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Exchange Rates

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Exchange Rates: Introduction

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So if you've ever traveled to a foreign country you had to exchange your dollars for a foreign currency. Let's learn a little bit more about these exchange rates. So $1 does not equal €1 does not equal one yen does not equal ₹1 does not equal any other currency. Right? We have to exchange our dollars for other currencies based on the exchange rate. So the exchange rate determines how much of a foreign currency you can get for your domestic currency say your U. S. Dollars, right? U. S. Dollars. So exchange rates are basically a ratio. So the ratios between the values of two currencies. Okay. And we're gonna learn a little bit more of how to examine an exchange rate because this can generally be a kind of a confusing topic when it comes to doing some math here. So when we talk about ratios we're always going to divide one number by another number. That's how we do a ratio. We're gonna take a number divided by another number and that's gonna tell us. Okay so it's important to be able to calculate the ratio but also important to be able to analyze the results. What does it mean when we get the answer to the ratio. So first let's start with a generic ratio interpretation and then we'll apply it to currency exchanges here. So ratio like I said we're dividing one number by another. So it's gonna be a divided by B. And this is generally going to be when we talk about it different currencies, the amount of a foreign currency divided by the amount of dollars, something like that. So when we interpret a ratio we're gonna do the division and say that this division gave us 1.54. Right? Like I have in my example let me do it in another color here. 1.54. Right? So how do we interpret this ratio? Where we calculate the ratio by doing the division and then what this tells us this 1.54. It would tell us that for each unit of B. The denominator. So if the denominator was U. S. Dollars for each us dollar we would get 1.54 units of A. Whatever the foreign currency is let's say €1.54 per us dollar, something like that. Okay so that's how we interpret it because anytime you do a division A divided by B. You do that in your calculator you get 1.54. Well that's the same thing as 1.5 4/1. Right? So 1.54 A divided by one. Be right for every one unit of B. You'll have 1.54 units of A. So when we apply this to exchange rates it's just gonna be currency one divided by currency to write. And that's our ratio A over B currency one divided by currency to Now there's two ways to to explain the same exchange rate right? We can say how many euros per us dollar or how many us dollars per euro. Okay, now it gives us the same the same answer in either case. So for example, if $1 is worth €10.93. Well we can do this, we can do €0.93 divided by $1. And that tells us 0.93, right? 0.93 divided by one is €0.93 per dollar. So if you were to give them, you go to the bank and you say, hey, I want to exchange this €2 you give them $1. They'll give you 93 cents, €93 cents back. Okay, so each $1 will get you €93 cents. Now we could say the same thing because what if we had €1 and wanted to exchange it for dollars? How do we know what that calculation is? Well, we can do the opposite, we can do $1 divided by €0.93. And this is the same thing because they are equal to each other, right? So we're able to flip it and it still gives us a ratio. But the interpretation interpretation is a little different. So let's get our calculator out and let's do this one divided by .93 Gives us one point, I'm gonna round it to $1.07 per euro. So that means if you go into the bank and you hand them €1 and say, hey I want you american money, they'll give you a dollar and seven cents. Okay? And that's because of this exchange rate. If we had a different exchange rate, we would get different numbers here. Okay. So notice how we're analyzing this ratio. We did one divided by 0.93 and it told the calculator, said 1.7 when we did that. But we have to know what does that mean? That means 1.7 Of the top per one of the bottom, right? Just like we said in our ratio interpretation, that means for each one unit of b the bottom, there are 1.54 units of a the top. Right? So that's how we, how we interpret ratio. Whenever we put it in the calculator, it's always this amount of the top currency divide for each one of the bottom currency. Okay, so let's pause here and let's try an example and let's try uh some practice related to this as well.

2

Exchange Rates

6m

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Alright, so let's try this example together. But before we get into it, I want to teach you a little trick about exchange rates that comes into play with any kind of unit conversion. So let's do a simple example before we get to this one where we're gonna think about, we have we know our exchange of feet two inches, right? We know that there are 12 inches per foot, right? Per one ft, Which is the same thing as for every one ft there's 12 inches. Right? So if I were to ask you how many inches are in three ft, well, you would probably know that there's 36 inches, right? 12 inches per one ft 3 ft. 36 inches. Right, well how do we use this? And show show it mathematically. Okay, so this is technically our exchange rate here 12 inches for every one ft or one ft for every 12 inches. Right, And we want to know three ft how many inches? Right? three ft. How many inches? So the idea is we're gonna use our exchange rate from inches to feet and we're gonna multiply it by feet. Okay. The idea is that we want to end up with inches, right? Our our question is asking us how many inches for in three ft, how many inches? In three ft? So we want to cancel out the units of feet and be left with inches. Let me show you what I mean. So we're gonna use our exchange rate 12 inches for one ft and we're gonna multiply it by how many feet we want, we want three ft. So in three ft, how many inches are there? And what can happen here is we can cancel out these units. So notice that the feet is in the numerator here because it's 3/1, right? There's three and then there's feet in the denominator. So from a mathematical standpoint we can cancel out those units, the feet and the feet and we'll be left with inches. This is the way I want you to think about doing these currency exchanges when you have to do math. Like we see in this problem. So 12 divided by one times three. So we now we use the numbers we've we've canceled out the units and we're left with inches. 12 divided by one is 12 times three is 36 inches. Right? So that tells us that in three ft there's 36 inches, right? If there's 12 12 inches per foot three ft, well that gets us to 36 inches. So what you want to do is be able to cancel out the feet notice if we had used this, if we had to use this one right here, one ft divided by 12 inches, we would not be able to cancel out because feet would have both been in the numerator. We wanna cancel out feet and feet here. So this does not work. We want to use this one right here. Okay so you wanna you wanna think we can always flip the exchange rate so that we we can cancel out the units that we don't want. And end up in the units we do want. Okay so now let's look at our our actual example here, clutch topia is currency conversion is currently 1.7 clutch coin for $1. 1.7 clutch coin. Ccs per one U. S. Dollar. So there's our exchange rate. If a U. S. Citizen was planning to visit clutch Topia, how many dollars? So let me erase this right here, how many dollars would they need? Right how many dollars? So we want our final answer to be in dollars right so we want to cancel out the clutch coins and be left with dollars. How many dollars would they need to exchange to receive 100 clutch coins? So what we need to do is convert these units from clutch coins to dollars and were given are to exchange rates here. So I don't want to leave this empty. This was what it was over here before. Okay um What are our two exchange rates that are equivalent to each other? We either have 1.7 clutch coin per $1 or one U. S. Dollar per 1.7 clutch coin. And we want to do the same thing. Do we want to end up in dollars or do we want to end up in clutch coin? What is our question asking us? It's asking us how many dollars? Right so we want to end up in dollars. We want to cancel out the clutch coin. So what we need is clutch coin in the denominator and clutch coin in the numerator to cancel out just like we had in our example over here. So what are we gonna do? We're gonna use this one that has clutch coin in the denominator because we're gonna multiply it by 100 clutch coin. We want to know how many dollars are needed to receive. 100 clutch coins. So we want to go in the bank with a certain amount of dollars and then leave the bank with 100 clutch coin. So how many dollars is that? So what we're gonna do we're gonna do the one $1 divided by 1.7 clutch coin. And we're gonna multiply it by the 100 clutch coin. Right? We multiply it by 100 because this exchange rate is equal to one. That's what one would be. So we multiply it by the 100 clutch coins and we'll see how many dollars it would be. So notice what happens. We've got clutch coin in the denominator, clutch coin in the numerator and the clutch coins are gone and we're left with us dollars. Okay so what we need to do is one divided by 1.7. So now we do the math one divided by 1.7 times 100. And that gives us that equals 58.8 to 58.82. And that's in dollars. Right? That gives us an amount in dollars. Because we've canceled out these clutch coins here and we're left with us dollars. Okay? So that's what this this tells us here. It tells us the amount of us dollars we need to get 100 clutch coins. Okay. So I know it can be a little tricky when it comes to exchange rates but being able to do this unit conversion and flipping the exchange rate when you need to to cancel out the units. That's a big trick in being able to solve these exchange rate problems. Alright, let's pause here and now you guys can try a practice similar

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Problem

Clutchtopia currently exchanges 0.8 ClutchCoin (CC) for 1 US dollar (USD). If a ClutchBurger costs 3.50 CC, what is the USD equivalent price for a ClutchBurger?

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