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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
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June 3rd, 2015, 06:40 PM   #2
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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.
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June 3rd, 2015, 07:05 PM   #3
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Quote:
Originally Posted by matisolla View Post
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?
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June 4th, 2015, 07:44 AM   #4
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Quote:
Originally Posted by Monox D. I-Fly View Post
$\displaystyle \frac{5}{12}<\frac{p}{q}<\frac{3}{7}$
$\displaystyle \frac{5\times7}{12\times7}<\frac{p}{q}<\frac{3 \times12}{7\times12}$
$\displaystyle \frac{35}{84}<\frac{p}{q}<\frac{36}{84}$
$\displaystyle \frac{35\times2}{84\times2}<\frac{p}{q}<\frac{36 \times2}{84\times2}$
$\displaystyle \frac{70}{168}<\frac{p}{q}<\frac{72}{168}$
Can you continue?

Thanx but no, i cant. I dont understand why you follow that procedure. Could you explain it to me? Thanx!
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June 4th, 2015, 08:11 AM   #5
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It's just like v8archie said:
Quote:
Originally Posted by v8archie View Post
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.
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June 4th, 2015, 05:59 PM   #6
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(1)

$\displaystyle s+t=5p-2q\quad[1]$

$\displaystyle s-t=19p-8q\quad[2]$

$\displaystyle 4\cdot[1]-[2]\Rightarrow p=3s+5t$

$\displaystyle 19\cdot[1]-5\cdot[2]\Rightarrow q=7s+12t$

(2)

$\displaystyle \frac pq=\frac{3s+5t}{7s+12t}\Rightarrow\min(q)=19$
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