Download ABSOLUTE VALUE – INTEGERS- 4

ABSOLUTE VALUE – INTEGERS- 4-QUADRANT GRID NOTES
ABSOLUTE VALUE
The absolute value of x, denoted "| x |" (and which is read as "the absolute value of x"), is the
distance of x from zero. This is why absolute value is never negative; absolute value only
asks "how far?", not "in which direction?". This means not only that | 3 | = 3, because 3 is
three units to the right of zero, but also that | –3 | = 3, because –3 is three units to the left of
zero.
The absolute value expression:
If a negative sign is in front of the absolute value bars means to multiply the
absolute value of the expression by a negative one the expression becomes
negative not the absolute value
-| –3 | = ( -1 ) (| –3 | ) = ( -1 ) ( 3 ) = -3 because the absolute of | –3 | is 3 the
expression becomes negative because of the multiplication by the negative one
THE NUMBER LINE ALL THE POSITIVE AND NEGATIVE WHOLE NUMBERS AND
ZERO ORGANIZED BY NUMBER VALUE AS POSITIVE NUMBERS MOVE AWAY FROM
ZERO THE NUMBERS INCREASE IN VALUE BUT AS NEGATIVE NUMBERS MOVE
AWAY FROM ZERO THEY DECREASE IN VALUE.
ADDITIVE INVERESE
ANY NUMBER IN WHICH THE SAME NUMBER BUT THE OPPOSITE
SIGN ARE ADDED TOGETHER GIVES A SUM OF ZERO
If your number is –6, and you're adding the inverse of 6, then –6 + 6 = 0.
INTEGER
"Integers", which are zero, the natural numbers, and the negatives of the naturals
:..., –6, –5, –4, –3, –2, –1, 0, 1, 2, 3, 4, 5, 6, ...
POSITIVE INTEGER
All the whole numbers greater than zero
NEGATIVE INTEGER
All the whole numbers less than zero
CO-ORDINATE GRID
The two axes divide the plane into four sections called "quadrants". The quadrants are
labeled with Roman numerals, starting at the positive x-axis and going around counter
clockwise:
QUADRANT
Each of the 4 sections I ( + +) II ( - + ) III ( - - ) IV ( + - ) in order to be
recorded in a
guardant the number must be in the block not on the line
POINT OF ORGIN
The center point of the grid in which the x axis meets the y axis and x & y are zero
X AXIS
The horizontal axis of the positive and negative x values the independent variable
Of the ordered pair
Y AXIS
The vertical axis the y values positive and negative the dependent variable of the ordered pair
The x & y values plotted to create a point
ORDERED PAIR- the X & Y numbers that create a point X & Y are called the
coordinates , X &
Y , and THE RELATION
DOMAIN
The x value in an ordered pair
RANGE
The y value in an ordered pair
RULES OF INTEGERS
ADDITION OF LIKE SIGNSTOTAL THE NUMBERS KEEP THE SAME SIGNS 7 + 7 =14
-6 + -6 = -12
The sum of two negative integers is a negative integer.
ONCE START ON THE NUMBER LINE CONTINUE DOWN THE NEGATIVE LINE TO TOTAL
THE NEGATIVES
ADDITION OF UNLIKE SIGNS- POSITIVE AND NEGATIVES WILL CANCEL THE SIGN WILL
BE THE NUMBER WITH THE LARGEST ABSOLUTE VALUE
7 + ( -5 ) = +++++++ _ _ _ _ _ WHICH WILL LEAVE 2 POSITIVES FOR A + 2
SUBTRACTION OF INTEGERS- ADD THE INVERSE OF THE NUMBER
SO 7 -3 = 4 IS THE SAME AS 7 + (- 3) = 4
SUBTRACTION OF 2 NEGATIVES – YOU CONTINUE DOWN THE NEGATIVE NUMBER LINE
SO -20-10 = -30 BECAUSE YOU TAKE 10 MORE AWAY
SUBTRACTION WITH A DOUBLE NEGATIVE- 2 NEGATIVES MAKE A POSITIVE SO: -6 – (-3)
= -6 + 3 = -3
MULTIPLICATION AND DIVISION OF INTEGERS
When you multiply or divide two integers with the same signs, the result is always
positive.
Positive x positive = positive ( 3 ) ( 3 ) = 9 9/3 = 3
Negative x negative = positive ( -2 ) ( -2 ) = 4 -12/-4 = 3
When you multiply two integers with different signs, the result is always negative.
Positive x negative = negative ( 3 ) ( -3 ) = -9 9/-3 = -3
Negative x positive = negative ( -2 ) ( 2 ) = -4 -12/4 = -3