Nested fractions

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Ned Radenovic

September 09, 2014 15:23

I have been doing some of the nested fractions and am having trouble adding these types of fractions when the denominator is the same. If they are different I am OK. For example

1/3 + 3/5y = 5y/15y + 9/15y

But when the denominator is the same there is some short cut in the answers I am not following. For example:

1/3 + 1/3y - the first step in the hints is that 1/3 is changed to y/3y but it doesn't go into detail on how to do it. The only common thing that I can find is the denominators are the same.

Another example:

1/z + 3/2z again the first step in the hint is to change 1/z into 2/2z but I don't understand how they make this leap.

Why can't I do this type of question like I do 1/3 + 3/5y ?

multiply the denominator to get the least common and then change the numerators by the same amount

for example

1/z + 3/2z = 2z/2z^2 + 3z/2z^2

Help! Totally confused and didn't see any explanations in the videos.

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Permanently deleted user

September 09, 2014 18:08
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Hi!

The process is actually the same as what you used for 1/3 + 3/5y. For your example, you found that the common denominator was 15y...and so then multiplied the first fraction by 5y/5y to get 5y/15y.

Next, let's do the same with your second example of 1/3 + 1/3y. The denominators are not exactly the same...one has a y in it, the other doesn't. And so, you want to find the lowest common denominator. The lowest common denominator is 3y. And so, you want to multiply 1/3 by y/y to get y/3y. You now have y/3y + 1/3y. The denominators are now exactly the same...and so you can add.

One thing to keep in mind is that you want to find the LOWEST common denominator. In your last example of 1/z + 3/2z, you found that 2z^2 was a common denominator. It is a common denominator, but it isn't the lowest one. 2z is the lowest common denominator. And so....you want to multiply 1/z by 2/2 to get 2/2z.

You can think of the lowest common denominator as being the lowest common multiple of the denominators. Hope that helps!

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