How do you evaluate #-7\frac { 1} { 6} + 3\frac { 5} { 6} #?

1 Answer
smendyka
Oct 31, 2017

See a solution process below:

Explanation:

First, convert each mixed number to an improper fraction:

#-(7 + 1/6) + (3 + 5/6) =>#

#-([6/6 xx 7] + 1/6) + ([6/6 xx 3] + 5/6) =>#

#-(42/6 + 1/6) + (18/6 + 5/6) =>#

#-(42+ 1)/6 + (18 + 5)/6 =>#

#-43/6 + 23/6 =>#

#(-43 + 23)/6 =>#

#-20/6#

We can now convert this to a mixed number:

#-(18 + 2)/6 =>#

#-(18/6 + 2/6) =>#

#-(3 + 2/(3 xx 2)) =>#

#-(3 + color(red)(cancel(color(black)(2)))/(3 xx color(red)(cancel(color(black)(2))))) =>#

#-(3 + 1/3) =>#

#-3 1/3#

Another process starts with rewrite the expression as:

#-(7 + 1/6) + (3 + 5/6) =>#

#3 - 7 + 5/6 - 1/6 =>#

#-4 + (5 - 1)/6#

#-4 + 4/6 =>#

#-(6/6 xx 4) + 4/6 =>#

#-24/6 + 4/6 =>#

#(-24 + 4)/6 =>#

#-20/6#

We can now convert this to a mixed number:

#-(18 + 2)/6 =>#

#-(18/6 + 2/6) =>#

#-(3 + 2/(3 xx 2)) =>#

#-(3 + color(red)(cancel(color(black)(2)))/(3 xx color(red)(cancel(color(black)(2))))) =>#

#-(3 + 1/3) =>#

#-3 1/3#

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