How do you add #-5\frac { 2} { 3} + ( - 2\frac { 8} { 9} )#?

1 Answer
smendyka
Aug 31, 2017

See a solution process below:

Explanation:

First, convert each mixed number into an improper fraction:

#-5 2/3 + (-2 8/9) => -(5 + 2/3) + (-[2 + 8/9]) =>#

#-([3/3 xx 5) + 2/3) + (-[(9/9 xx 2) + 8/9]) =>#

#-(15/3 + 2/3) + (-[18/9 + 8/9]) =>#

#-17/3 + (-26/9)#

To add the two fractions we need to multiply the fraction on the left by the appropriate form of #1# to put it over a common denominator with the fraction on the right:

#(3/3 xx -17/3) + (-26/9)#

#-51/9 + (-26/9)#

We can now add the two fractions:

#(-51 + (-26))/9 => (-51 - 26)/9 => -77/9#

If necessary, we can convert this back into a mixed number:

#-77/9 => -(72 + 5)/9 => -(72/9 + 5/9) => (-8 + 5/9) => -8 5/9#

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