Associative Property of Multiplication of Integers, Whole Numbers

Multiplication is one of the common mathematical functions which we all are familiar with. But, there are four properties associated with multiplication, which are commutative, associative, multiplicative identity and distributive properties. The associative property of multiplication states that when three or more real numbers are multiplied, the result is the same regardless of the grouping of the factors, that is the order of the multiplicands.

Associative Property of Multiplication

Associative property of multiplication states that multiplication problem can be grouped in different ways but the answer remains the same. That is,

Theorem

( a x b ) x c = a x ( b x c ) Where, a, b and c are real numbers

Example :
Let us consider the values of a = 4, b = 5 and c = 2 ( 4 x 5 ) x 2 = 4 x ( 5 x 2 ) Step 1: Multiply the values inside the parenthesis (). ( 4 x 5 ) = 20 Step 2: Multiply the last number with the result to get your LHS product. 20 x 2 = 40 Step 3: Repeat the same for right hand side multiplication ( 5 x 2 ) = 10 Step 4: Multiply the result with 4. 4 x 10 = 40 Step 5: LHS = RHS 40 = 40 Hence associative property of multiplication is proved.

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