thumbnail of The Power of Algebra; No. 009; Fractions
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<v Watson>[music playing] [water rushing] Oh by George, Holmes. What a romantic sight. <v Watson>Niagara Falls by moonlight. <v Holmes>Yes, indeed, quite breathtaking. <v Watson>Well what the ?deuce? is that? <v Holmes>Just some ducks quacking Watson. Relax and enjoy the view. <v Watson>Uh yes, but I say, isn't it a bit too dangerous standing right on the edge of the falls <v Watson>in the middle of the night? I mean, what if Moriarty- <v Holmes>Don't worry about that bird brain, Watson. <v Holmes>I'm much too clever to fall for any of his tricks. <v Moriarty>[boat engine whirring] [laughing] Those two flat foots are going to fall a lot further <v Moriarty>than they think. [music plays] <v Watson>?inaudible?. Oh, oh, oh good grief! <v Watson>It's Moriarty. <v Moriarty>I knew I'd triumph in the end. <v Moriarty>If you two are so fond of Niagara Falls, now's your chance to get a really good <v Moriarty>close up view! <v Holmes>But you can't push us over the falls just like that. <v Holmes>It's it's simply not cricket. <v Watson>No, it's just not done, old chap. <v Moriarty>Isn't it? Well, how should I push you over then?
<v Moriarty>[music playing] <v Holmes>In a barrel, of course. That's the proper way. <v Moriarty>Oh, good idea. Oh what am I saying! <v Moriarty>I left my barrel 40 kilometers upstream. <v Moriarty>Oh I know! I'll tie you two up against this tree, then I'll canoe up the <v Moriarty>river to fetch the barrel. After all, there's plenty of time. <v Moriarty>I've got all night. <v Holmes>I wouldn't be so sure Moriarty. The current in this river runs at 6 <v Holmes>kilometers per hour. It's now just about midnight and the park ranger comes <v Holmes>on duty shortly after 5 A.M. so he'll rescue us before you can get back. <v Moriarty>Curses. Could Holmes be right? Let me see. <v Moriarty>I have 5 hours to go 40 kilometers against the current and 40 kilometers <v Moriarty>with the current. So how fast must I go? <v Moriarty>Ah... ah yes, I must average 8 kilometers an hour <v Moriarty>over the whole trip. But that's exactly the speed of my motorized canoe! <v Moriarty>[laughs] I'll be back before the park ranger <v Moriarty>gets here. No problem.
<v Moriarty>Then you two will really be for the high jump. <v Moriarty>[water rushing] [laughter] <v Watson>Are you quite sure Moriarty can't make it back in 5 hours Holmes? <v Holmes>Absolutely certain. Instead it'll take him nearly 23 hours to do the roundtrip. <v Watson>You're certain? <v Holmes>Yes. In fact, and, here comes the clue Watson, I'll bet you a <v Holmes>bill [water rushing] of any denomination that I'm right. <v Man 1>Welcome to the 9th program in the Power of Algebra series. <v Man 1>[music playing] In the previous program, we continue the exploration of factoring <v Man 1>and saw how what appears to be a quite complicated equation can <v Man 1>be simplified by looking for the common factor, which in this case is 4. <v Man 1>In this program, we're going to see how to simplify algebraic expressions that involve <v Man 1>fractions. Algebraic fractions are no more difficult to do than any other <v Man 1>fractions. Exactly the same rules apply whether you're talking about three eighths
<v Man 1>or X over Y. <v Man 1>You still have a numerator on top and a denominator on the bottom. <v Man 1>But beware of unknowns in the denominator. <v Man 1>You can't divide by zero. <v Man 1>You can reduce a more complicated looking arithmetic fraction to its lowest terms <v Man 1>by looking for the factor common to the numerator and the denominator. <v Man 1>Here it's 7. <v Man 1>When you have a more complicated looking algebraic fraction, you can use the same <v Man 1>technique. In this case, the common factors are 3, X, <v Man 1>and Y. So the fraction can be reduced to 2 X over 3. <v Man 1>Here's one that looks even trickier but works in exactly the same way. <v Man 1>Only here, in order to see what the common factor is, we have to first factor <v Man 1>the top and bottom into binomials. <v Man 1>X minus 1 square becomes X minus 1 times X <v Man 1>minus 1 and X square minus 9 X plus <v Man 1>8 becomes X minus 1 times X minus 8.
<v Man 1>Now it's easy to see that the common factor is X minus 1, which allows us <v Man 1>to reduce the original fraction to something much simpler. <v Man 1>If factoring works the same way for fractions and algebra as it does for fractions and <v Man 1>arithmetic, so do all the basic operations. <v Man 1>When you multiply three eighths by five sevenths, you first multiply the two numerators <v Man 1>to get 15 and then multiply the two denominators to get 56. <v Man 1>So when you multiply A over B by C over D, <v Man 1>you first multiply A times C, then B times D to get <v Man 1>AC over BD. <v Man 1>The same goes for division. If you have to divide three eighths by five sevenths, <v Man 1>you replace the divisor, five sevenths, by its reciprocal. <v Man 1>In other words, you turn it upside down and multiply by seven fifths to get <v Man 1>twenty one fortieths. And that's exactly what you'd do in algebra. <v Man 1>If you have to divide A over B by C over D, you replace the divisor <v Man 1>by its reciprocal and multiply by D over C to get
<v Man 1>AD over BC. <v Man 1>[water flowing] [birds chirping] That's easy for multiplication and division. <v Man 1>Unfortunately, it's not quite so straightforward for addition and subtraction. <v Man 1>I need to get this straight because I've got to figure out how long it would take me to <v Man 1>fill this pool if I didn't have a fill pipe and instead I had to just do <v Man 1>it with this garden hose. [music plays] <v Orville Baker>My name is Orville Baker. I'm a technician here at WLPB. <v Orville Baker>I just received my B.S. degree in physics here at Southern University in Baton Rouge. <v Orville Baker>Algebra is important to all mathematics. <v Orville Baker>And regardless of what type of mathematics that you do, algebra is always <v Orville Baker>?inaudible? in order to get the end result you're trying to find in any mathematical <v Orville Baker>endeavor. And in physics in particularly no matter how complex the equation is, <v Orville Baker>you always have to use algebra to find the solution. <v Orville Baker>Mathematics and particularly algebra, the language of science. <v Orville Baker>In fact, it would be s-almost safe to say that any physicist that is competent
<v Orville Baker>is also a very competent mathematician. <v Orville Baker>If you 'xpect to survive in the next century, you gon' have to have a background in <v Orville Baker>mathematics. Because our technology, our job force, our job descriptions <v Orville Baker>are changing more and more to mathematically inclined understanding. <v Orville Baker>If you're going to deal with the computers, if you're going to deal even with car <v Orville Baker>manufacturing, you have to understand the difference between metric and English <v Orville Baker>system and be able to make those conversions usin' mathematics, usin' algebra. <v Orville Baker>Those will survive the next century. Those who have the jobs and those who have a better <v Orville Baker>standard living were those who have- who are not afraid to look at math <v Orville Baker>and tackle it. <v Man 1>[water rushing] [music playing] I said that adding and subtracting algebraic fractions <v Man 1>isn't quite as straightforward as multiplying and dividing them. <v Man 1>The big difference is that when you're multiplying any fractions, you can multiply both <v Man 1>the numerators and the denominators. <v Man 1>When it comes to addition, you can only add the numerators if both of the denominators <v Man 1>are the same. In other words, you can only add fractions if they have a common
<v Man 1>denominator. Here's a very simple example. <v Man 1>Add two ninths and five ninths. <v Man 1>You add the numerators and keep the same denominator to get two plus five over <v Man 1>nine or seven ninths. <v Man 1>It's the same when adding algebraic fractions. <v Man 1>When you add A over C and B over C, you get A plus B <v Man 1>over C. <v Man 1>The identical process takes place with subtraction. <v Man 1>[birds chirping] But you can only do that if the two fractions that you're adding or <v Man 1>subtracting have got a common denominator. <v Man 1>What if they don't? What if you're faced with adding, say, oh, three sevenths and two <v Man 1>fifths? How do you take those two different denominators and turn them into a common <v Man 1>denominator? Well, we look for the least common denominator, the smallest <v Man 1>multiple of 7 and 5, which is 35. <v Man 1>And to change these two denominators into 35, we multiply both terms in the first <v Man 1>fraction by 5 and both terms and the second fraction by 7, which gives us <v Man 1>15 35ths plus 14 35ths.
<v Man 1>Now we can add these fractions to get 29 35ths. <v Man 1>We use precisely the same technique to add algebraic fractions with unlike denominators. <v Man 1>Hmm as here, the least common denominator, LCD, in <v Man 1>this case is 12 X. To change the two unlike denominators into <v Man 1>12 X, we multiply both terms in the first fraction by 4 <v Man 1>and both terms in the second fraction by 3, which gives us 20 <v Man 1>over 12 X plus 27 over 12 X. <v Man 1>Then we add the two fractions to give us 47 over 12 X. <v Man 1>[water rushing] So once you understand how the least common denominator process works for <v Man 1>adding and subtracting fractions and arithmetic, you'll also know how it works in <v Man 1>algebra. Which brings me back to the swimming pool problem. <v Man 1>How long would it take to fill this pool if I didn't have that fill pipe? <v Man 1>[bubbles popping] And instead I had to do it with just a garden hose. <v Man 1>Well, with the fill pipe running alone, takes it 5
<v Man 1>hours to fill the pool. With both the fill pipe and the hose running, it only takes <v Man 1>3 hours. So I take the formula for a rate of work, which is rate quals <v Man 1>work divided by time. <v Man 1>Now the work to be done is to fill one pool. <v Man 1>So work equals one. <v Man 1>And since the fill pipe takes 5 hours to fill the pool, we can say that its rate is <v Man 1>1 over 5. But since the hose's rate is unknown, we can only <v Man 1>say it's one over X hours. <v Man 1>In other words, the total rate is 1 over 5 plus 1 <v Man 1>over X. And since this combined rate fills the pool in 3 hours, <v Man 1>our time here is 3. <v Man 1>Now, if we rearrange all this into the equation for work, which is work equals <v Man 1>rate multiplied by time we get this. <v Man 1>And if we multiply that out, we get 1 equals 3 over 5 plus 3 <v Man 1>over X. The least common denominator here is 5 X. <v Man 1>Since we're working with an equation, we keep it balanced by multiplying both sides
<v Man 1>by 5 X and we end up with 5 X equals 3 X <v Man 1>plus 15 or 2 X equals 15 or <v Man 1>X equals 7.5. <v Man 1>[water running] So, I've been able to figure out that should this fill up ever be out of <v Man 1>action [bubbles popping], I'll be able to fill the pool with this garden <v Man 1>hose in 7 and a half hours. <v Man 1>All thanks to knowing about the least common denominator. <v Man 1>Holmes and Watson should thank their lucky stars that Moriarity didn't have access to the <v Man 1>same information. <v Watson>[music playing] I wish we knew the time Holmes, but I can't get my pocket watch. <v Holmes>Look at the sun man, it's just coming over the horizon. <v Holmes>[water rushing] The sun rises just after 5:00 A.M. <v Holmes>today. <v Watson>And still no sign of Moriarty. <v Holmes>They're right on cue, here comes the park ranger to set us free! <v Holmes>[grunts] Thank you, Ranger. <v Holmes>Now we can take a leisurely stroll along the river. <v Holmes>Moriarty won't make it back until just before 11 o'clock tonight.
<v Watson>Oh what an ?intellect?! But what was the clue this time? <v Watson>Eh something to do with uh denomination? <v Holmes>Least common denominator. <v Holmes>Do I have to spell everything out for you? <v Watson>Well ?inaudible? [sighs] But what exactly did Moriarty do wrong? <v Watson>[music plays] <v Holmes>Well what did he want to calculate? <v Watson>How fast his canoe should go to get from the top of the falls, eh point <v Watson>A uh 40 kilometers upstream to <v Watson>where his barrel was at point B. <v Watson>Ran back again. <v Holmes>Facing a current as he goes upstream of 6 kilometers per hour. <v Holmes>Don't forget that. <v Watson>Uh yes and having to compete the round trip between midnight and <v Watson>5 A.M., a total time of 5 hours. <v Holmes>So the equation we want here is time equals distance divided by <v Holmes>rate. <v Watson>Right. The time is 5 hours, the distance <v Watson>is 40 kilometers upstream, divided by the rate which is our unknown
<v Watson>X minus the current, which is 6 kilometers an hour, because <v Watson>the current would be going against Moriarty. <v Holmes>And then we add to that the distance downstream, which is also 40 kilometers <v Holmes>divided by X, plus the current of 6 kilometers an hour because <v Holmes>now Moriarty would have the current going with him. <v Watson>But I say, you can't add those two fractions because they have unlike denominators. <v Watson>Oh, I see it all now. We have to look for the least common denominator. <v Holmes>Which is very simple here. The smallest multiple of X minus 6 <v Holmes>and X plus 6 is X minus 6 times <v Holmes>X plus 6. <v Watson>So we multiply everything in the equation by that. <v Holmes>So the whole thing multiplies out to this. <v Holmes>And then this. And then this. <v Watson>Which we change into the standard for import a quadratic equation. <v Watson>Then simplify by factoring out the five.
<v Watson>And then factor that into two binomials. <v Holmes>Revealing that the two possible values of X are negative two, which is <v Holmes>impossible or positive 18. <v Holmes>Which tells us that the speed at which Moriarty should have gone to make the round trip <v Holmes>was 18 kilometers per hour, not 8 kilometers per hour. <v Watson>Well, then how did Moriarty arrive at that incorrect answer? <v Holmes>Because instead of looking for the least common denominator, he not only added <v Holmes>the numerators, but he also tried to add the unlike denominators. <v Holmes>Then he simplified that to get 40 over X, which gives X <v Holmes>a value of 8. <v Watson>No wonder you said the round trip would take nearly 23 hours. <v Moriarty>[geese honking] [music] Huh. Call me a bird brain, would they? I'll give them birds on the brain! <v Holmes>[geese honking] Hey! Get away you nasty things. Shoo. Shoo! Hey I say! [water splashing]
<v Man 2>In 1964, China exploded its first nuclear bomb. <v Man 2>In 1974, India followed suit. <v Man 2>Once the exclusive servant of the superpowers, the nuclear genie now had many <v Man 2>masters. Today, the anxiety and the arsenals continue to <v Man 2>grow. The politics and dangers of nuclear proliferation. <v Man 2>Next time on War and Peace in the Nuclear Age. <v Man 3>Cut 4 National Geographic, special number 1403, 30 seconds.
<v Richard Kiley>A dog's work is never done. <v Richard Kiley>I'm Richard Kiley. Join me when a new National Geographic special <v Richard Kiley>covers canines in action. <v Richard Kiley>Guiding, herding, performing, racing with their human partners. <v Richard Kiley>Don't miss those wonderful dogs. <v Richard Kiley>A new look at man's best friend. <v Man 3>Cut six. Nature number 715. <v Man 3>30 seconds. <v Man 4>When it's springtime in Antarctica, temperatures can soar to a balmy zero degrees. <v Man 4>Perfect weather for penguins to have fun. <v Man 4>Ice sliding, egg rolling and boxing are very popular. <v Man 4>So is posing with the kids for a family portrait.
<v Man 4>And of course, there's always time for romance. <v Man 4>You'd make time, too, if you only made it once a year. <v Man 4>Join us for a formal affair with the best dressed bird in town. <v Man 4>The Iceberg. Next time on nature. <v Woman 1>Cut seven core promo number 891. <v Woman 1>30 seconds. <v Man 5>[SImon and Garfunkel singing] It was the concert of the decade. <v Man 5>A legendary reunion after 11 years. <v Man 5>Two old friends singing the songs that evoked an era.
<v Man 5>Join half a million people for Simon and Garfunkel, the concert in Central <v Man 5>Park. <v Woman 1>Cut 27, the Power of Excellence with Tom Peters, the Forgotten Customer. <v Woman 1>30 seconds. <v Tom Peters>Our jobs are at stake and more significantly, in my mind, our way of <v Tom Peters>life is at stake. <v Tom Peters>We are losing economically- <v Narrator 1>[Tom still speaking] Tom Peter's Power of Excellence shocks us with remarkable examples <v Narrator 1>of service in America. <v Tom Peters>I've seen the good news examples. I know it can be done. <v Tom Peters>They include no magic, but the terror is that we're not movin' fast enough.
Series
The Power of Algebra
Episode Number
No. 009
Episode
Fractions
Producing Organization
Louisiana Public Broadcasting
Contributing Organization
Louisiana Public Broadcasting (Baton Rouge, Louisiana)
The Walter J. Brown Media Archives & Peabody Awards Collection at the University of Georgia (Athens, Georgia)
AAPB ID
cpb-aacip/17-07tmqb4p
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Description
Episode Description
This episode of the series "The Power of Algebra" from 1988 teaches students how to solve algebraic equations involving fractions. It also includes an interview with Orvall Baker of LPB, who discusses the importance of mathematics to his work as a television engineer. Host: David Stringer
Episode Description
This episode's guest is Orville Baker, a technician at WLPB television. He just received a B.S. degree in physics from Southern University in Baton Rouge. He talks about the importance of algebra for jobs of the future such as computer science.
Other Description
"THE POWER OF ALGEBRA was designed as a teaching [supplement] for Junior and Senior High School teachers to help students better comprehend the formulas and concepts of the subject. With the assistance of educators and educational production specialists, several major stumbling blocks of algebra were identified and became the focus of the series. In-house graphics are used to create robotic versions of Sherlock Holmes, Watson and Moriarty who use algebra to plot against one another and escape perilous situations. The graphics are also used by the host of the series to explain how formulas work. An additional portion of every episode goes on-location to speak with professionals utilizing algebra in their daily work. One teacher using the series, Jim Miller of Capital High School in Baton Rouge, says the students often approached the subject with the attitude, 'Why do I have to learn this'' but 'now that students can actually see real people using algebra skills everyday in their jobs, it makes a tremendous difference.'"--1989 Peabody Awards entry form.
Date
1988-00-00
Asset type
Episode
Media type
Moving Image
Embed Code
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Credits
Copyright Holder: Louisiana Educational Television Authority
Guest: Baker, Orvall
Host: Stringer, David
Producing Organization: Louisiana Public Broadcasting
AAPB Contributor Holdings
Louisiana Public Broadcasting
Identifier: C5854 (Louisiana Public Broadcasting Archives)
Format: U-matic
Generation: Master
Duration: 00:14:50
Louisiana Public Broadcasting
Identifier: H1377 (Louisiana Public Broadcasting Archives)
Format: 1 inch videotape: SMPTE Type C
Generation: Master
Duration: 00:14:50
Louisiana Public Broadcasting
Identifier: B8/4 (Louisiana Public Broadcasting Archives)
Format: Betacam: SP
Generation: Master
Duration: 00:14:50
Louisiana Public Broadcasting
Identifier: LPOWA-109-GPN (Louisiana Public Broadcasting Archives)
Format: Betacam: SP
Generation: Master
Duration: 00:15:05
Louisiana Public Broadcasting
Identifier: LPOWA-109-EM (Louisiana Public Broadcasting Archives)
Format: 1 inch videotape: SMPTE Type C
Generation: Master
Duration: 00:14:50
Louisiana Public Broadcasting
Identifier: LPOWA-109-DM (Louisiana Public Broadcasting Archives)
Format: 1 inch videotape: SMPTE Type C
Generation: Dub
Duration: 00:14:50
Louisiana Public Broadcasting
Identifier: LPOWA-109-GPN2 (Louisiana Public Broadcasting Archives)
Format: Betacam: SP
Generation: Master
Duration: 00:15:05
Louisiana Public Broadcasting
Identifier: LPOWA-A5/4 (Louisiana Public Broadcasting Archives)
Format: Betacam: SP
Generation: Master
Duration: 00:15:00
The Walter J. Brown Media Archives & Peabody Awards Collection at the University of Georgia
Identifier: 89008cyt-arch (Peabody Object Identifier)
Format: U-matic
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Citations
Chicago: “The Power of Algebra; No. 009; Fractions,” 1988-00-00, Louisiana Public Broadcasting, The Walter J. Brown Media Archives & Peabody Awards Collection at the University of Georgia, American Archive of Public Broadcasting (GBH and the Library of Congress), Boston, MA and Washington, DC, accessed June 28, 2022, http://americanarchive.org/catalog/cpb-aacip-17-07tmqb4p.
MLA: “The Power of Algebra; No. 009; Fractions.” 1988-00-00. Louisiana Public Broadcasting, The Walter J. Brown Media Archives & Peabody Awards Collection at the University of Georgia, American Archive of Public Broadcasting (GBH and the Library of Congress), Boston, MA and Washington, DC. Web. June 28, 2022. <http://americanarchive.org/catalog/cpb-aacip-17-07tmqb4p>.
APA: The Power of Algebra; No. 009; Fractions. Boston, MA: Louisiana Public Broadcasting, The Walter J. Brown Media Archives & Peabody Awards Collection at the University of Georgia, American Archive of Public Broadcasting (GBH and the Library of Congress), Boston, MA and Washington, DC. Retrieved from http://americanarchive.org/catalog/cpb-aacip-17-07tmqb4p