Question

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

Answer 1

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)

Answer 2

`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`