Compléter Full numerical setsVersion en ligne Full text of numerical sets according to the consistency. par Luz Dary Moreno Cruz 1 two absolute numbers integers positive WHOLE NUMBERS : The set of integers is comprised of natural numbers and their opposites , it ie positive numbers and their opposites that are negative . Example : The set of integers is defined as follows : Z + = Positive integers Z = negative integers ( 0 = neutral element , zero is neither positive nor negative ) ABSOLUTE VALUE : If a number is positive , the absolute value is the same number and if it is negative its absolute value is the opposite . The absolute value is never negative . Example : - 3 = 3 reads : absolute value of minus three three 5 = 5 reads : absolute value five five Operations with integers : SUM : The sum of integers is divided into : SUM OF integers : The sum of positive is performed in the same way that two natural numbers are added . WHOLE SUM OF NEGATIVE : The sum of two negative integers is obtained by adding the absolute values ? ? of the and putting a negative sign to the result . Procedure : to . We place the numbers to be added in parenthesis b . We add their values c . The result will put a minus sign Example : ( - 48 ) + ( - 32 ) = Numbers to add I - I - 32I 48I + = add their absolute values - 80 = As a result we put a minus sign SUM OF WHOLE WITH DIFFERENT SIGNS : The sum of two integers of different signs is obtained by subtracting the absolute value greater whole , the entire lower absolute value . in the result the sign of integer greater absolute value is written . Example : ( 36 ) + ( - 15 ) + ( 14 ) + ( - 9 ) = ( ( - 15 ) + ( - 9 ) ) = L - 24l = L - 24l ( ( 36 ) + ( 14 ) ) = l 50 l 50 - 24 = 26 Operation to be performed We add negative integers and the result we add its absolute value . We add the positive integers and its outcome will find absolute value . We subtract these two results and let the result the sign of the larger number having greater absolute value . PROPERTIES OF THE ADDITION OF WHOLE NUMBERS Clausurativa : The sum of two integers gives results in another integer . Commutative : The order of the addends does not change the result . Associative : When you add more than two integers , how are grouped does not change the result . Modulativa : Adding any integer zero , the result is the same integer . PROPERTIES EXAMPLES Clausurativa ( - 3 ) 18 + = 15 Commutative ( - 33 ) + ( - 142 ) = ( - 142 ) + ( - 33 ) - 175 - 175 = Associative ( ( - 2 ) + 12 ) + ( - 5 ) = ( - 2 ) + ( 12 + ( - 5 ) ) ( 10 ) + ( - 5 ) = ( - 2 ) + ( 7 ) 5 = 5 Modulativa ( - 3 ) + 0 = ( - 3 ) ABDUCTION : In operation a - b = c , the minuend is a , b and c is the subtrahend is the difference . Since a reverse operation is subtraction gives the addition is performed as follows : When we add the minuend opposite the subtrahend and the result of the sum is the difference . Symbols : Destruction in parentheses 12 - 8 + ( 36 - 7 + 10 - 15 ) + 9 12 - 8 + 36 - 7 + 10 to 15 + 9 67 - 30 = 37 Multiplication : Multiply integers abbreviated means adding several integers either identical or different sign . Procedure for multiplying integers : 1 . Multiply the numbers as if they were natural 2 . operate the signs using the following principles Example . ( - 3 ) X ( 8 ) = - 24 Properties multiplying integers : 1 . Clausurativa : The multiplication of two natural numbers as a result gives us another natural number . 2 . commutative : The order of the factors does not alter the product . 3 . Associative : Multiplying over two natural numbers , the way they are grouped not alter the product . 4 . Modulativa or neutral element : Multiplying any natural number by one , the product is the same natural number . 5 . Distributive of multiplication with respect to addition : The product of a natural number by a specified amount , is equal to the sum of partial products of the whole for each of the addends . EXAMPLE PROPERTIES Clausurativa to . 12 X 3 = 36 b . 17 x 7 = 119 Commutative 6 x 53 = 53 x 6 318 = 318 Associative ( 7X49X8 = 7X ( 4X8 ) ( 28 ) X8 = 7X ( 32 ) 224 = 224 Neutral element 2 , 574 x 1 = 2 , 574 1 X 2 , 574 = 2 , 574 The distributive multiplication to the sum 4X ( 5 + 2 ) = ( 4x5 ) + ( 4x2 ) = 20 + 8 = 28 DIVISION : In integer division may be the case that both numbers are positive , negative or both are having different sign . Considering the above possibilities can draw the following conclusions : 1 . The quotient of two positive integers is a positive integer ( 15 ) / ( 3 ) = 5 2 . The negative quotient of two integers is a positive integer ( - 24 ) / ( - 6 ) = 4 3 . The ratio of the division of two integers different sign is a negative integer . ( - 24 ) / ( 6 ) = - 4 In integer division the same laws that are used for multiplication are met .
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