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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