How do you evaluate #4\frac { 6} { 7} + 8\frac { 4} { 9}#?

2 Answers
Sep 2, 2017

See two solution process below:

Explanation:

First, we can convert the two mixed numbers to improper factions:

#4 6/7 + 8 4/9 => (4 + 6/7) + (8 + 4/9) =>#

#([7/7 xx 4] + 6/7) + ([9/9 xx 8] + 4/9) =>#

#(28/7 + 6/7) + (72/9 + 4/9) =>#

#34/7 + 76/9#

Next, we need to put each of the fractions over a common denominator by multiplying each fraction by the appropriate form of #1#:

#34/7 + 76/9 => (9/9 xx 34/7) + (7/7 xx 76/9) =>#

#306/63 + 532/63 => 838/63#

Now, we can convert the improper fraction into a mixed number:

#838/63 => (819 + 19)/63 => 819/63 + 19/63 => 13 + 19/63 => color(red)(13 19/63)#

A second begins with rewrite the expression as:

#4 6/7 + 8 4/9 => (4 + 6/7) + (8 + 4/9) =>#

#4 + 6/7 + 8 + 4/9 => 4 + 8 + 6/7 + 4/9 => 12 + 6/7 + 4/9#
Next we can add the fractions by putting them over a common denominator:

#12 + 6/7 + 4/9 => 12 + (9/9 xx 6/7) + (7/7 xx 4/9) =>#

#12 + 54/63 + 28/63 => 12 + (54 + 28)/63 => 12 + 82/63#

Now, we can convert the improper fraction to a mixed number and add it to the integer:

#12 + 82/63 => 12 + (63 + 19)/63 => 12 + 63/63 + 19/63 =>#

#12 + 1 + 19/63 => 13 + 19/63 => color(red)(13 19/63)#

Sep 3, 2017

#=13 19/63#

Explanation:

When adding mixed numbers you can add the whole numbers first and then add the fractions:

#color(blue)(4) 6/7 + color(blue)(8) 4/9#

#=color(blue)(12) + 6/7 +4/9#

#= 12 (color(white)(xxxxxx))/color(red)(63)" "larr# find the common denominator

#= 12 (color(green)((9xx6) +(7xx4)))/63" "larr# make equivalent fractions

#=12 (color(green)(54+28))/63#

#=12 color(magenta)(82/63)#

#=12 + color(magenta)(1 19/63)" "larr# improper fraction to mixed number

#=13 19/63#

Answers should be given in the same form as the question.