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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 does real number mean?
It is a number which satisfies all the conditions that are given below:For any three real numbers x, y and z and the operations of addition and multiplication,• x + y belongs to R (closure under addition)• (x + y) + z = x + (y + z) (associative property of addition)• There is an element, 0, in R, such that x + 0 = 0 + x = x (existence of additive identity)• There is an element, -x, in R, such that x + (-x) = (-x) + x = 0 (existence of additive inverse)• x + y = y + x (Abelian or commutative property of addition)• x * y belongs to R (closure under multiplication)• (x * y) * z = x * (y * z) (associative property of multiplication)• There is an element, 1, in R, such that x * 1 = 1 * x = x (existence of multiplicative identity)• For every non-zero x, there is an element, 1/x, in R, such that x * 1/x = 1/x * x = 1 (existence of multiplicative inverse)• x * (y + z) = x*y + x * z (distributive property of multiplication over addition)
