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June 3rd, 2015, 06:03 PM   #1
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Fraction inequality (hard)

Hi, can someone help me with this problem? I have nooo clue Attached Images fraction inequality.jpg (21.3 KB, 26 views) June 3rd, 2015, 06:40 PM #2 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,674 Thanks: 2654 Math Focus: Mainly analysis and algebra Part 1) is a system of two simultaneous equations. For part 2) you should start by expressing the two fractions using a common denominator, then work out how you might get a fraction with a value between the two. Thanks from matisolla June 3rd, 2015, 07:05 PM   #3
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Quote:
 Originally Posted by matisolla Hi, can someone help me with this problem? I have nooo clue $\displaystyle \frac{5}{12}<\frac{p}{q}<\frac{3}{7}$
$\displaystyle \frac{5\times7}{12\times7}<\frac{p}{q}<\frac{3 \times12}{7\times12}$
$\displaystyle \frac{35}{84}<\frac{p}{q}<\frac{36}{84}$
$\displaystyle \frac{35\times2}{84\times2}<\frac{p}{q}<\frac{36 \times2}{84\times2}$
$\displaystyle \frac{70}{168}<\frac{p}{q}<\frac{72}{168}$
Can you continue? June 4th, 2015, 07:44 AM   #4
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Quote:
 Originally Posted by Monox D. I-Fly $\displaystyle \frac{5}{12}<\frac{p}{q}<\frac{3}{7}$ $\displaystyle \frac{5\times7}{12\times7}<\frac{p}{q}<\frac{3 \times12}{7\times12}$ $\displaystyle \frac{35}{84}<\frac{p}{q}<\frac{36}{84}$ $\displaystyle \frac{35\times2}{84\times2}<\frac{p}{q}<\frac{36 \times2}{84\times2}$ $\displaystyle \frac{70}{168}<\frac{p}{q}<\frac{72}{168}$ Can you continue?

Thanx but no, i cant. I dont understand why you follow that procedure. Could you explain it to me? Thanx! June 4th, 2015, 08:11 AM   #5
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It's just like v8archie said:
Quote:
 Originally Posted by v8archie you should start by expressing the two fractions using a common denominator, then work out how you might get a fraction with a value between the two. June 4th, 2015, 05:59 PM #6 Global Moderator   Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,958 Thanks: 1146 Math Focus: Elementary mathematics and beyond (1) $\displaystyle s+t=5p-2q\quad$ $\displaystyle s-t=19p-8q\quad$ $\displaystyle 4\cdot-\Rightarrow p=3s+5t$ $\displaystyle 19\cdot-5\cdot\Rightarrow q=7s+12t$ (2) $\displaystyle \frac pq=\frac{3s+5t}{7s+12t}\Rightarrow\min(q)=19$ Thanks from Hoempa and matisolla Tags fraction, hard, inequality 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 yo79 Math Events 1 January 15th, 2013 01:10 AM henry12345 Trigonometry 2 July 7th, 2012 02:44 AM sharp Elementary Math 9 September 25th, 2010 10:31 PM ime Algebra 0 August 23rd, 2009 02:37 AM caugust Applied Math 0 February 23rd, 2007 06:39 PM

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