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Digits and Decimals

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blawrence08
 Post subject: Digits and Decimals
 Post Posted: Thu Jan 06, 2011 11:54 am 
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Course Students


Posts: 3
If I multiply an a numerator and denominator of a division problem by 10/10 to eliminate decimals, do I also have to divide the answer by 10 to get the correct answer?

Thanks,

Betty
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emailnaik
 Post subject: Re: Digits and Decimals
 Post Posted: Thu Jan 06, 2011 1:47 pm 
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Students


Posts: 7
Your querry can be beter explained by the problem given below:

Q. 9.2 is the same as:
i. 92/10
ii. 46/5
iii. 184/20

A. only i
B. only iii
C. i, ii & iii
D. ii & iii
E. None of the above

Ans: 'C'

9.2 can be expressed as 92/10 (multiplying both numerator and denominator by 10)

92/10 = 2*46/2*5 = 46/5 (the common factor '2' cancels out)

92/10 can be expressed as 184/120 which is equal to 92*2/10*2

All that I am trying to say by the above self-created problem is that the correct answer depends upon the answer choices.

Points to remember:
i. 2 = 2/1
ii. 2*(10/10) = 20/10 (if you again divide 20/10 by 10 it is incorrect. Since (20/10)/10 = (20/10)*(1/10) = 20/100 = 0.2 which is not equal to 2. This goes against a basic maths rule.

I hope I answered your query. If not let me know.
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blawrence08
 Post subject: Re: Digits and Decimals
 Post Posted: Thu Jan 06, 2011 5:30 pm 
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Course Students


Posts: 3
blawrence08 wrote:
If I multiply an a numerator and denominator of a division problem by 10/10 to eliminate decimals, do I also have to divide the answer by 10 to get the correct answer?

Thanks,

Betty



I'm not sure if my question is clear. Let's say you have a division problem where the numerator has decimals and is divided by a denominator that is an integer. To save time, I wouldn't actually do the arithmetic as is. I would multiple the numerator and denominator by 10/10 to eliminate decimals. It would be faster doing the arithmetic using whole numbers. If the answer is 1.2, I would need to divide the answer by 10 to get 0.12 as the final answer. Since I multiplied the the numerator and denominator by 10/10 or 1, why do I need to divide by 10 again?

Thanks!
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emailnaik
 Post subject: Re: Digits and Decimals
 Post Posted: Sat Jan 08, 2011 3:49 am 
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Students


Posts: 7
1.2/5 can be expressed as:
= 12/50 (multiplying by 10/10)
= 2*6/2*25
= 6/25 (Canceling out the common factor 2)
= 1.2*5/5*5
= 1.2/5 (Canceling out the common factor 5)
= 0.24

A fraction whose denominator equals 1 is an integer.

All integers can be expressed as a fraction but all fractions cannot be expressed as an integer.

Refer the Manhattan Foundations Math Supplement for more information; else you can visit: http://mathforum.org/dr.math/faq/faq.integers.html
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jnelson0612
 Post subject: Re: Digits and Decimals
 Post Posted: Sun Jan 09, 2011 3:02 pm 
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ManhattanGMAT Staff


Posts: 1857
blawrence08 wrote:
blawrence08 wrote:
If I multiply an a numerator and denominator of a division problem by 10/10 to eliminate decimals, do I also have to divide the answer by 10 to get the correct answer?

Thanks,

Betty



I'm not sure if my question is clear. Let's say you have a division problem where the numerator has decimals and is divided by a denominator that is an integer. To save time, I wouldn't actually do the arithmetic as is. I would multiple the numerator and denominator by 10/10 to eliminate decimals. It would be faster doing the arithmetic using whole numbers. If the answer is 1.2, I would need to divide the answer by 10 to get 0.12 as the final answer. Since I multiplied the the numerator and denominator by 10/10 or 1, why do I need to divide by 10 again?

Thanks!


Betty,
You do not have to divide by 10 again. When I multiply a numerator and denominator BOTH by 10, or 10/10, I am multiplying by 1. Multiplying by 1 will not change the value of the original number.

For example, .5/.1 = 5. If I multiply the top and bottom by 10, I then have 5/1 = 5. Notice I obtain the same answer either way.

_________________
Jamie Nelson
ManhattanGMAT Instructor
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