Ian at 09:21, 22 September 2008

Ian — Mon, 22 Sep 2008 09:21:37 GMT

←Older revision		Revision as of 09:21, 22 September 2008
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-	{{~~NAVCONTENT_START~~}}	+	It is quite easy to see that
-	<~~center~~> ~~[[Image:1_1_5c-~~1(2).~~gif]]~~ </~~center~~>	+
-	<~~center~~> ~~[[Image~~:~~1_1_5c-~~2(2).~~gif]]~~ </~~center~~>	+
-	{{~~NAVCONTENT_STOP~~}}	+	<math>\begin{align}
		+	& \frac{1}{2}=0.5 \\
		+	& \\
		+	& \frac{2}{3}=2\centerdot \frac{1}{3}=0.666... \\
		+	& \\
		+	& \frac{3}{5}=3\centerdot \frac{1}{5}=3\centerdot 0.2=0.6 \\
		+	\end{align}</math>
		+
		+	<math></math>
		+
		+
		+	which means that
		+
		+
		+	<math>{1}/{2<{3}/{5<{2}/{3}\;}\;}\;</math> .
		+
		+	Because it is more difficult to evaluate the decimal expansion of
		+	<math>{5}/{8}\;</math>
		+	and
		+	<math>{21}/{34}\;</math>, we compare instead
		+	<math>{5}/{8}\;</math>
		+	and
		+	<math>{21}/{34}\;</math>
		+	with
		+	<math>{1}/{2,\ \ {3}/{5}\;}\;</math> and
		+	<math>{2}/{3}\;</math>
		+	by rewriting the fractions so that they have a common denominator. We start by comparing
		+	<math>{5}/{8}\;</math>
		+	with
		+	<math>{1}/{2,\ \ {3}/{5}\;}\;</math>
		+	and
		+	<math>{2}/{3}\;</math>
		+
		+
		+	* We have
		+	<math>\frac{1}{2}=\frac{1\centerdot 4}{2\centerdot 4}=\frac{4}{8}</math>
		+	and thus
		+	<math>\frac{1}{2}<\frac{5}{8}</math>
		+	.
		+
		+	* Then, we have
		+	<math>\frac{3}{5}=\frac{3\centerdot 8}{5\centerdot 8}=\frac{24}{40}</math>
		+	and
		+	<math>\frac{5}{8}=\frac{5\centerdot 5}{8\centerdot 5}=\frac{25}{40}</math>
		+	, which gives that
		+	<math>\frac{3}{5}<\frac{5}{8}</math>.
		+
		+	* Finally,
		+	<math>\frac{2}{3}=\frac{2\centerdot 8}{3\centerdot 8}=\frac{16}{24}</math>
		+	and
		+	<math>\frac{5}{8}=\frac{5\centerdot 3}{8\centerdot 3}=\frac{15}{24}</math>, and this gives that
		+	<math>\frac{5}{8}<\frac{2}{3}</math>.
		+
		+	Thus,
		+	<math>{1}/{2}\;<{3}/{5}\;<{5}/{8}\;<{2}/{3}\;</math>.
		+
		+	When we compare
		+	<math>{21}/{34}\;</math>
		+	with
		+	<math>{1}/{2,\ \ {3}/{5}\;}\;</math>
		+	and
		+	<math>{2}/{3}\;</math>, we obtain:
		+
		+	* because
		+	<math>\frac{1}{2}=\frac{1\centerdot 17}{2\centerdot 17}=\frac{17}{34}</math>, so
		+	<math>\frac{1}{2}<\frac{21}{34}</math>
		+
		+
		+	* furthermore,
		+	<math>\frac{3}{5}=\frac{3\centerdot 34}{5\centerdot 34}=\frac{102}{170}</math>
		+	and
		+	<math>\frac{21}{34}=\frac{21\centerdot 5}{34\centerdot 5}=\frac{105}{170}</math>, i.e.
		+	<math>\frac{3}{5}<\frac{21}{34}</math>.
		+
		+	* we have
		+	<math>\frac{5}{8}=\frac{5\centerdot 17}{8\centerdot 17}=\frac{85}{136}</math>
		+	and
		+	<math>\frac{21}{34}=\frac{21\centerdot 4}{34\centerdot 4}=\frac{84}{136}</math>, which gives that
		+	<math>\frac{21}{34}<\frac{5}{8}</math>.
		+
		+	The answer is
		+	<math>{1}/{2}\;<{3}/{5}\;<{21}/{34}\;<{5}/{8}\;<{2}/{3}\;</math>.

Tekbot: Lösning 1.1:5c moved to Solution 1.1:5c: Robot: moved page

Tekbot — Tue, 09 Sep 2008 08:11:43 GMT

Lösning 1.1:5c moved to Solution 1.1:5c: Robot: moved page

←Older revision

Revision as of 08:11, 9 September 2008

Tekbot: Robot: Automated text replacement (-[[Bild: +[[Image:)

Tekbot — Thu, 21 Aug 2008 06:20:29 GMT

Robot: Automated text replacement (-[[Bild: +[[Image:)

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Lina — Thu, 20 Mar 2008 11:20:56 GMT

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Solution 1.1:5c - Revision history

Ian at 09:21, 22 September 2008

Tekbot: Lösning 1.1:5c moved to Solution 1.1:5c: Robot: moved page

Tekbot: Robot: Automated text replacement (-[[Bild: +[[Image:)

Lina: Ny sida: {{NAVCONTENT_START}} Bild:1_1_5c-1(2).gif Bild:1_1_5c-2(2).gif {{NAVCONTENT_STOP}}