SOLUTION: I am really struggling in math and the book is helping alot because it explanes everything with examples and the problem i am trying to do has no example in the book i am hopeing y

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Question 7402: I am really struggling in math and the book is helping alot because it explanes everything with examples and the problem i am trying to do has no example in the book i am hopeing you can help me solve it or will show me a good example.
#110. Find the reciprocal of the number.
-12.1/-0.11
All other questions have fractions but this one dosent.
thank you - Amy
Found 3 solutions by bonster, MathTherapy, KMST:
Answer by bonster(299) About Me  (Show Source):
You can put this solution on YOUR website!
When faced with a problem with decimals, put it in fraction form:

-12.1/-0.11

-121%2F10 / -11%2F100

121%2F10/-11%2F100

At this point, you can change the problem from a division to a multiplication problem by using the reciprocal of -11%2F100 which is -100%2F11
121%2F10*-100%2F11

simplify
(11)(-10)
=-110

Answer by MathTherapy(10858) About Me  (Show Source):
You can put this solution on YOUR website!
I am really struggling in math and the book is helping alot because it explanes everything with examples and the problem i am trying
to do has no example in the book i am hopeing you can help me solve it or will show me a good example. 

#110. Find the reciprocal of the number. 

-12.1/-0.11 

All other questions have fractions but this one dosent. 
thank you - Amy 
***************
The following by the other person is WRONG!! "(11)(-10)=-110"

Plus, converting the decimals to fractions to get to the answer is, in this author's opinion, OVERKILL!

The reciprocal of a number, when expressed as a fraction, is obtained by SWITCHING the numerator and the denominator. In other words, the
denominator and the numerator of the original fraction become the NEW numerator and NEW denominator, respectively, of the reciprocal.

I don't know why you say this, "All other questions have fractions but this one dosent....", because -12.1/-0.11 is a FRACTION!

So, the RECIPROCAL of %28-+12.1%29%2F%28-+0.11%29 is merely %28-+0.11%29%2F%28-+12.1%29 = 0.11%2F12.1 = 1.1%2F121 = highlight%280.1%2F11%29, or 1%2F10 รท 11%2F1 = %281%2F10%29+%2A+%281%2F11%29 = highlight%281%2F110%29

Answer by KMST(5396) About Me  (Show Source):
You can put this solution on YOUR website!
I can see 11%5E2=121 in the number, so it's mental math for me.
If it was an SAT question, I could pick give the answer in seconds, but I can explain my reasoning in minutes as follows:
The number is
The reciprocal of 110 is highlight%281%2F110%29