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What is the definition and example for associative property?
The associative property of a binary operation states that the order in which the operations are carried out does not affect the result. If x, y and z are elements of a set and # an operation defined on the set then (x # y) # z = x # (y # z) and so either can be written as x # y # z, without ambiguity. Addition and multiplication are associative operations. So, for example, (3 + 2) + 4 = 5 + 4 = 9 and 3 + (2 + 4) = 3 + 6 = 9
Associative properties of addition and multiplication?
Associative propertyThe associative property states that when three or more expressions are added or multiplied, they may be grouped without affecting the answer. The commutative property applies within the associative property.(x + y) + z = x + (y + z)(xy)z = x(yz)This law applies with a larger number of expressions, as well as grouped expressions.(x + xy) + 3z + 5xz/2 =x + (xy + 3z) + 5xz/2 =x + (xy + 3z + 5xz/2)Again, you should think of subtraction as addition of a negative number.
What is the meaning of distributed property?
The DISTRIBUTIVE (not distributed) property is a property of multiplication over addition (OR subtraction). In its simplest form, if x, y and z are three numbers then, according to the distributive property of multiplication over addition, x*(y + z) = x*y + x*z
Is x plus y equals y plus x the associative property?
No, this is the commutative property. For addition, the associative property is: x + (y + z) = (x + y ) + z
What are the different properties of a rational number?
The set of rational numbers is a mathematical field. This requires that if x, y and z are any rational numbers then their properties are as follows:x + y is rational : [closure of addition];(x + y) + z = x + (y + z) : [addition is associative];there is a rational number, denoted by 0, such that x + 0 = x = 0 + x : [existence of additive identity];there is a rational number denoted by -x, such that x + (-x) = 0 = (-x) + x : [existence of additive inverse];x + y = y + x : [addition is commutative];x * y is rational : [closure of multiplication];(x * y) * z = x * (y * z) : [multiplication is associative];there is a rational number, denoted by 1, such that x * 1 = x = 1 * x : [existence of multiplicative identity];for every non-zero x, there is a rational number denoted by 1/x, such that x * (1/x) = 1 = (1/x) * x : [existence of multiplicative inverse];x * y = y * x : [multiplication is commutative];x * (y + z) = x * y + x * z : [multiplication is distributive over addition].
