Free Tutoring Online Free Tutoring Online We have different free online tutors available on the internet. free tutors online guide us to solve the different problems time to time. Free online tutors are instant guiding tools. We have free online tutors to enhance our knowledge time to time. Here we are discussing integers in this unit. Integers are the group of positive and negative numbers which extends endlessly in both the directions on the number line. The middle most number in integers is zero, which is neither negative nor a positive number. Every integer has a successor and the predecessor. We can get successor by adding 1 to the number and we can get a predecessor by subtracting from the given number.
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As we say successor of 312 is 312 + 1 = 313. Similarly predecessor of a number can be found by subtracting 1 from it. Predecessor of 124 is 124 – 1 = 123. Every integer in the set has a successor and the predecessor. All the integers satisfy the closure property with respect to all mathematical operators, which means that if a, b are any integer numbers, then, Sum of the two integers i.e. a + b is also an integer. The difference of the two integers i.e. a – b is also an integer. The product of the two integers i.e. a * b is also an integer. The quotient of the two integers is a/b is also an integer. Commutative property of integers holds true for addition and multiplication and it does not holds true for subtraction and division, which means if a and b are any two integers (positive or negative ) then we have a + b = b + a, by this we mean if the order of doing addition is changed the result remains unchanged. a * b = b * a, by this we mean if the order of doing multiplication is changed the result remains unchanged. a - b <> b - a, by this we mean if the order of doing subtraction is changed the result remains changes and does not remain same. a / b <> b / a, by this we mean if the order of doing division is changed the result remains changes and does not remain same. Associative property of integers holds true for addition and multiplication and it does not holds true for subtraction and division, which means for any integers a, b, c we have.
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(a+b)+c= a+(b+c) (a*b)*c= a*(b*c) ( a - b ) - c <> a - ( b - c ) ( a + b ) + c <> a + ( b + c ) Property of zero: here exist an integer zero such that if it is added or subtracted from any given integer a, then the result remains unchanged. SO we can say: a+0=a
and a – 0 = a
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