Question 114218: The reciprocal of 4 plus the reciprocal of 5 is the reciprocal of what number? I am having such a hard time with this one I don't know why but I just can't get it!!
Found 2 solutions by stanbon, jgr45:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The reciprocal of 4 plus the reciprocal of 5 is the reciprocal of what number?
-----------------
(1/4) + (1/5) = (5+4)/20 = 9/20,
which is the reciprocal of 20/9
====================
Cheers,
Stan H.
Answer by jgr45(31)  (Show Source):
You can put this solution on YOUR website! The reciprocal of a number is what you multiply it by to get 1. So the reciprocal of 4 is  because x 4 equals 1. Similarly, the reciprocal of 5 is  because x 5 equals 1.
So this becomes an addition of fractions: + .
Here's a little shortcut I saw on educational television one day: Contrary to what we've been taught in school all these years, you do not need a common denominator to add fractions; there is a much easier way: Take the cross-products and add them and put that over the product of the denominators, and reduce if possible. For example,  +  = 3x5 + 8x2 over 8x5, or 15+16 over 40, or  (no further reduction is possible). Try it and see for yourself; this is the same answer you will get if you want to labor through the common denominator process.
If the numerators are both 1, as in your problem, the shortcut is even easier because now you're multiplying by 1 in each cross-product. So the answer here is simply the sum of the denominators over product of the denominators,  .
Now your problem is asking for the reciprocal of this number, . What number times = 1? Well, you simply turn the fraction upside down:  , because x =  which is 1. So your answer is , or 2 . :)
|
|
|
