ASSOCIATIVE COMMUTATIVE DISTRIBUTIVE LAWS Using these laws with

ASSOCIATIVE, COMMUTATIVE & DISTRIBUTIVE LAWS Using these laws with algebra

Commutative Law � � Turn arounds The "Commutative Law" says that you can swap numbers around and still get the same answer when you add or when you multiply 3+6=6+3 5 x 4=4 x 5 and = and

Associative Law � � � The "Associative Law" says that it doesn't matter how you group the numbers when you add or when you multiply. (In other words it doesn't matter which you calculate first. ) (2 + 4) + 5 = 2 + (4 + 5) 5 x (6 x 2) = (5 x 6) x 2

Distributive Law � � � The "Distributive Law" says you get the same answer when you: * multiply a number by a group of numbers added together * as when you do each multiply separately then add them. 3 x (2 + 4) = (3 x 2) + (3 x 4) In this example the 3 is distributed across the addition of 2 and 4

Task 1 � Prove that the commutative law does not apply to subtraction

Task 2 � Prove that the associative law will not work with division

Task 3 � � Complete these distributive examples – 5 x ( 4 + 7) = (__ x 4) + ( __ x 7) = ___ 3 x ( 1 + 6) = ( __ x __) + ( __ x __ ) = ___ (9 x 3 ) + (9 x 2) = __ x ( __ + __ ) = ___

Task 4 � � Jeremy is organising a party. He has invited 9 guests. Each guest will be provided a party hat costing $1. 50 per hat, and a party bag @ $2 each. Work out Jeremy’s party costs Include the distributive law in your workings Create an algebraic formula that will assist you to work out the party costs for 20 guests

Task 5 If s=4 and t=5, these statements are true: 3(s+t)=27 2 s+3 t=23 2 t-2 s=2 Choose values for p and q. Write three true statements using those variables. See if a partner can figure out what your values are.