SOLUTION: What are the steps to solving 5/12+7/30 ?

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Question 571228: What are the steps to solving 5/12+7/30 ?
Found 2 solutions by nerdybill, Theo:
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
5/12+7/30
determine a common denominator (60)
convert both fractions to have the same denominator:
25/60+14/60
(25+14)/60
39/60
reduce fraction:
13/20

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
5/12 + 7/30 have different denominator so they can't be added very easily, if at all.
the easiest way to add them together is to convert them to a fraction that has the same denominator.
then they can be added very easily.
since 12 doesn't divide into 30 easily, you are looking for some multiple of 12 and 30 that can be divided by both evenly.
the simplest one to find would be 12 * 30 = 360.
this may not be the least common multiple but it is definitely a common multiple and can be used if you can't find a smaller common multiple.
assuming you could not find a smaller common multiple, then you would do the following:
5/12 + 7/30 is your expression.
multiply the first term by 30/30 and multiply the second term by 12/12 to get:
5*30/12*30 + 7*12/12*30
simplify this to get:
150/360 + 84/360
add these together to get:
234/360
simplify this to get:
13/20
assuming you could find a smaller common multiple, you would obtain that by doing the following:
separate 12 into its elemental factors.
you will get 2 * 3 * 2
separate 30 into its elemental factors.
you will get:
2 * 5 * 3
if you eliminate the common factors, you will be left with 2 and 5.
2 * 30 = 60
5 * 12 = 60
the least common multiple of 12 and 30 appears to be 60.
go back to your original expression of:
5/12+ 7/30
multiply 5/12 by 5/5 and multiply 7/30 by 2/2 to get:
5*5/12*5 + 7*2/30*2 which results in:
25/60 + 14/60 which results in:
39/60 which can be reduced to 13/20
you will get the same answer either way.
you are told that you want to find the least common multiple, but you can solve the problem by any common multiple and the easiest common multiple to find is to multiply the denominators together.
in the world of manual calculations, finding the least common multiple makes sense because it makes subsequent calculations easier.
in the world of calculators, find the least common multiple is not quite as important and the only real reason for doing so would be if the numbers were so large that they couldn't be solved through use of the calculator unless they were reduced beforehand.
since you are in school, and they teach you to use the least common multiple, that's another good reason to try to find it if possible.
in this particular example, the least common multiple was 60 and it was used to get the fractions to have a common denominator.
we did, once again.
multiply 5/12 by 5/5 and multiply 7/30 by 2/2 to get:
25/60 + 14/60 which could then be added easily to get 39/60 which was then reduced to 13/20.