Adding & Subtracting factors

Question

I have come across this problem,... and after trying to analyze the author's answer, I can't figure out how he came up with one "break-down" of it. Before I post the answer, could someone else try it and let me know how they came up with the answer  and  perhaps the best way to approach  adding and subtracting  factors?

Many thanks.

madeinafrica · Answer

basically I would do it like this:

1/[10^9 - 1/10^10= 1/10^9x(1-1/10) 
 = 1/10^9x9/10 = 9/10^10

mnpqxyzt · Answer

D

1/a - 1/a*b = 1/a * (b-1)/b = (b-1)/(a*b) = 9/ 10^10
Here a= 10^9
 b=10

stilite · Answer

Here is the answer,... but I simply do not see where the "1" is coming from in the thrid break-down.

How is the  ( 1/10*9  x  1/10 )

all of a sudden  (  1   -  1/10 )

??

Jivana · Answer

You are factoring out the 1/10^9 from both the fractions, that's why those number become, 1 - 1/10. If you were to multiply the two fractions with the 1/10^9 number you will get your original back. Try it out.

stilite · Answer

Thank you everyone,...I see now. What I didn't understand is that the factoring was at the first stage of the full (original) equation. The answer I have **in the atachment** was throwing me off as it is not clearly laid out (in my opinion).

It looks like the author has not clearly shown the "factoring out" of the 1/10^9 in the second part...but in the third. His "second" factor of the answer should not even be there.

Adding & Subtracting factors

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