How do you add #\frac { 5} { 6} + \frac { 3} { 4} + \frac { 2} { 3} - \frac { 5} { 7}#?

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Answer 1 · 2017-10-29T11:40:30

#=>\frac { 129} { 84} = 1 45/84#

#\frac { 5} { 6} + \frac { 3} { 4} + \frac { 2} { 3} - \frac { 5} { 7}#

First make the denominators equal:

LCM of 6,4,3,7 is 84, so

#=>\frac { 5} { 6}xx(14/14) + \frac { 3} { 4} xx(21/21)+ \frac { 2} { 3}xx(28/28) - \frac { 5} { 7}(12/12)#

#=>\frac { 5xx14} { 6xx14} + \frac { 3xx21} { 4xx21} + \frac { 2xx28} { 3xx28} - \frac { 5xx12} { 7xx12}#

#=>\frac { 70} { 84} + \frac { 63} {84} + \frac { 56} { 84} - \frac { 60} { 84}#

#=> \frac { 70+63+56-60} { 84} #

#=> \frac { 189-60} { 84} #

#=>\frac { 129} { 84} #

#= 1 45/84#

Answer 2 · 2017-10-29T11:46:05

#129/84#

#=>5/6 + 3/4 + 2/3 - 5/7#

#=> [5/6 + 3/4 + 2/3] - 5/7#

#=> [(5/6 × 2/2) + (3/4 × 3/3) + (2/3 × 4/4)] - 5/7#

#=> [10/12 + 9/12 + 8/12] - 5/7#

#=> (10 + 9 + 8)/12 - 5/7#

#=> 27/12 - 5/7#

#=> (27/12 × 7/7) - (5/7 × 12/12)#

#=> 189/84 - 60/84#

#=> (189 - 60)/84#

#=> 129/84#