Question 476760: Can you please tell me if the following is correct: 3/12 + 3/4x = 3x/12x + 9/12x =
(3x + 9)/12x I'm not sure if I'm supposed to reduce 3x/12x to 1x/4x
Thanks
l68m@live.com
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! you want to add 3/12 and 3/4x.
you need to multiply the first fraction by 4x/4x to get:
3/12 = 12x/48x
you need to multiply the second fraction by 12/12 to get:
36/48x
now you can add them together to get:
(12x + 36)/48x
this can be reduced to:
(1x+3)/4x
the final expression is:
(x+3)/4x
the original expression is:
(3/12) + (3/4x)
take any value for x and solve it using the original expression and then solve it using the final expression and the answer should be the same.
for example:
let x = 15
the original expression yields .3
the final expression yields .3
you get the same answer which means the expressions are equivalent.
looking at what you did, i see the following:
3/12 + 3/4x = 3x/12x + 9/12x looks wrong.
in order for the denominators to be the same, they have to be a combination of 12 and 4x.
12 * 4x = 48x.
that would be a common denominator.
if you multiply the first fraction by 4x/4x, then you will get:
(3/12)( * (4x/4x) = 12x/48x
if you multiply the second fraction by 12/12, then you will get:
(12/12) * (3/4x) = (36/48x)
now you have a common denominator and you can add them together.
you get:
(12x/48x) + (36/48x) which can be combined under one denominator to become:
(12x + 36)/48x
this can be reduced by multiplying the fraction by (1/12)/1/12) to get:
(12x + 36)/48x * (1/12)/(1/12) becomes:
(x+3)/4x
your problem was in finding what the common denominator was.
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