How do you add #5\frac{2}{9}+6\frac{8}{9}#?

In this case, you would make these two fractions improper:

#5 2/9 + 6 8/9# would become #47/9 + 62/9#

You can get this value by multiplying the denominator (in the case of the first question, 9) with the number in front (in this case 5) and adding that to the numerator (in this case 2) as follows:

# 5 2/9 #
#= (45 + 2)/9#
#= 47/9#

You can do the same with the other equation:

#6 8/9#
#= (54+ 8)/9#
#= 62/9#

Since the denominator is the same you can just add the two fractions:

#47/9 + 62/9#
#= 109/9#

You can split the mixed numbers into the sum of the whole and fractional parts.

(Basically, you can write the mixed number as the bigger number plus the fraction.)

This is what it would look like:

#color(red)5 color(blue)(2/9)=> color(red)5+color(blue)(2/9)#

Now, let's use this in the actual problem. First, split both mixed numbers. Then, add together the whole number parts and the fraction parts. Lastly, simplify anything needed.

#color(white)=color(red)(5 2/9)+color(blue)(6 8/9)#

#=color(red)5+color(red)(2/9)+color(blue)6+color(blue)(8/9)#

#=color(red)5+color(blue)6+color(red)(2/9)+color(blue)(8/9)#

#=color(purple)11+color(red)(2/9)+color(blue)(8/9)#

#=color(purple)11+color(purple)(10/9)#

#=color(purple)11+color(purple)((9+1)/9)#

#=color(purple)11+color(purple)(9/9)+color(purple)(1/9)#

#=color(purple)11+color(purple)1+color(purple)(1/9)#

#=color(purple)12+color(purple)(1/9)#

#=color(purple)12color(purple)(1/9)#

That's the result. Hope this helped!