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Algebra Lesson 4-1 Ratios & Proportions

Added Sep 16, 2015 •

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this lesson is on ratios and proportions lesson 4-1 in your book on page 182 get ready to take notes for papers in half or Draw your line down the middle for Cornell notes remember you can pause the recording if I move too quickly or on the extra samples that you're supposed to be doing in your still need positive recording to complete those problems  First Amendment define ratios on the left side of your paper a ratio is a comparison of two numbers and there are three ways that we can write this a to be a colon b or A over B we're going to be using this forum  throughout but these are also ways to write ratios a rate is A&B quantities measured in different units so for example miles per hour would be irate and a unit is a rate where the denominator is 140 miles per hour would be a unit rate how to record making me more time an example one more on page 182 still so you can follow along in your we're going to comparison-shop it says the table at the left gives prices for different sizes have the same brand of apple juice find a unit rate or cost per ounce for the 16 outside so here's the 16 outside we want to know how much it cost per ounce  so $0.72 416 Oz wheeler now how much it is per ounce  so to make the denominator one we would have to divide  the denominator by 16 because 16/16 a setback 15/16 would leave us with one but if we divide the denominator by 16 we also have to divide the numerator by 16 you're going to want your calculator for this we're going to take .72 divided by 16 and we get .045  now if we Brown that in money  it would actually be  $0.05 announced now we're going to be also finding the cost per ounce for the dollar 25 and the dollar sixty size so we're going to just move our decimal two spaces to the right that changes your decimal  to the number of sense so it's four and a half cents now I know we get paid for and a half cents somewhere we would actually pay 5 but since we're comparing here at one of these may also round five we want to know exactly to the decimal how much it is per unit the four and a half cents per unit on the 16 outside now in your notebook on the right hand side you guys the cost for the dollar 22:30 to find out how much that is per ounce and find out how much the 64 ounces so I'll help you set these up you're going to do a dollar twenty divided by 32 are you how much that is per ounce  and the dollar 60/64 how much does the r per ounce need to have your calculator handy pause the recording to complete those we are skipping over the unit analysis and moving on page 183 and defining what a proportion is a proportion is an equation that states two ratios are equal so we have a equals c over D so we have this ratio is equal to this greccio and that is called a proportion sew-in example 3 we are going to solve the proportion after two ways to solve a proportion in example 3 we're going to solve by  multiplying both pipes in order to get T by itself  we're going to multiply both sides by 9 or Hangover 1  that makes the noise cancel so he is now by itself this side we could multiply 5 x 9 to get 45 / 6  6 x 1 at 6 and then we could Distance by 3 or we could reduce this by 3 now 3 goes into Six Flags and then two nine three times 5 * 3 is 15 / 2 * 1 is 2 if we reduce 45/6 by 3 we would also get 15/2 you can change that to a mixed fraction or a decimal that you don't have to you can leave it as 15 / 2 remember I do not want you to change it to a decimal if the decimal does not terminate so now on the right side of your notes you guys solve the next three using the multiplication method so I'll get you started on letter a copy the problem down you're going to multiply both sides by 8 or 8 / 1 remember to pause the recording if you need more time and your sweaters pause recording these are also under example 3 on page 183 the second method for solving proportions in this is more common and some of you may have been thinking about this method when we did example 3 is that you would cross multiply now we have a negative sign here we need to assign that negative sign to are the three or the four you need to pick I'm going to go ahead and put it with the three when we cross multiply we take for X Y  to get for vibe and that will equal then we're going to multiply -3 x 2 and 1/2 so that'll give us -7 and a half what 7.5 again have your cat Andy please  so then we would divide both sides by 4 to get y by itself so why is -7 1/2 / 4 1 .875  hey we would not want to leave that as 7.5 over 4 week get rid of the decimals by multiplying the numerator and denominator by 10 so we could change it to -75 / 40 and then we could reduce by 575 divided by 5 is 15 + 40 / 5-8 so negative 15 8 could be the fraction equivalent to -1.87 but don't leave it as 7.544 don't leave the decimal in your great ship that's the cross multiplication methods so now you guys try these on the right side of your paper and these are at the top of page 184 the top of page 184 I hope you get started here you're going to take 12 * X is 12x whoops  and then we're going to take 4 * 25 is 100 and then you'll / 12 to self rats pause the recording complete a BNC for example for on the right side of your paper  at the bottom of page 180 it says you can use proportions to solve real-world problems to write a correct proportion form rates on each I said compare units in the same way  such as kilometers per hour equals kilometers per hour so example 5 says in 2001 Lance Armstrong won the Tour de France completing the 3454 km horse and about 86.3 hour traveling at his average speed how long would it take him to ride 180 5 kilometers round the answer to the nearest tenth  said it's time we can round it's a real world problem so wood round your answer to the nearest tenth here so we're going to set up a proportion 3454 kilometers and 86.3 hours so 185km in how many flowers so we use a variable to represent the number of hours they want us to find how long they were using X Matt  spot so we have kilometers over hours equals kilometers over hours bamboo cross multiply so 3454 axe Big Falls and then for the other products will need our calculator  185 times 86.3 we get 15965 .5 then to solve for the number of hours that he it will take him to go 185 km will divide both sides by 3454 smoothies cancel loops  stop moving around okay so we're going make the 1500s 15965.5 / 3454 and we'll get to the nearest tenth 4.6 and don't forget to label your answer when you're doing so take him about 4.6 hours if he's writing at approximately the same rate and you guys try extras amplify because if you walk 2 miles in 35 minutes write a proportion to find how far you would walk in an hour  if you were to continue at the same rate now be careful we're going to do miles over minutes we're going to have to convert this hour to minutes how many minutes are in an hour this is your your problem to do on the right side of your notes so I'm now set it up 2 miles in 35 minutes equals  how many miles in 60 minutes  now cross multiply and saw for the distance that you can go in 60 minutes pause the recording the last example it says ratios that form the proportion have variable expressions with more than one term to solve for the variable you will cross multiply and distribute so this is just like what we were doing but now there is an expression in the numerator  so when we multiply 7 by x + 4 we're going to end up Distributing and on this side we're going to have five times the quantity of x minus 2 so when we distribute 7 * X is 7x + 7 * 4 is 28 5 * X is 5 X -5 2 is 10 now we have a variable on both sides  remember I like to take the smaller variable from the bigger  7X - 5x is 2 and lost my point that's a negative 10 so make sure you bring the turn it down  and now we just have a two step equation so if we want by itself we're going to subtract 28 sorry about that get a little quick for it I think there we go  now when you subtract 28 from -10 remember that'll be negative 38 10 / 2 -38 / 2X equals -19 and you can check your answer just like we did or have been doing for the last couple of weeks -19 + 4 would be negative 15 negative 19-2 would be -21 so if we take -15 divided by 5 would get -3 and -21 / 7 is also negative three so the two sides would be equal if x is -19 so again just cross multiply that you'll need to distribute  and then solve your to store your equation with a variable like we did last week  so this is the last example you guys have let's see it looks like for you tries so pasta recording it letter a complete these are at the top of page 185 letter b pause the recording letter c pause the recording and letter d see you in class

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Algebra Lesson 4-1 Ratios & Proportions

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