IR 2.1 ASSOCIATIVE PROPERTY There are two Associative Properties 1) Associative Property of Addition ο· It states that changing the groupings of the addends will not affect the sum. It is represented by π + (π + π) = (π + π) + π ο· This property is applicable for any number of groups of addends. 2) Associative Property of Multiplication ο· It states that changing the groupings of the factors will not affect the product It is represented by π × (π × π) = (π × π) × π ο· This property is applicable for any number of groups of factors. Example of proofs Associative Property of Addition π + (π + π) = (π + π) + π IR2.1 π =π π =π π =π Given Substitute then evaluate π + (π + π) = (π + π) + π π + ππ = ππ + π ππ = ππ Shows that changing the groupings of the addends does not affect the sum. Associative Property of Multiplication π × (π × π) = (π × π) × π Given π =π π =π π =π Substitute then evaluate IR 2.1 π + (π + π) = (π + π) + π π + ππ = ππ + π πππ = πππ Shows that changing the groupings of the factors does not affect the product. Example 1) State whether the equation is true or false. Explain using the Associative Property. + ( + ) = ( + )+ Explanation Both sides contains same shapes with same operations, hence the equation adhere to associative property of addition, therefore the equation is true. Considering the shapes sides IR 2.1 π + (π + π) = (π + π) + π π + ππ = ππ + π ππ = ππ Which is equal, therefore equation follows to associative property of addition. Example 2) State whether the equation is true or false. Explain using the Associative Property. Explanation Both sides contains same shapes with same operations, hence the equation adhere to associative property of multiplication, therefore the equation is true. Considering the shapes sides π × (π × π) = (π × π) × π π × ππ = ππ + π ππ = ππ IR 2.1 Which is equal, therefore equation follows to associative property of multiplication. Example 3) State whether the equation is true or false. Explain using the Associative Property. ( × )× = ×( × ) Explanation Though the operations are same but the factors have changed hence the equation does not adhere to associative property of multiplication, therefore the equation is false. Considering the shapes sides (π × π) × π = π × (π × π) ππ × π = π × ππ πππ = ππ Which is not equal, therefore the equation does not adhere to associative property of multiplication. IR 2.1 Summary! Associative Property of Addition ο· It states that changing the groupings of the addends will not affect the sum. ο· It is represented by π + (π + π) = (π + π) + π Associative Property of Multiplication ο· It states that changing the groupings of the factors will not affect the product. ο· It is represented by π × (π × π) = (π × π) × π
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