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Algebra with fractions

I have to find out what n equals for the equation below:
12n+13n=7\frac{1}{2n}+\frac{1}{3n}=7
I'm confused on how I start off. This is mainly because of n being the the denominator. :confused:
Think about what would happen if you were to multiply both sides by something?
Reply 2
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krisshP
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14
Do you mean by 6n as it's the LCM of 3n and 2n? or by just 6?
Reply 3
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books28
Original post by krisshP
I have to find out what n equals for the equation below:
12n+13n=7\frac{1}{2n}+\frac{1}{3n}=7
I'm confused on how I start off. This is mainly because of n being the the denominator. :confused:


You need to put it all over a common denominator e.g. 6n like you suggested :smile: it can't just be six a 'n' is also a common factor between the two. LCM is exactly right :wink:
Reply 4
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krisshP
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14
Original post by books28
You need to put it all over a common denominator e.g. 6n like you suggested :smile: it can't just be six a 'n' is also a common factor between the two. LCM is exactly right :wink:

Okay. I understand why I have to make 6n be the denominator. But how do I do that. The fact that the 2n and 3n are the denominators puts me off and makes it all hard for me.
12n=36n\frac{1}{2n}=\frac{3}{6n}

Does that help?
Sophie's suggestion is easier by the way!
Reply 7
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krisshP
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14
I think I worked it out but I'm not sure:
12n+13n=7\frac{1}{2n}+\frac{1}{3n}=7
I multiply both sides by 3n, giving the following:
3n2n+1=21n\frac{3n}{2n}+1=21n
I minus 1 from both sides to give the following:
3n2n=21n−1\frac{3n}{2n}=21n-1
the Ns on the faction cancel out to give:
32=21n−1\frac{3}{2}=21n-1
This causes in a different form:
1.5=21n−11.5=21n-1
Adding 1 to both sides provides:
2.5=21n2.5=21n
Then dividing both sides by 21 to get n on its own gives:
0.11904761904761904761904761904762=n0.11904761904761904761904761904762 = n

Is this a right method or not?
1/2n+1/3n=7
1/2*1/n+1/3*1/n=7
(1/2+1/3)*1/n=7
You finish it off.
(edited 12 years ago)
Original post by krisshP
Then dividing both sides by 21 to get n on its own gives:
0.11904761904761904761904761904762=n0.11904761904761904761904761904762 = n

Is this a right method or not?


Yes but horribly long winded. Can you use fractions rather than decimals?

Easier would be just to multiply by 6n.
Reply 10
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krisshP
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14
so answer is 2.5/212.5/21
Thanks! :smile::smile::smile:
Original post by krisshP
so answer is 2.5/212.5/21
Thanks! :smile::smile::smile:


Have you ever seen a fraction that looks like that?
Original post by krisshP
so answer is 2.5/212.5/21
Thanks! :smile::smile::smile:


It's 5/42.
Reply 13
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krisshP
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14
I know. sorry. My clumsy mistake

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