How do you solve #x+ \frac { 3} { 4} = 5\frac { 4} { 5}#?

1 Answer
smendyka
Aug 1, 2017

See a solution process below:

Explanation:

First, convert the mixed number on the right side of the equation into an improper fraction:

#x + 3/4 = (5 + 4/5)#

#x + 3/4 = ([5/5 xx 5] + 4/5)#

#x + 3/4 = (25/5 + 4/5)#

#x + 3/4 = (25 + 4)/5#

#x + 3/4 = 29/5#

Next, subtract #color(red)(3/4)# from each side of the equation to isolate the #x# term while keeping the equation balanced:

#x + 3/4 - color(red)(3/4) = 29/5 - color(red)(3/4)#

#x + 0 = 29/5 - 3/4#

#x = 29/5 - 3/4#

Then, to subtract we need to put each fraction over a common denominator by multiplying each fraction by the appropriate form of #1# to solve for #x#:

#x = (4/4 xx 29/5 - (5/5 xx 3/4)#

#x = (4 xx 29)/(4 xx 5) - (5 xx 3)/(5 xx 4)#

#x = 116/20 - 15/20#

#x = 101/20#

Now, if necessary, we can convert the improper fraction into a mixed number:

#x = (100 + 1)/20#

#x = 100/20 + 1/20#

#x = 5 + 1/20#

#x = 5 1/20#

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