ND
NUMBER GIVES DIRECTION
2) SIGN OF RESULT = SIGN OF BIG NUMBER
++ = +ADD > Biggest
- - = -ADD > Smallest
-+ = SUB > Medium
⊕
+- = SUB > Medium
⊕
PROPERTIES OF INTEGERS
1.CLOSURE
IF A = INTEGER IF B= INTEGER
AND
THEN
A + B = INTEGER CLOSURE UNDER ADDITION
A - B = INTEGER CLOSURE UNDER SUBSTRACTION
A X B = INTEGER CLOSURE UNDER MULTIPLICATION
A / B ≠ INTEGER NOT CLOSED UNDER DIVISION
8.
PROPERTIES OF INTEGERS
2.COMMUTATIVE
IF A = INTEGER IF B= INTEGER
AND
THEN
A + B = B + A COMMUTATIVE UNDER ADDITION
A X B = B X A COMMUTATIVE UNDER MULTIPLICATION
A + B ≠ B + A NOT COMMUTATIVE UNDER SUBSTRACTION
A / B ≠ B / A NOT COMMUTATIVE UNDER DIVISION
9.
PROPERTIES OF INTEGERS
3.ASSOCIATIVE
IF A = INTEGER IF B= INTEGER
AND
THEN
A + (B+C) = (A+B) + C ASSOCIATIVE UNDER ADDITION
A - (B-C) ≠ (A-B) - C NOT ASSOCIATIVE UNDER SUBSTRACTION
A X (BXC) = (AXB) X C ASSOCIATIVE UNDER MULTIPLICATION
A / (B/C) ≠ (A/B) / C NOT ASSOCIATIVE UNDER DIVISION
10.
PROPERTIES OF INTEGERS
4.DISTRIBUTIVE
IF A = INTEGER IF B= INTEGER
AND
THEN
A X (B+C) = AXB + AXC DISTRIBUTIVITY OF MULTIPLICATION
OVER ADDITION
A X (B-C) = AXB - AXC DISTRIBUTIVITY OF MULTIPLICATION
OVER SUBTRACTION
11.
PROPERTIES OF INTEGERS
5.IDENTITY
IF A = INTEGER THEN
1) ADDITIVE IDENTITY(0)
A + 0 = 0 + A = A
2) MULTIPLICATIVE IDENTITY(1)
A X 1 = 1 X A = A
12.
DIVISION BY 0
A
0
=NOT DEFINED = MEANINGLESS
0
0
= NOT DEFINED = MEANINGLESS
0 X 0 = NOT DEFINED = MEANINGLESS
MULTIPLICATION BY 0
A X 0 = 0 X A = 0
