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Mathematics 13 Online
OpenStudy (anonymous):

perform the indicated operation. Express your answer in simplest form: 9/48 + 4/54

OpenStudy (anonymous):

when adding or subtracting fraction, first and foremost, make sure that the denominators are same. in this case, they are 48 and 54; not same to make them same, we use their least common multiple (LCM). now, tell me what the LCM for 48 and 54 is..

OpenStudy (anonymous):

2592?

OpenStudy (anonymous):

no, 2592 is a common fact but not the least one

OpenStudy (anonymous):

\[ 48=\underline{2}\times2\times2\times2\times\underline{3}\\ 54=\underline{2}\times\underline{3}\times3\times3\\ {\rm LCM}=2\times2\times2\times2\times3\times3\times3=? \]

OpenStudy (anonymous):

432

OpenStudy (anonymous):

yes. but also, if you notice, there is a short cut for this problem. \[ {9\over48}+{4\over54}={\cancel{3}\times3\over\cancel{3}\times16}+{\cancel{4}\over\cancel{4}\times16}\\ ={3\over16}+{1\over16}={3+1\over6}={4\over16}={4\over4\times4}=\boxed{\displaystyle{1\over4}} \]

OpenStudy (anonymous):

\[\begin{align} {9\over48}+{4\over54}&={\cancel{3}\times3\over\cancel{3}\times16}+{\cancel{4}\over\cancel{4}\times16}\\ &={3\over16}+{1\over16}&\mbox{we got common denominator!! yay!}\\&={3+1\over6}\\&={4\over16}\\&={4\over4\times4}\\&=\boxed{\displaystyle{1\over4}} \end{align}\]

OpenStudy (anonymous):

kapeesh?

OpenStudy (anonymous):

kapeesh lol thanks ! :)

OpenStudy (anonymous):

now, you want to try using the LCM of 48 and 54?

OpenStudy (anonymous):

sure

OpenStudy (anonymous):

ok, then why do you show me step by step and I guide ya

OpenStudy (anonymous):

9/48 + 4/54 = 432?

OpenStudy (anonymous):

no.

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