The distributive property to solve. 4•47

Question

Test practice. 

Answer 1

The first method looks like elementary multiplication:

       47

    *   4

    -------

 

    4(47) = 4(7+40) = 28 + 160 = 188

 

 

Then, there is subtraction:

    4(47) = 4(50-3) = 200 - 12 = 188    [this can be quick!]

 

 

Then, there is factoring (use distributive law twice) for F-O-I-L):

    (x+1)(x-1) = x² - 1

  What is 49*51 ?  (50-1)(50+1) = 50*50 -1 = 2500-1 = 2499

 

 

Here is an example of using this concept:

   Gauss' formula for the sum of the numbers from 1 to N is (N)(N+1)/2.

   What is the sum of the numbers from 1 to 100 ?     100*101/2 = 50*101 = 5000+50 = 5050

 

Here's a very practical one:

   If Joe earns $15/hour, what is his yearly salary?

   ($15/hour)(40 hr/wk)(52 wk/yr) = $15*40*52/yr

              = $15*(2080)/yr

              = $15*2000 + $15*80  /yr

              = $30000 + $800 + $400  /yr    [$15/hr is less than 10% more than $(2*15),000/yr]

              = $31200/yr