Solution 1.2:3b - Revision history

Tek at 08:42, 19 September 2008

2008-09-19T08:42:59Z

←Older revision		Revision as of 08:42, 19 September 2008
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-	If we divide the denominators in succession by	+	If we divide the denominators in succession by 2, we see that
-	~~<math>~~2~~</math>~~	+
-	, we see that	+

		+	{{Displayed math\|\|<math>\begin{align}
		+	24&=2\cdot 2\cdot 2\cdot 3\,,\\
		+	40&=2\cdot 2\cdot 2\cdot 5\,,\\
		+	16&=2\cdot 2\cdot 2\cdot 2\,,\\
		+	\end{align}</math>}}

-	<math>~~\begin{align}~~	+	i.e. they all have a factor <math>2\cdot 2\cdot 2=8</math> in common,
-	~~& 24=~~2\~~centerdot~~ 2\~~centerdot~~ 2~~\centerdot 3 \\~~	+
-	~~& 40~~=~~2\centerdot 2\centerdot \centerdot 5 \\~~	+
-	~~& 16=2\centerdot 2\centerdot 2\centerdot 2 \\~~	+
-	~~\end{align}~~</math>	+

		+	{{Displayed math\|\|<math>\frac{1}{3\cdot 8}+\frac{1}{5\cdot 8}-\frac{1}{2\cdot 8}\,</math>.}}

-	~~i.e. they all have~~ a factor	+	Hence we do not need to take 8 as a factor when we multiply the top and bottom of each fraction by the product of the other fractions' denominators, but instead we
-	~~<math>~~2~~\centerdot 2\centerdot 2=8</math>~~	+	obtain the lowest common denominator by multiplying top and bottom by the other factors, 2, 3 and 5,
-	~~in common~~,	+

		+	{{Displayed math\|\|<math>\frac{1\cdot 2\cdot 5}{3\cdot 8\cdot 2\cdot 5}+\frac{1\cdot 2\cdot 3}{5\cdot 8\cdot 2\cdot 3}-\frac{1\cdot 3\cdot 5}{2\cdot 8\cdot 3\cdot 5}=\frac{10}{240}+\frac{6}{240}-\frac{15}{240}\,</math>.}}

		+	The LCD is 240 and the answer is

-	~~<math>\frac~~{1}{~~3\centerdot 8}+\frac{1}{5\centerdot 8}-\frac{1}{2\centerdot 8}</~~math>	+	{{Displayed math\|\|<math>\frac{10}{240}+\frac{6}{240}-\frac{15}{240}=\frac{10+6-15}{240}=\frac{1}{240}\,</math>.}}
-	,	+
-		+
-	~~and hence we do not need to take~~	+
-	~~<math>8</math>~~	+
-	~~as a factor when we multiply the top and bottom of each fraction by the product of the other fractions' denominators, but instead we~~	+
-	~~obtain the lowest common denominator by multiplying top and bottom by the other factors,~~	+
-	~~<math>2,\ 3</math>~~	+
-	~~and~~	+
-	~~<math>5</math>~~	+
-	:	+
-		+
-		+
-	<math>\frac{1\centerdot 2\centerdot 5}{3\centerdot 8\centerdot 2\centerdot 5}+\frac{1\centerdot 2\centerdot 3}{5\centerdot 8\centerdot 2\centerdot 3}-\frac{1\centerdot 3\centerdot 5}{2\centerdot 8\centerdot 3\centerdot 5}=\frac{10}{240}+\frac{6}{240}-\frac{15}{240}</math>	+
-		+
-		+
-	~~The LCD is~~	+
-	~~<math>240</math>~~	+
-	~~and the answer is~~	+
-		+
-		+
-	<math>\frac{10}{240}+\frac{6}{240}-\frac{15}{240}=\frac{10+6-15}{240}=\frac{1}{240}</math>	+

Ian at 13:10, 11 September 2008

2008-09-11T13:10:46Z

←Older revision		Revision as of 13:10, 11 September 2008
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-	{{~~NAVCONTENT_START~~}}	+	If we divide the denominators in succession by
-	<~~center~~> ~~[[Image~~:~~1_2_3b.gif]]~~ </~~center~~>	+	<math>2</math>
-	{{~~NAVCONTENT_STOP~~}}	+	, we see that
		+
		+
		+	<math>\begin{align}
		+	& 24=2\centerdot 2\centerdot 2\centerdot 3 \\
		+	& 40=2\centerdot 2\centerdot \centerdot 5 \\
		+	& 16=2\centerdot 2\centerdot 2\centerdot 2 \\
		+	\end{align}</math>
		+
		+
		+	i.e. they all have a factor
		+	<math>2\centerdot 2\centerdot 2=8</math>
		+	in common,
		+
		+
		+
		+	<math>\frac{1}{3\centerdot 8}+\frac{1}{5\centerdot 8}-\frac{1}{2\centerdot 8}</math>
		+	,
		+
		+	and hence we do not need to take
		+	<math>8</math>
		+	as a factor when we multiply the top and bottom of each fraction by the product of the other fractions' denominators, but instead we
		+	obtain the lowest common denominator by multiplying top and bottom by the other factors,
		+	<math>2,\ 3</math>
		+	and
		+	<math>5</math>
		+	:
		+
		+
		+	<math>\frac{1\centerdot 2\centerdot 5}{3\centerdot 8\centerdot 2\centerdot 5}+\frac{1\centerdot 2\centerdot 3}{5\centerdot 8\centerdot 2\centerdot 3}-\frac{1\centerdot 3\centerdot 5}{2\centerdot 8\centerdot 3\centerdot 5}=\frac{10}{240}+\frac{6}{240}-\frac{15}{240}</math>
		+
		+
		+	The LCD is
		+	<math>240</math>
		+	and the answer is
		+
		+
		+	<math>\frac{10}{240}+\frac{6}{240}-\frac{15}{240}=\frac{10+6-15}{240}=\frac{1}{240}</math>

Tekbot: Lösning 1.2:3b moved to Solution 1.2:3b: Robot: moved page

2008-09-09T08:18:03Z

Lösning 1.2:3b moved to Solution 1.2:3b: Robot: moved page

←Older revision

Revision as of 08:18, 9 September 2008

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

2008-08-21T06:26:09Z

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

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2008-03-26T10:00:51Z

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