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jlo4451
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Number Properties, pg.52 #14

by jlo4451 Sun Mar 17, 2013 2:44 pm

Number Properties, 3rd Edition - pg. 52 # 14

a/b has a remainder of 4
what is the smallest possible value of a+b?

I have looked at previous answers to this question in the forum, but I just don't get it. I guessed that the answer was 14.
9/5 = 1 r 4 (9+5 = 14)

The text says the answer is 9. (4+5)
I don't see how 4/5 = r 4
Is it 0 r 4 or something?
To my knowledge, this chapter doesn't mention factors equal to 0 with an integer as the remainder.
I saw the errata where the words are corrected to change the meaning of the text, but I don't even see how that text would change the original problem.
I'm just perplexed by this problem.

Any clarifications would be greatly appreciated.
Thanks!
Jen
sowjanyaangara
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Re: Number Properties, pg.52 #14

by sowjanyaangara Mon Mar 18, 2013 4:52 pm

If A/B=4(remainder), then B (divisor) must be greater than 4.here we asked for smallest possible value so B should be 5. A (dividend) could be anything 0,9,14 which satisfies the given condition,but the smallest possible value for A is 0.so adding A+B gives 5+4=9.
tommywallach
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Re: Number Properties, pg.52 #14

by tommywallach Tue Mar 19, 2013 5:15 pm

Hey Jen,

This is definitely in the book, but it is indeed quite surprising. Yes, when the quotient is zero (dividend is less than the divisor), than the original dividend is the remainder.

4/7 --> quotient of zero, remainder of 4

4/8 --> quotient of zero, remainder of 4

5/11 --> quotient of zero, remainder of 5

This is shocking to many people, but it is indeed a true math fact!

-t