How do you simplify #2/3(6r+9s)+ 1/4 (8r+12s)#?

2 Answers
Feb 7, 2016

6r+9s

Explanation:

Firstly,we get rid of the brackets by multiplying.
2/3 x 6r= 4r
2/3 x 9s=6s
1/4 x 8r=2r
1/4 x 12s=3s

4r+6s+2r+3s=6r+9s

It can also be written as 3(2r+3s)

Feb 7, 2016

#6r+9s#

Explanation:

Given: #" "color(brown)(color(green)(2/3)(6r+9s))color(blue)(+)color(magenta)(1/4)color(black)((8r+12s))#

#color(blue)("What this is really saying?")#

#" Everything inside of "color(brown)((6r+9s)) " is multiplied by "color(green)(2/3)#

#" Everything inside of "(8r+12s) " is multiplied by "color(magenta)(1/4)#

#color(blue)("Lets apply this!")#

#[(color(green)(2/3)xx color(brown)(6r))color(brown)(+)(color(green)(2/3)xxcolor(brown)(9s))] color(blue)(+)[(color(magenta)(1/4)xx8r)+(color(magenta)(1/4)xx12s)] #

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
When multiplying you must be very careful about signs. Fore example: #""#

#(-1)xx(+1)=(-1) " and that " (-1)xx(-1)=(+1)#. In
#""#
this instance it is very straight forward in that everything is positive!
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#=> 4r+6s+2r+3s#

#=>6r+9s#