We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
409
2
avatar+314 

Is there a "distributive property of division"??

Like as in this question:

(-3)2n+1 /(27*(-3)2n)  n is a positive whole number.

Can you do this:

((-3)2n+1 /27)*((-3)2n+1 /(-3)2n) ??????

THANK YOU

 Aug 26, 2017
 #1
avatar+99580 
+2

(-3)2n+1 /(27*(-3)2n)

 

Note that we can write this as

 

(-3)2n+1 / (-3)2n   * ( 1 /27 )

 

And remember that we have the property that    am / an  = a ( m - n)

 

So   ...we have....

 

(-3) [ (2n + 1) - 2n ]  *  (1/27)  =

 

(-3)1  * (1/27)  =

 

(-3)  / 27  =

 

-1 / 9

 

 

cool cool cool

 Aug 26, 2017
 #2
avatar+7354 
+4

Also...

 

\(\frac{(-3)^{2n+1}}{27\,\cdot\,(-3)^{2n}}=\frac{(-3)^{2n+1}}{27}\,\cdot\,\frac{(-3)^{2n+1}}{(-3)^{2n}}\)

 

This is not true.

If you multiply the two fractions on the right side together, you will get   \(\frac{[ (-3)^{2n+1})]^2}{27\,\cdot\,(-3)^{2n}}\)     .

 

\(\frac{a}{bc}\,\neq\,\frac{a}{b}\,\cdot\,\frac{a}{c}\)

 

 

But..you can distribute division the same as you distribute multiplication, like this....

 

\(\frac{8 + 6 +10}{2}=\frac12(8+6+10)\,=\,(\frac12)(8)+(\frac12)(6)+(\frac12)(10)\,=\,4+3+5\,=\,12\)     smiley

 Aug 26, 2017
edited by hectictar  Aug 27, 2017

5 Online Users