Brackets are used in an expression when we want a set of operations to be performed before the others.The order in which operations are performed is division, multiplication, addition and finally subtraction (DMAS). That is, each operation has its own precedence. When expression has different types of operations, some operations have to be performed before the others.Any integer when multiplied or divided by 1 gives itself and when multiplied or divided by - 1 gives its opposite.All the properties applicable to whole numbers are applicable to integers in addition the subtraction operation has the closure property.To find the quotient of one integer divided by another non-zero integer, we divide their absolute values and give the result a plus sign if both the numbers have the same sign or a minus sign otherwise.To find the product of two integers, we multiply their absolute values and give the result a plus sign if both the numbers have the same sign or a minus sign otherwise.-m and m are negative or additive inverses of each other.If m and n are two integers, then (m - n) is also an integer.All properties of operations on whole numbers are satisfied by these operations on integers.To subtract an integer y from another integer x, we change the sign of y and add it to x.The sum of two integers of opposite signs is an integer whose absolute value is the difference of the absolute values of addend and whose sign is the sign of the addend having greater absolute value.The sum of two integers of the same sign is an integer of the same sign whose absolute value is equal to the sum of the absolute values of the given integers.The absolute value of an integer x is denoted by |x| and is given by The absolute value of an integer is the numerical value of the integer without regard to its sign.The sum of an integer and its opposite is zero.The greater the number, the lesser is its opposite.Two integers that are at the same distance from 0, but on opposite sides of it are called opposite numbers.Every positive integer is greater than every negative integer.0 is less than every positive integer and greater than every negative integer.On an integer number line, all numbers to the right of 0 are positive integers and all numbers to the left of 0 are negative integers.0 is an integer which is neither positive nor negative.In integers we will discuss on this in details and solve various types of examples on integers.
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