Expert: Sherry Wallin - 4/19/2011

Question
QUESTION: Hello:

How is the answer determined for adding these two complex fractions?

2/(2/3) + 3/(1/5)

If I divide 2 by 2/3 and divide 3 by 1/5 and add the result, will that be the solution?


Would 2/(2/3) = 3 and would 3/(1/5) = 15? Add them together the answer is 18.

I thank you for your reply.

ANSWER: Hi Kenneth, how are you doing? It's been awhile since I'e answered a question for you. I will respond for your question the way you asked and then I will show you a cool easy way, ok?

So to answer your question, yes to everything you asked, exactly, one way to do it.

Now there is a process named outer/inner that says to write each complex fraction as a fraction of fractions. What does that mean you say? Well your first complex fraction is 2/(2/3)  but the 2 is not written as a fraction so the first step is to write 2/(2/3) as a fraction over a fraction like so:

(2/1)/(2/3). Now if this fraction was written on top of each other which is hard to show hear but let me try:

 2     this is an outer number
__
 1     this is an inner number
_____
 2     this is an inner number
___
 3      this is an outer number

and you multiply the outer numbers(2*3) and put them on top and then multiply the inner numbers (1*2) and put them on the bottom gettting

(2*3)
_____  =  3 because the 2's cancel
(1*2)


You would do the same for 3/(1/5) and write it as (3/1)/(3/5) getting 15/3 = 5

If You are interested I have a cool trick for adding fractions without having to get a denominator.

Math Prof

---------- FOLLOW-UP ----------

QUESTION: Hello Sherry (Math Prof):

I want to thank you for your reply and answer and especially for your kind opening to your reply.

Did you make a slight topographical error in the following:

"You would do the same for 3/(1/5) and write it as (3/1)/(3/5) getting 15/3 = 5"

Should the (3/1)/(3/5) be (3/1)/(1/5)? You used 3/5 instead of 1/5.

Yes, what is the "cool trick for adding fractions without having to get a denominator"?

I thank you for your follow-up reply.

Answer
Hi Kenneth~

Absolutely I did make a typo, good catch :)

Ok say you want to add 2/7 + 4/11. You know your common denominator would be 77 so let's quickly do the problem the 'usual' way:
2/7 = 22/77 and 4/11 = 28/77 so 2/7 + 4/11 = (22+28)/77 = 50/77 right?

Now the method I named is whip, whip, whap and this is how you do it: a/b + c/d = (a*d+b*c)/(b*d) the a*d is a whip, the b*c is a whip, and the b*d is a whap so in our problem [(2*11) + (7*4)]/(7*11) = (22+28)/77 = 50/77

Math Prof

If you send me an email address I can send you a little video I made for both these techniques. Just send the question as private and no one else will see your email but me.