what is 24x15 using only commutitivity and associativity

Question

I can only use commutativity and associativity

 

Answer 1

Most people can process more than five operations "in their heads" for each operation performed with pencil and paper.

 

Also using the Distributive Property:

 

   24 * 15

   (20 + 4)*15

   20*15 + 4*15

   20*15 + 4*(10+5)

    20*15 + 4*10 + 4*5

      300 + 40 + 20

       360

 

Extra credit:  If Joe earns $25/hr and there are 2080 hours in a year (52*40), then how much does Joe earn during a year?

      $25*2080

       $25*(2000+80)

       $25*2000 + $25*80

         $50000 + $(100/4)*80

         $50000 + $8000/4

         $50000 + $2000

           $52000

 

Now, multiply 52*40 this way.

Answer 2

Interesting. See, the commutative and associative properties is manipulating the order of multiplication and addition properties, usually to find easier paths to get to the final answer.

In this case, however, we only have two numbers:

24 * 15

That means to use commutative, we would switch the number and solve like that:

15 * 24