How do you evaluate #-2\frac { 1} { 8} + 1\frac { 1} { 4} + - \frac { 9} { 16} #?

2 Answers
smendyka
Sep 29, 2017

See a solution process below:

Explanation:

First, we can rewrite the expression using the rule "pus a minus is a minus":

#-2 1/8 + 1 1/4 - 9/16#

Next, we need to convert the two mixed numbers to improper fractions:

#-(2 + 1/8) + (1 + 1/4) - 9/16#

#-([8/8 xx 2] + 1/8) + ([4/4 xx 1] + 1/4) - 9/16#

#-(16/8 + 1/8) + (4/4 + 1/4) - 9/16#

#-(16 + 1)/8 + (4 + 1)/4 - 9/16#

#-17/8 + 5/4 - 9/16#

Then we need to put all of the fractions over common denominators by multiplying by the appropriate value of #1# which will not change the value of the fractions:

#(2/2 xx -17/8) + (4/4 xx 5/4) - 9/16#

#(2 xx -17)/(2 xx 8) + (4 xx 5)/(4 xx 4) - 9/16#

#-34/16 + 20/16 - 9/16#

Next, we can add and subtract the numerators over the common denominator:

#(-34 + 20 - 9)/16#

#(-14 - 9)/16#

#-23/16#

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

#-(16 + 7)/16#

#-(16/16 + 7/16)#

#-(1 + 7/16)#

#-1 7/16#

EZ as pi
Sep 29, 2017

#-23/16 = -1 7/16#

Explanation:

Re-arrange the fractions for ease of working:

#1 1/4 -2 1/8 -9/16#

Change to improper fractions:

#=5/4-17/8-9/16#

#=5/4xx4/4-17/8xx2/2-9/16#

#=(20-34-9)/16" "larr# common denominator

#=-23/16#

#=-1 7/16#

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