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

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Answer 1 · 2017-08-11T01:20:36

See a solution process below:

First, rewrite the expression as:

#-7/2 + 2/5#

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

#(5/5 xx -7/2) + (2/2 xx 2/5) =>#

#(5 xx -7)/(5 xx 2) + (2 xx 2)/(2 xx 5)#

#-35/10+ 4/10#

We can now add the two numerators over the common denominator:

#(-35 + 4)/10 =>#

#-31/10#

Answer 2 · 2017-08-11T01:28:47

#-31/10#

Find the LCD:

We can write out the factors of both #2# and #5# to determine this.

#2: 2, 4, 6, 8 , color(red)10 #
#5: 5, color(red)10, 15#

The LCD is thus #10#, therefore:

#[-7/2(5/5)]+[2/5(2/2)] larr# We manipulate the fractions in such a way that the denominator is 10

#-35/10+4/10#

#=-31/10#