Question #c1d36

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Answer 1 · 2017-07-07T22:00:36

See a solution process below:

First, we need to covert the mixed numbers to improper fractions:

#2 7/27 + 8 5/9 => 2 + 7/27 + 8 + 5/9 =>#

#(27/27 xx 2) + 7/27 + (9/9 xx 8) + 5/9 =>#

#54/27 + 7/27 + 72/9 + 5/9 => (54 + 7)/27 + (72 + 5)/9 =>#

#61/27 + 77/9#

Next, we can put the fractions over common denominators by again multiplying by the appropriate form of #1# so we can add the numerators:

#61/27 + 77/9 => 61/27 + (3/3 xx 77/9) => 61/27 + (3 xx 77)/(3 xx 9) =>#

#61/27 + 231/27#

Then, we can add the numerators over the common denominator:

#61/27 + 231/27 => (61 + 231)/27 => 292/27#

Now, we can convert this improper fraction to a mixed number:

#292/27 => (270 + 22)/27 => 270/27 + 22/27 => 10 + 22/27 =>#

#10 22/27#

Answer 2 · 2017-07-08T20:53:24

#= 10 22/27#

#color(blue)(2) 7/27 + color(blue)(8) 5/9" "larr# add the whole numbers

#= color(blue)(10) (?+?)/27" "larr# find the common denominator

#=10 (7+15)/27" "larr# make equivalent fractions: #[5/9 xx3/3]#

#= 10 22/27" "larr# add the numertors

The question was given as mixed numbers, so the answer should be given in the same form.