WEBVTT mathematics/basic-math/pyo
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Welcome back to Educator.com; for the next lesson, we are going to continue proportions.
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We are going to actually write proportions and then solve them.
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When we write proportions, it is easier if you first create a ratio that you can base your proportion on.
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I like to call it a word ratio because you are going to look at what you have
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and then create a word ratio meaning a part to a part.
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You are going to find out what you are going to leave on the top
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and what you are going to put on the bottom of your ratio.
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Here I have my example, 2 miles in 20 minutes.
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I want to find out how many miles it will be in 30 minutes.
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I want to create my word ratio; for example, I could put miles over minutes.
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That means all the numbers that have to do with miles is going to go on the top.
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All the numbers that have to do with minutes is going to go on the bottom
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because when we write a proportion, remember a proportion has to be two ratios that equal each other.
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The first ratio I am going to write is going to have to do with this part right here.
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2 miles in 20 minutes; remember ratio, I am comparing two things.
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I am comparing the miles and I am comparing the number of minutes.
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All the miles is going to go on the top.
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That means I am going to write 2 miles... mi for miles
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Over 20 minutes because that is on the bottom; 2 miles in 20 minutes.
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Then I have to create my next ratio.
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Remember I am making a proportion; I am making this ratio equal to this ratio.
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That way I have a proportion, I can solve for whatever is missing, my X, my variable.
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Again the miles is going to go on the top because that is what I set.
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That is my word ratio; it is going to be X miles over... 30 minutes.
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That is minutes; that is going to go on the bottom.
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As long as I keep all the miles on the top and all the minutes on the bottom, I can create my proportion.
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Let's say I created my word ratio so that it was minutes over miles.
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That is OK.
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As long as you keep all the minutes on the top and all the miles on the bottom,
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you are still going to get the same answer.
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You are still going to get the correct answer.
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Again this ratio is equal to this ratio; that is how I get my proportion.
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That is how I am going to write my proportion.
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From here, I need to solve this out; I can cross multiply.
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If I can solve it in my head, then I want to do that instead so I don't have to do all the work.
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2/20 is going to equal X/30.
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I just rewrote the proportion without all of the units so you can see it a little bit easier.
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Here I can create an equivalent ratio; remember equivalent ratios from the previous lesson.
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2/20 is the same thing as 1 over... because here I divided this by 2.
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2 divided by 2 is 1.
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If I want to do 20 divided by 2, then it is going to equal 10.
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I can also do the same thing here.
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I want to make this ratio the same as 1/10.
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I can multiply this by 3 to get 30.
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Then I have to multiply this top by 3 to get 3.
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My X is going to be 3.
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Here I just used mental math to solve for X.
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I just made this equivalent ratio, 1/10, and then turned this into the same thing, 1/10.
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If you want, you can use cross products instead; that is another method.
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You are going to multiply all this together; make it equal to this.
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2 times 30... actually let's go this way first.
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It doesn't matter which way you go first.
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20 times X is 20X; equal to... 2 times 30 is 60.
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If I double 30, it is 60; 20 times what equals 60?
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20 times 3 equals 60.
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20, 40, 60; that is 3; X will become 3.
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That is the same thing; it doesn't matter which way you solve.
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As long as you make it so that this ratio is equal to this ratio.
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Let's do a few examples.
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We are going to write a proportion and then solve them out.
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5 pounds for $15; find the cost for 4 pounds.
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I want to first create a word ratio; word ratio, what am I comparing?
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Or what am I using?--I am using pounds and I am using money.
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I can say money or dollars on the top.
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Then I am going to keep the pounds on the bottom.
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It doesn't matter if you do pounds over money; that is fine too.
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Here is my word ratio; that means when I create my proportion,
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I am going to keep all the dollars on the top and then all the number of pounds on the bottom.
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5 pounds for $15, here is my first ratio, comparing these two things.
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$15, that is the dollars; that is going to go on the top; 15.
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Over 5 pounds; that is going to go on the bottom because that is what I made my word ratio.
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Find the cost for 4 pounds.
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4 pounds, does the 4 go on the top or the bottom?
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It is pounds; it is going to go on the bottom.
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I want to find the cost; that is what I am looking for.
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I am going to make that my variable; I can say X.
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That is the money part; find the cost; cost is money.
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That is going to go on the top.
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Here I am going to solve for X; again you can solve this two ways.
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You can find the equivalent ratio; I am going to simplify this.
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This is going to become... divide this by 5.
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15 divided by 5 is going to be 3.
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5 divided by 5 is going to be 1; there was my equivalent fraction.
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Same thing here; I want to make this the same as 3/1.
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How did I go from 1 to 4?--this was multiplied by 4.
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Or I can just do 4 divided by 4 is 1.
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Same thing here; 3 times... whatever I do to the bottom, I have to do to the top.
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X becomes 12; or again you can just do cross multiplying.
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You can do 15 times 4 equal to 5 times X.
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Then you can see what you have to multiply by 5 to get this number.
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My X is going to be 12 because 12/4 is going to be 3/1.
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That is the same thing as 15/5.
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I have to look back and see what am I looking for?
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I know that X is 12; but it is asking for the cost.
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We know cost is money.
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How much is it going to cost for 4 pounds? $12.
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The next one, 15 feet for every 4 minutes; find how many feet in 10 minutes.
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My word ratio, I am going to make it 50 over minutes.
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My 16 feet is going to go on the top.
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My 4 minutes is going to go on the bottom.
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Equal it to how many feet?--find how many feet.
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That is what we are looking for; feet, that is the top number.
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That is X; over the number of minutes is 10.
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Again you can look for equivalent fraction.
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This is going to be the same... 16/4 is going to be the same as...
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If you divide this by 4, divide this by 4, you are going to get 4/1.
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I am going to use that fraction to help me solve for X.
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1 times 10 equals 10; it is 4 times 10 is 40.
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That means X has to be 40.
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Again these two have to be equal; this is the same as 4/1.
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That means this has to be the same as 4/1.
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1 times 10 is 10; 4 times 10 has to be 40.
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How many feet?--X is going to be 40 feet.
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Example two, write a proportion and solve.
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5 chocolate bars costs 7.50; find the cost of 2 chocolate bars.
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My word ratio, chocolate bars; you can do money on the bottom.
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Or you can just do money on the top and then the number of chocolate bars on the bottom.
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It doesn't matter; there is my word ratio.
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Chocolate bars; 5 chocolate bars; 5 on top; over money; 7.50 on the bottom.
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Equal to chocolate bars... that is 2 on the top; over the amount of money on the bottom.
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For this one, I can solve this proportionally.
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You can also use this as a ratio.
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Remember 7.50 for 5 chocolate bars; you can make that as a ratio.
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Then find the unit rate; find how much it costs per chocolate bar.
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If you remember from a couple of lessons ago, you can use unit rate also for the same problem.
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Let's just go ahead and solve this using cross products.
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I am going to multiply this and this; that is going to be 5X.
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Again if you are multiplying number times variable, then you can just put it together like that.
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Equals 7.50 times 2; 7.50 times 2.
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If you want, you can just multiply it out like that.
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0; 5 times 2 is 10; 2 times 7 is 14; add the 1; 15.
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You know that this is 7.50; that is money; 7 times 2 is 14.
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If you have 50 cents and you double it, that is a dollar.
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You can think of it that way too; 5X equals $15.
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I am not going to put the 0.00 because that is just change.
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This is my whole number, $15; I can now find X.
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5 times... I know 3 equals 15; X is going to be 3.
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That means if for 5 chocolate bars, it costs 7.50,
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for 2 chocolate bars, it is going to cost me $3.
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I need to write my dollar sign here to give me the answer.
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The next one, Sharon types 60 words per minute.
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Find how long it will take for her to type 80 words.
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My word ratio could be words over minute; 60 words per minute.
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That is over 1 because the number of minutes is 1.
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How long will it take... they are asking how long it will take.
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They are asking for words or minutes?--they are asking for minutes; how long.
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This will be X down here; then they are asking for 80 words.
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Again you can use proportions; you can use cross products.
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60 times X is 60X; equal to 1 times 80 is 80.
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Remember if you want to find what 60 times X is and what X is, then you can divide the 60.
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Anytime you have a number times 60, you have a number times a variable,
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you can just divide that number to find X.
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X is going to equal... I am going to cross out these 0s.
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I am going to have 8/6; but then here I can simplify that.
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Divide this by 2; divide this by 2; it is going to be 4/3; 4/3.
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If I want to change this to a mixed number, this will be... 3 goes into 4 one whole times.
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How many do I have left over?--1; my denominator is 3.
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It will be 1 and 1/3 of a minute.
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If you have a problem like this on your homework or at school,
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it depends on how your teacher wants it, but you can change this to a decimal.
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Or since it is minutes, you can take this fraction.
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It is 1 whole minute and then some seconds; 1/3 is part of a minute.
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You can just figure out how many seconds that would be by doing 60 divided by 3.
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60 divided by 3; that is going to give you 20.
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That means this is going to be 1 minute and 20 seconds.
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Or you can just leave it like this if your teacher doesn't mind.
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Then it is 1 and 1/3 of a minute.
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The third example, Susanna estimates that it will take 4 hours to drive 600 kilometers.
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After 3 hours, she has driven 500 kilometers.
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Write a proportion to see if she is on schedule.
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Basically they are asking if you make a ratio of this and you make a ratio of the next part,
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are they the same?--that is all it is asking.
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My word ratio, hours over kilometers.
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It is going to be 4 hours over 600 kilometers.
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We are going to see if this equals the same as 3 hours over 500 kilometers.
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Let's see here; let's simplify these.
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Here I can say that if I simplify this, 4 goes into 600 how many times?
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Here is 1, 4, 2; I am just dividing it.
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That is 5; 20; bring down this 0; 150.
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If I divide this by 4 and I divide this by 4, I am going to get 1/150.
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That means every hour, Susanna should drive 150 kilometers.
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If 4 hours, she estimates she is going to be driving 600 kilometers,
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that means every 1 hour, she is going to be driving 150 kilometers.
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Is that the same thing as this?
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If 1 hour, 150 kilometers, does she get this in 3 hours?
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This is 1 times 3 equals 3 hours; 1 hour times 3 is 3 hours.
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Does that mean 150 times 3 is 500?--let's see.
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This times 3; 0; 5 times 3 is 15; add that; that will be 450.
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No, if she drives 150 kilometers for every hour,
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then in 3 hours, she should be driving 450 kilometers.
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But she drove 500 kilometers; that means she is not really on schedule.
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I mean, she is a little bit faster.
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But according to what she has estimated, it is not the same.
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So this one is no; she is not on schedule.
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She is actually a little bit early because she drove more than what she thought she would be at.
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This is not the same ratio.
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If it is 4 hours for 600 kilometers, then in 3 hours, she should be driving 450 kilometers.
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Because 1 hour is 150 kilometers; this needs to have the same ratio also.
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1 hour is 150; this has to equal this too.
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This one is no; she is early.
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That is it for this lesson; thank you for watching Educator.com.