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 Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion

 December 23rd, 2015, 07:48 PM #1 Senior Member   Joined: Oct 2013 From: Far far away Posts: 429 Thanks: 18 A fraction problem The book I'm reading provides the following definition of "less than" and "equal to" for rational numbers x/y: 1) a/b < c/d IFF ad < bc 2) a/b = c/d IFF ad = bc Then it asks a question as follows: True or false? 15/(-9) > (-13)/4 To answer my question I use one of the definitions above i.e. I cross multiply: (15)(4) = 60 (-9)(-13) = 117 So according to the definition 15/(-9) < (-13)/4 since 15*4 < (-9)*(-13) But if you do division you get 15/(-9) = -1.6666... and (-13)/4 = -3.25 But -1.666...> -3.25 So 15/(-9) > (-13)/4 How come then that doing it one way results in 15/(-9) < (-13)/4 and doing it in another way results in 15/(-9) > (-13)/4? Thanks December 23rd, 2015, 08:01 PM #2 Math Team   Joined: Nov 2014 From: Australia Posts: 689 Thanks: 244 You're cross multiplying be a negative number, so the inequality sign should flip. I think the books definition of less than is only for non-negative rational numbers. Thanks from shunya December 24th, 2015, 01:21 AM   #3
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Quote:
 Originally Posted by Azzajazz You're cross multiplying be a negative number, so the inequality sign should flip. I think the books definition of less than is only for non-negative rational numbers.
As you said this a/b < c/d IFF ad < bc is true only if b > 0 and d > 0. December 24th, 2015, 02:05 AM #4 Global Moderator   Joined: Dec 2006 Posts: 20,965 Thanks: 2214 The a/b < c/d IFF ad < bc rule applies whenever bd > 0, so it applies if b and d are both negative. To apply this to 15/(-9) > (-13)/4, rewrite the right-hand side as 13/(-4). 15/(-9) > 13/(-4) if and only if 15(-4) > 13(-9), i.e., if and only if -60 > -117, so the original inequality is true. Thanks from shunya December 29th, 2015, 09:36 AM #5 Senior Member   Joined: Jan 2014 From: The backwoods of Northern Ontario Posts: 392 Thanks: 71 15/-9 = -(15/9) and -13/4 = -(13/4) Cross multiply without the negative signs: 60<117 implies 15/9 < 13/4 But with negative signs, the greater number becomes lesser. Thus: -(15/9)> -(13/4) This implies: 15/-9 > -13/4 December 29th, 2015, 09:43 AM   #6
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 Originally Posted by shunya As you said this a/b < c/d IFF ad < bc is true only if b > 0 and d > 0.
No. It is also true if both b<0 and d< 0, then a/b< c/d if ad< bc. Tags fraction, problem Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Spark Elementary Math 2 August 28th, 2014 06:19 PM dthomas86 Algebra 1 October 3rd, 2011 06:49 AM jskrzy Calculus 5 April 23rd, 2011 05:54 PM cherryperry Elementary Math 2 June 7th, 2010 02:24 PM clayson Elementary Math 1 October 4th, 2009 06:15 AM

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