Hello everyone, thanks for coming. My name is Fernando Abaldi and I work as a security consultant for IOACTIP. I would like to show you today how XSL implementations are vulnerable to multiple practical attacks. And for that matter, the very first question that I would like to be addressed if I would be sitting over there is why are we talking about XSLT? This is a programming language that is not so common and has been created when XML was created and it was a way to parse XML data. So a couple of years ago, I came across Ariel Sanchez, a co-worker, founder of an XML vulnerability and an external entity expansion that allowed him to retrieve some passwords. And I thought this is pretty cool. I want to learn more about XML, schemas and XSLT. Those are all the technologies related to XML. And I was doing that, I noticed that there were no things breaching about how to exploit XSLT implementations. When you're reviewing a language, you may want to know that. So what we will be doing here is to analyze what are those weaknesses. So we're presenting five different issues in here and how you can practically explode them.  Or just trying to abuse any implementations, hopefully this will help. One of the things is that even today, no one of the vulnerabilities have been fixed, so everything will work. And you may be able to affect the confidentiality and the integrity of multiple implementations. And that means that you may get even some profit in certain scenarios. So the good thing is that you're not exploiting flaws in a way that a malicious virus of my world would do it in here. You will see no assembly code, you will see just XSLT and how that can be used to get some fun things. So we will briefly talk today about how you can identify your target, how numbers will let you affect the integrity, how random numbers may be predictable sometimes. I will show you how to bypass the same origin policy in a web browser using XSLT. And finally, some information disclosure through Evers. So basically the idea here is to tell you what XSLT does briefly and how XSLT can be attacked. And finally, if you don't know, hello. I was actually expecting this. I know. That's why I'm here. So this is your first time at DEF CON, huh? How's it going? A little bit anxious. You seem a little nervous.  We have a medicine for that. It comes in that bottle, right? Yes, it does. I gave him the right one, right? Okay. No. That was like, dude, wait. Why am I getting the water? I don't know. I don't want the water. Moron. Over at DEF CON. Thank you very much. Yes. This will get interesting. You feel much better, don't you? I feel like a man, right? Thank you very much. I would expect that. And as I was saying, you can identify your target, maybe. Thank you. So basically, XSLT is a language that is being used to modify an XML. So what it does is receive as an input an XML document. It creates a text document or an HTML document or a new XML document for that matter. So there are different versions when it comes to XSLT there are three. V1, V2, V3. And the different versions doesn't mean that they are improvement, they should be, but they have more functionalities. Each version has more functionality. And V1 is the most implemented version in here because it has been supported by web browsers and because it is supported by previous versions. So an XSLT processor supporting V1, V2 will be supporting V1. So I tested two types of software, server-side processors and client-side processors. Server-side processors means those are standalone things that you can run in command line or they could be libraries that are hooked up to different languages, Python, Perl, Java, whatever. I want to come to client-side processors. Basically, I believe you have two types. You will have web browsers or eventually XML or XSLT editors. And I believe that that is a very narrow set of people that are using those. So the some of the processors in libraries are mostly three. These are the most important ones. Developed by Nomi, Apache, and Saxonica. Live XSLT is the most widely deployed one. It is not only implemented by server-side processors but also by client-side processors, web browsers. And you also have Salem developed by Apache people, which comes in two flavors, C++ and Java, and the similar thing goes for Saxon. And the client-side processors here, we have the browsers, all the things that I tested was in the latest versions available of all the server-side libraries and web browsers. So we have three ways to do this. The first one involves an XSLT processor receiving an XML and an XSLT. This normally happens when you're calling a common line processor. And eventually you will get a new document. You will do this if you need to parse an XML. So people will be using this if they need to parse something, server sign. Another possibility, which is more common from a client-side perspective, is when the XSLT processor is grabbing the XSLT document. So there is a small portion in the XML that says you will find here the XSLT document, go get it for me, and create the new result document. And finally you can embed the XSLT document along with the XML, and by doing that you just supply one file to the processor to get the new result. So you may want to know if you don't know already who is your target, which kind of properties do the target have. So by getting which type of version and vendor they have, you may know what type of vulnerabilities you could exploit in this target. Since clients may also support JavaScript, and that would be the case for a typical web browser, you may also retrieve some JavaScript information. All this code that you're seeing here and you will be seeing here, it is all in the white paper. You can do a copy paste and try on your target of choice to see what happens. So at the end of each section I will show you a brief summary of the server size. Here we have all of them. XSLT pro, that's the standalone version of live XSLT. And PHP, Python, Perl, Ruby are all related to live XSLT in this example. Then you have the client, which will be the web browser. You will see the first column for the version, the vendor over there. And if it supports JavaScript or not, basically, of course, all web browsers supports JavaScript. There is one final thing and that's that normally live XSLT is most widely deployed than other things. So you will notice that it is sometimes when everything is affecting server size, it may also affect the client. Let's start talking about the issues. So this is something present in client side and server side. And it doesn't matter if you're talking about floating point numbers or integers, all numbers will introduce errors in here. So as I was testing this, it felt a little bit weird that sometimes calculation was not working as I expected to be. Certain additions, subtractions were not doing what I was expecting. So the very first thing that I did was to define a style sheet as simple calculation. What I was trying to do was just to add a few numbers. So for that matter, I had defined a style sheet which has a specific output in here saying that it is a text output. And in the middle, you will have this simple thing, 0.2 plus 0.1 minus 0.3. That should be 0, right? Pretty simple. May not be that simple for processors. Only two say that this was 0. That was the case for Opera and Chrome. The rest said, well, close to that. Why is this happening? This is weird. And the weird thing is that you will see this across all implementations. Okay. This is cool. But it will be better if we do something with this. I mean, these are just numbers that were not properly rounded by the programming language. So this is the thing that is present in all programming languages. I realize that you will have these in JavaScript, Perl, Python, C, whatever. This is a common thing. Floating point numbers will have certain decimals that are over there hanging around that you may take. So I created a simple JavaScript application simulating a bank. This is not a real bank. I wouldn't try this on my real bank. Hopefully my real bank will limit the amount of transactions. I wouldn't allow a very small decimal to be transferred from one account to the other. So the very first thing that I tried was to see, I created this application. I deposited a million dollars on the first account. And the second account has a zero balance at the moment. This is where I will deposit my profit. So I noticed that if I remove a very small number from the million dollar account, it will not get subtracted. But it will be added to the secondary account because it has a lower number than a million. It has a zero. And that decimal means more for a zero than it gets for the million. So this program will try to do, the first portion of the program will try to see how big of a number can retrieve. It is a small number. And then it will do millions of transactions to move it to the secondary account. So you will see here that we will be seeing V8 and that's the Chrome JavaScript processor on the standalone version. And we will try to see what's the best profit to get in here. How much money can I steal from a million dollars that would not be noticed? And I will try to, I will start moving that money, where that money from the account number zero to account number one. And hopefully that will give me a daily profit of around $1,300. It is moving, right? Yeah. So this was good. But it would be better if it would be higher than number. So let's talk about integers. I would find an XMO with 10 numbers. And this would be fairly easy to understand even if you are not developing. You will see that you have five exponential numbers in here and the same five exponential numbers written just the number one with a bunch of zeros. The thing is that programming languages do not handle very well when you have more than 16 digits because of the precision. But what I tried to do was to print in here the same number that I was having on the XML document and then formatted with the commas and the periods and such. So it would be more legible. In here, you will see that Saxon is doing great. This is what you want to see. You will see number one followed by a bunch of zeros. This is pretty clear. This is awesome. You will have the same for the non-exponential notation. Internet Explorer and Firefox argued they weren't able to show the exponential notation, but that's okay. The problem comes when you're introducing errors because there's nothing worth believing that you have the right number when in fact you do not. In fact, I was noting today how they are finishing is different depending whether you're using exponential notation or not. So we will try to use this number in a couple of minutes. Say hello for Java. Almost there. And for C, they just don't care about what's going on over there. So anything can happen here. So first I thought, okay, this is something related to an error in the standard. So I went to read this standard 754. But the problem is not over there. All implementations have problems. So it is what you do with floating point numbers and integer, what matters. You should be saying, okay, a number should be between these values and not allowing a value to be so big if you are not able to handle it. Either way, this shouldn't be working like this. So I reported all the issues including this one and the floating point numbers to the vendors. And the first thing that I heard was that I should be reading Wikipedia to understand how floating point numbers work. That was interesting. But probably you wouldn't find the answer over there. Then I heard that I should be reading the accessibility to specification. But this was affecting purely V1. That was nice as well. But clearly it was not solving the problem that was in here. And the very same person also said that this is something that you will see in JavaScript as well. I mean, that's fine. I know that you can't find this in JavaScript. But I wouldn't like to have this in my programming language. On any programming language because these errors are everywhere. So we stole some decimals before. Now we're trying to do a similar thing but with integers. The thing is that if you put a number one followed by 17 zeros and you subtract the number one, programming language will not notice that the one is missing. So perhaps I created in here a fake cryptocurrency which I named fakecoin that the value is very small. Very, very small. So I bought a number one followed by 17 zeros of these coins. So I have a lot of coins with a total net value of $1,100,000. And I will try to transfer one coin at a time to a secondary account which will be my profit account. And hopefully by the end of the day I will have a better profit than moving decimals. The profit will be better if I use more coins. I will be able to transfer more coins at the same time. And here I'm just going for the minimum amount possible just to show you. The minimum amount in here would be, would give me a profit of $2,300. If you had a zero to the coins, you should add a zero to the daily profit as well. So that was nice. That was nice. So the very next thing that I did was to see how random numbers work. I mean if you are developing, if you have ever developed, you need random numbers. This is something that you should normally see it on server-side processors. And you should also know that, of course, not any random number generator should be used for cryptographic purposes. I mean, random numbers, you have to be careful with them. In XSLT, this is a function that comes from the extended XSLT, which is an extension of XSLT. It is defined as a function that returns a value between zero and one, as any random function should be. Supposedly any random number should be a number that doesn't have any pattern. I mean, you shouldn't know what would be the number before calling this method. It would be fairly logical from a random point of view. So we normally have two types of random functions you have ever developed. You may know that you have functions that are less secure, like random in Python, and you have more cryptographically secure mechanism like system random in Python. You may want to use that if you are moving cryptographic things. Some of the software that I tested, the server-side processors, you are able to see the code, you are able to see how that was developed. For XSLT, XSLT for C, XSLT for J, and you will see that in all these areas, they are using pseudo-random number generator. Which is fine. The thing comes, the problem may come on the implementation. If people are using random numbers for any cryptographic proposal, that may be a problem, because you may know with pseudo-random number generator what's going on. These were the functions of which I see, in C and C++ and in Java, and a good definition comes from the MAM base. These are just by random number generator. You have to take that into consideration and shouldn't use them for cryptographic proposals. But there's one more thing when it comes to random numbers that you normally pay attention to, or you should, at least. What happens if there is no initialization vector? This is something basic from any random number. And that's that you need to have some sort of something that is changing when you're getting a random number. Otherwise, you may get always the very same value. And that's not very useful if you're expecting a random number. And that's because you may know in advance which numbers you will be getting. So once you have a proper IV in place, you will have different values every time that you're calling the random functions. But let's see again how the functions that we saw before are working when it comes to the initialization vector. And here there is only one that doesn't have the IB. Again, live XSLT. This is not something new to live XSLT. They know about this since 2006. But this is how it works. So if you try to create an XSLT that will produce a random function, or you see anyone who's trying to produce a random value out of live XSLT, you will see something like this. And you will see these kind of results if you're executing that on common line. I executed twice on the same terminal. And I go twice the same number. You can see that the 7.82, you always get that first number every time that you're executing the random function from live XSLT. So the next thing that I do is to try to understand how this can be used in cipher modes when they're doing block ciphers. That's not a way to cipher things if you're using random. So I created two executions at the very first time to understand how these numbers look like. So first I printed the Python version of random, random. And you get two different numbers. Of course, this upsets the random number generator. They may not be the best, but they are not predictable. And they are not the same every time that I'm executing that function. But live XSLT, we can recognize again the very same number that we saw on the previous line, the 7.82 thing. That's the very same number. If you're calling Python again with a print random, random function, we will see that we have again two different numbers. So so far, four for Python and one for live XSLT. If we're calling a live XSLT again, you will notice that in the second position, we will always have this new value, this 0.13. And it will be repeated every second time that you're calling this. So without having an external seed value such as time, you may know in advance which will be the sequence of numbers that will be generated by live XSLT. Which is pretty cool because you may know in advance what is being encrypted if they are using this or encrypt something.  So again, you may predict values when you're seeing random numbers. The same origin point is something that is present in client-side processors. This means web browsers. Basically, this says that if you're on a website, you shouldn't be reading information from other websites. But again, as always, that may not be the case for certain engineers. So this is important. The origin is always defined by the scheme, the host on the port of a URL. We will be an example of this. The HTTP at the very beginning or HTTPS will be the scheme. The host should be example.com. And the port should be either port 80 or port 443 or something like that. So generally speaking, when we are retrieving documents from different origins, the web browsers will not share the information. I mean, when we are taking the same origin over and over, we may have, we will be sending the same cookie over and over to the same website. And that would be okay. Normally, JavaScript is used to try to alter this, but you don't necessarily need to use it to affect the same origin policy. You shouldn't be expecting that when you're connecting to Google.com, your browser will be sending the very same cookie to this website because it has the very same origin. If you're connecting to Microsoft.com, you should be seeing a different cookie. This will be a very valid scenario. You just connect to a website. You're on the main web page. You're trying to access a second web page that is being stored over there. And that will be fine. That's okay. You're allowed to see that. In fact, you're even to allow, you're even allowed to see other web page on the very same domain. But if you're changing the scheme, if you're changing the host name, or if you're changing the port, you shouldn't be allowed to see any of the information that is present on that other website. I mean, you're not sharing the private information between websites. That's what you would expect at least. So there's only one function that reads documents, and that's document. Okay. So you may try to use that to read another XML document. In fact, since we're speaking about websites, we could also see in here XHTML, which is a fairly common way to represent a web page by certain web servers. Once we retrieve the XHTML documents, we can see what's inside using either of these two functions, copy off and value off, which will show either an XML representation or an external representation. So the very first thing that you want to do, if you want to abuse this, you need to find a server that uses XHTML. Okay. Bing.com uses XHTML. I'm logging in here. What can you do with this? So on the upper right corner, you will see that my name, it is a red box, and that is also reflected in the code. And since it is XHTML, this is some sort of XML. And my name is within an element named ID underscore M. So you may be able to target your web browser to retrieve that value. So let's see how using the document, how using any other functions, we can retrieve that information. In here, we can see that the document function is accessing the URL, www.bing.com. And then right in the middle, we are retrieving the information that we just grabbed from the document. And finally, because I'm lazy, on JavaScript, I will be subtracting the ID underscore M element, which has my name. So let's see a demo of this. First, I will open Safari, and I will show you that I'm using Bing.com as my home page. And then I will open the document that is on the desktop that it is not sharing the same origin. Because one, Bing.com, it is being housed on HTTPS, Bing.com. And the other one, it is file, it is a local file. So let's see what happens. You will notice again, my number in the upper right corner, and when I open that file, I'm reading the document that is being stored by Bing.com. And I'm able to retrieve my name from using XSLT. Even though it is not hosted on Bing.com, Safari doesn't care. I will show you that information. So, basically, Safari will allow you to read this. Internet password may show your warning message. We will retrieve the information, but you won't be sharing anything related to this. And the other browsers just didn't do anything. Another cool thing would be that you may use some of these stuff to try to scan internal networks in case you wanted to. There are multiple ways to try to scan internal networks when you're executing something locally. And this could be another way as well. So another vulnerability that I found, and I thought that would be very interesting to discuss, would be an information disclosure on file reading through errors. This is something that is present in server-side and client-side processors. The focus in here is, of course, on server-side processors because we wouldn't care what will happen on a web browser. So the cool thing about this is that it is not possible to read text files in XSLTV1. It is only possible to read XML documents, or as we saw XHDML documents. And since it is not possible to read plain text files, it doesn't matter what function we are trying to use in here, because all functions shouldn't be capable of doing this. So let's see what happens, even though when the W3C consortium says it is not possible. So we saw before that there was one function to read XML documents, and that's the document function. This document will allow access to other XML documents other than the main document. Okay, we have that. We can try to use that. There are also other functions used for accessing XSLTV documents, and that would be the functions include and import. These functions do just retrieve a style sheet, and I would try to use it, combine with other style sheets. We don't care about what the manual says about this, because either way we are not trying to read a style sheet in here. So I created a text file that contains three lines, very simple. If you see the contents of my test file, you will see a line one, a line two, and a line three. Pretty simple. And if you read the documentations, you will see that when you're reading a file, this comes from the XML documentation. If you're reading a file, there are a couple of possibilities. The first one is that you may show that the XSLTV processor is found an error, and that's what some of the processors do. They say this is not allowed in Prolog. Okay, that would be, that's okay. The other possibility would be to return an empty XML document. That's what Ruby does. Ruby will show you that there's nothing to see in here, and this is something that is also expected as well. But again, this doesn't solve the problem that we want to read something that was on the test file. LibXSLT comes again to help us with this. So when you send a document, XSLT, PROC, PHP, and Perl, will show you the first line of our test file. Remember the line one of the test file? That's not too much, but it's cool. Perhaps we can do something with that. We also try to use other functions to try to access these files later. But having this unexpected behavior in place may allow us to do something with it. So you may know in advance where I'm going with this. Which type of files may have an interesting first line that would be valuable for us. There are certain specific files that sort the most valuable information of a computer on the very first line. So what if we will be able to read, for example, a password file where we could find those passwords. The most common answer for any Linux system would be an instant password. The next one, if you go for bit, they are running this as route, could be the instant shadow. The possibilities are in your imagination here. Depending what you are trying to read, you may be able to retrieve certain information that may be valuable for you or for someone else. You also have the Apache password and you also may have databases passwords. There are possibilities down there. The thing is that this is what you will be seeing when using, for example, one of the processors when trying to read the access to your password. You will see an error and also something else. The password. Which is cool. You can also now use access to retrieve this information. Another example you are seeing PHP could be to try to use PHP to read the HD password of an Apache. This is something you store in the very first line. You may see a bunch of errors and write in the middle what you are planning to see. The password for John. In this case. As I was saying before, just in case they do not care about what they are doing, you could also have someone using the et cetera shadow leaving that available if they are running this as root. This will happen if you are using Ruby to try to retrieve that file. Again, expect all the errors, but also the password for the root over there. This is pretty neat because I believe this opened the possibility for XSLT to be interesting perhaps as external entity expansions as a way to retrieve some information if an attacker is able to compromise an XSLT because the application is a low and there are applications that allow XSLT to be uploaded or XML that are reliant in document input that may be out there in any way to try to read files. Either if you are able to control an XML and you have an XSLT processor in the backend parsing this, or you are able to control the XSLT, you may compromise the security of an application. So I would recommend that in place to have the confidentiality and the integrity affected because sometimes when using random function or integers, they may be doing that to our profit without doing anything on our sign. So I would recommend as a very last thing that you should check your code or someone else in case just wants to see what's going on today, if anyone has any questions, so happy to answer them. Thank you very much and thank you for all these people who helped me with the presentation.


Hello everyone, my name is Mariella, one of the client management team from CMC Markets and today I'm going to be giving you a brief explanation of the price depth ladder. So the benefit of the price depth ladder is that it allows you to execute much larger trades in a single transaction when entering a stake size larger than the normal market size or the level one price, which is the price you see when you open an order ticket on the platform. So the platform will use the price depth ladder to offer you different prices to execute your trade at depending on your position size. So the price depth ladder is designed to reflect in part the underlying order book per individual product, the bid offer prices available to trade by volume. It's not an exact representation of the order book in the market, rather a volume weighted average price. So there will always be a minimum amount of volume available at level one and a maximum at level 10.  The volume available at each different level down the ladder to sell or to buy may vary throughout a trading session depending on the volume or liquidity available in the market at the time. Where a product is very liquid, there will generally be a much higher volume available to trade at level one. If we compare Euro against the dollar to the Swiss franc against the New Zealand Rand, we can see at level one here, we can buy or sell up to 251 pounds a point, whereas here we can only trade up to 60 pounds a point. So to allow clients to place larger bets or trades on a product, we will widen the spread accordingly. The lower down the ladder and order is filled, the wider the spread will become. That's all from me today. If you have any questions regarding the price step ladder, please feel free to reach out to us by the live help section of the platform. Thank you.


Lecture 21. As-Salaam-Alaikum. Welcome to the virtual university's course on business and technical communication. In this lecture, we will learn to strengthen your persuasive message with an appropriate appeal. We'll also look at how to gain credibility by supporting your persuasive message with relevant facts and how to use attention, interest, desire and action of the AIDA plan to organize persuasive messages. We'll also look at how to write a message persuading your audience to take action or to grant you an adjustment and how to design a sales letter around selling points and benefits. When we talk of motivating with persuasive messages, then in business terms, the term persuasion means to influence an audience by informing them about something and by aiding their understanding, by helping them to understand something and then leaving them free to make their choice. But once you've given them the information that will help them in making a choice, there you are giving the information in such a way that you are hoping that the choice that they will make will be the choice that you want them to make. Ethical business people inform customers of the benefits of a product or an action so that customers can recognize how well that product or action will fill a need that these customers truly have. So it's just by informing how a need is going to be fulfilled. That is how you are actually motivating people or persuading people to buy a product or take a particular action. Your consideration of customer needs is more than ethical. It is the proper use of persuasion.  You have kept an eye on them and you have their knowledge. And this is a very ethical way to persuade customers. Also, it's more likely that this consideration of customer needs will evoke the desired response from your customers and colleagues. If you let them know that you are actually aware of their needs, then they are more likely to respond to you the way you want them to respond. Since persuasive messages aim to influence audience who may resist as well, who may not be very open to the ideas that you are trying to sell them, therefore persuasive messages depend heavily on strategic planning. Because it is possible that whatever you are trying to sell, or whatever audience you are trying to buy, they are resistant to taking that action. They are not very easily prepared. That is why you have to do a little more persuasion. That is why it is better to plan your message beforehand and think a lot and plan how you will organize that message, how you will use the words in it, so that you will get the same response you are trying to get. So before you begin to write a persuasive message, ask yourself what you are writing about. What are you writing about? Who you are writing to? Who is the person who will read your message? What are their needs? And what do you want to happen as a result? What are the consequences of writing this message? When you are analyzing your audience, take into account their cultural expectations, what they expect from you. The expectations might be different in one culture from another culture. And also they practice what they do in different cultures as well if you are writing across cultures. So that you don't undermine your persuasive message by using an inappropriate appeal or by organizing your message in such a way that it seems unfamiliar or uncomfortable. Keep in mind the audience's cultural perceptions as well when you are organizing your message. When you are writing persuasive messages, you need to keep four things in mind about your audience and these are needs and appeals, emotion and logic, credibility and semantics. Let's have a look at each of these individually. Needs and appeals, what do we mean when we talk about the audience's needs and appeals? Some researchers believe that certain needs have priority and that the most basic needs such as safety and security must be met before a person will seek to fulfill higher level needs such as esteem and status. Obviously, if a person's basic needs are that he is secure, he is safe and the rest of the needs, whether status is good, self-esteem or society's esteem, they come later. But you need to keep in mind that different people have different needs and everyone's needs differ. So people respond differently to any given message and based on that, based on what their needs are, you will organize your message. For example, not everyone is interested in economy or fair play. Some people's innermost needs make appeals to status and greed much more effective. So if you know that these people have their, what is more important to them is status or greed, then you will make an appeal accordingly. To accommodate these individual differences, you need to analyze the members of your audience and then construct a message that appeals to their needs. So whatever your needs are, you will make a message accordingly so that they can appeal to their needs. They feel that our needs will be fulfilled and our desires will be fulfilled. Now, another thing that we mentioned was emotion and logic, which we had mentioned in the audience. When people's needs are not being met, they are likely to respond emotionally. For example, a person who lacks a feeling of self-worth is likely to be sensitive to the tone of respect in a message. A collection letter to such a person carefully avoids any hint that the person might be considered dishonorable because you realize that that person lacks self-worth and that the person who has a sense of self-worth might be considered dishonorable because you realize that that person lacks self-worth and they are more likely to feel sensitive about anything that you say and they are more likely to read more into a message which even hints at them being dishonorable. All the emotional issues can be a pitfall for persuasive messages. Emotional issues are at home. It becomes difficult to encompass and deal with them in persuasive messages. But you can actually call on human emotion as long as your emotional appeal is subtle. If you are not using a very obvious emotional appeal, then with a subtle emotional appeal you can actually reach out to your audience. You can make use of the emotions surrounding certain words. For instance, the word freedom evokes strong feelings and also words such as success, prestige, credit record, etc. All these evoke strong feelings, strong emotions amongst the readers. So you can make use of these words to make sure that you are actually using the right type of appeal to reach out to their needs. Now emotion and logic work together in a unique way. People need to find rational support for an attitude that they have already embraced emotionally. So if people have an attitude, they have an emotion that you are aware of, then those people are trying to find a logical appeal to that need as well. And to help satisfy this need, a logical appeal calls on human reason. If you feel that your audience needs and you use the same appeal to reach out to their needs, then you need to keep an eye on human reasoning as well. Now the third thing that we will look at is credibility.  The credibility of your audience will be established if your readers feel that you are true, then you are credible and they will believe in what you say. If you get insincerity from your message and your readers feel that you have insincerity, then your credibility will be reduced. Similarly, if in your previous correspondence or your previous interaction with your client, they feel that you are sincere or not sincere, then your credibility will be different and the way they will respond to your future messages will be affected. For you to persuade skeptical or hostile audience members, the audience must believe that you know what you are talking about and that you are not trying to mislead them. If you feel that your audience is hostile, then it is very important for you to have a relationship with them so much that they believe that you are misleading them or you may not know about your field. One of the best ways to gain credibility is to support your message with facts. Testimonials, documents, guarantees, statistics, research results, etc. are all facts, information, material that provide seemingly objective evidence for what you have to say. They make your message more credible. If you include any of these as appropriate, then your message is likely to come across as being more credible and consequently you are likely to come across as being a more credible person. Obviously if, for example, you are using statistics that are not relevant to the message that you have to give, then they will not really do much to add to your credibility. So you have to add information, add facts that are relevant to the information that you are giving out and also if you are using any sources or if you have referred to any sources or you have gained your information from somewhere else, then it helps to name your resources, especially if they are respected by your audience because then you are showing your audience how credible you are and that these, even the people that you are consulting or the sources that you are consulting are credible as well. It helps put you in the same bracket as those sources and it gives you more credibility as well. Other ways of gaining credibility are being enthusiastic, your excitement about the subject of your message can infect your audience. If you are enthusiastic, then your audience will be enthusiastic as well. Also being sincere, your honest, genuineness, good faith and truthfulness helps you focus on your audience's needs. If you come across as being sincere, then the audience feels that you are aware of their needs and you are actually sincere to their needs as well. Also if the audience perceives of you as being an expert, your knowledge of your message's subject area or even of some other area helps you give your audience the quality information necessary to make a decision.  You are also credible if you have good intentions. Your willingness to keep your audience's best interest at heart helps you to create persuasive messages that are ethical. So if you really have your audience's good will at heart and your intentions are really good, then your persuasive messages will obviously come across as being ethical. If you are trustworthy, you are honest and dependable, then that can also help you get your audience's respect. Also if you can establish common ground, if your beliefs, attitudes and background experiences are like those of your audience, then you can help your audience identify with you. You and your audience can actually share common ground and if you feel that you think similarly about certain things, then you can actually use that to your benefit and to stress your credibility. Now lastly, the last thing that we need to keep in mind or the final thing that we need to keep in mind is semantics. The words you use or the words you choose to state your message say much more than their dictionary definitions. Depending on what you want to say, you need to choose the right word. For example, useful, beneficial and advantageous. Maybe considered synonyms, they all have the same meaning, yet these three words are not interchangeable. You cannot use any of these. You cannot say that I will use either one or the other and the meaning will remain the same. Let's have a look at what I mean. If you say she suggested a useful compromise, then what you're implying is that the compromise allowed the parties to get to work. It was useful and work could begin. On the other hand, if you're saying she suggested a beneficial compromise, then you're implying that the compromise not only revolved, but also had a positive effect perhaps for both parties. It was beneficial and perhaps it was beneficial for both. In the third instance, if you're saying she suggested an advantageous compromise, then you're implying that the compromise benefited her, the person who suggested it, or her company much more than it benefited the other party. So although all of these useful beneficial advantages, all of these have a similar meaning. Their use makes their meaning very different. So you need to be careful of that as well. What is the word you're choosing and what is the implication of choosing that particular word. Another way semantics can affect persuasive messages is the variety of meanings that people attribute to certain words. This means that there may be words which can have more than one meaning. We just saw that there were two or three words and their meaning was the same, but their meaning changed in their use. Similarly, it can be that there are multiple meanings. So you need to make sure that you're actually choosing a word where the meaning in which it is to be used is clear because abstractions are subject to interpretations because they refer to things that people cannot experience with their senses as well. Also you need to keep in mind that abstractions are subject to interpretations because they refer to things that people cannot experience with their senses. So basically if you're talking of abstract things, if you're talking of things which are not tangible, then you need to be very careful in how you refer to them because they will be interpreted differently by different people. The things that are tangible and the facts which can have the same meaning, everyone will have the same meaning. But the abstract things which can have different meanings, you need to carefully express them for them. You may be able to sell more flags by appealing to your audience's patriotism which may be interpreted in many ways then by describing the color and size of the flags for example. Obviously when a patriotism has a feeling, different people interpret it differently. You can sell flags or flags with any interpretation. But if you say that you are buying Pakistani flags and they have this color and they have this moon color then you will not be able to sell flags and no one will be able to motivate you to buy flags. But if you persuade them to appeal to their emotions and their patriotism then they will sell your flags for example. You may also have better luck collecting an overdue bill by mentioning honesty and fair play then by repeating the sum owed and the date on which it was due. Now if say you are a collecting agency or if you are providing a service for which you have not been paid the bill is overdue it would be more persuasive if you wrote to the customer and talked to them about fair play and honesty and just mention the amount and when it was due rather than stressing on the amount and when it was due because by that you are actually putting your customer at guard and you are putting them off. But if you are talking about honesty and fair play then you are actually reaching out to their need to be approved off and everybody wants to be seen as an honest person. Everybody wants that other people consider them to be honest so if you include those things then you will include such words by which you will praise them and we know that you are an honest tax-paying customer but they stay on your side and you return them to us so it will have a more positive effect. Now you need to also remember that when you are organizing persuasive messages persuasion requires the indirect approach. We talked about routine messages in many places you can use the direct approach because people are happy by reading routine messages but in persuasive messages you have to use the indirect approach because it is not necessary that you want to persuade them to persuade them immediately. One specialized version of the indirect approach is the AIDA plan. This basically means attention, interest, desire and action. In the attention phase you convince the audience right at the beginning that you have something useful or interesting to say. You don't say what it is but you catch their attention you let them know that what is to be followed will be interesting and useful. The audience wants to know what's in this message for me without making extravagant claims or threats and without bringing up irrelevant points. Obviously an audience wants to know what's the benefit for me when they read a letter. So you won't make extravagant claims or talk too much but to the point you will tell them what's the benefit of your actions. For example, if you say something like you've mentioned several times in the past two weeks that constructing an employee schedule becomes increasingly difficult. Let me share an idea that could substantially reduce the time you spent making and revising the schedule. Now in this message as you see you are actually as the writer you're actually letting them know letting the reader know that you're going to be sharing an idea that will reduce their time. So you are actually catching the audience's attention and letting them know that what will follow will be beneficial to the audience. In the interest phase you explain how your message relates to the audience. You will continue the theme that you started with and by doing that you paint a more detailed picture with your words. Your goal is to get the audience thinking. This is an interesting idea. Couldn't it possibly solve my problems? So in the attention phase you've identified what it is that you're going to be talking about you've caught the audience's attention. In the interest phase you are now getting them interested in your way of thinking and you are actually getting them slightly getting them a bit towards what you want them to be. For example if you say something like Incorporated Magazine ran an article in the July 2 issue about a scheduling concept called FlexTime. It gives employees leeway to schedule their own work within certain guidelines. Two companies profiled in the article were having problems as we have been with late arrivals, long lunches, early departures and too many sick days. Everyone would adhere to however once these companies instituted FlexTime their problems practically dissapeared. The same message we saw how they started the interest, the attention of the readers is the next section in which they are giving details. They are developing some interest in their audience and they are talking about a concept that can be solved. Now this interest section ties together a factual description and the benefits of instituting this FlexTime program. Also the benefits relate specifically to the attention phase that came earlier to this paragraph that we looked at earlier as well. And even though the FlexTime system might help improve employee morale that benefit is secondary to the main interest of the intended audience and that is to reduce the frustration of devising useless schedules. And therefore employee morale is not mentioned. So now let's see how they meet the needs of the audience that they have mentioned. The audience that they were going to read that time is not wasted. That is why they have highlighted the other benefits of this program by adopting it. In the third phase the desire phase of a persuasive message you back up your claims and thereby you increase your audience's interest and your audience's willingness to take the action that you will suggest in the final in the next section. So you are making sure that you are backing your claims. You are toasting them and your audience is coming closer to getting persuaded. Whatever you use to prove your claim, make sure that the evidence is directly relevant to your point. Don't use evidence that is irrelevant. Now as you see in this example, the writer has continued talking about what he was talking about earlier. He is still referring to the articles that were profiling that had adopted Flexitime and here he says, one of the people interviewed in the article, the head of manufacturing for a $10 million company said, I seem to be spending all my time making schedules and then tearing them up. Now I let my employees figure out their own schedules. I have more time to oversee the work that is being done and to track the quality of the products we ship. Now as you can see, this information has been added that the head of manufacturing has been quoted in the interview and he has only put the same thing in the interview which was relevant for the reader to understand how the head of manufacturing saved his time. Let's continue this example. It says, this company had a Flexitime program in full operation within three months of deciding to start. Attached is a copy of an article about the factors to consider before going to work and the three steps involved in instituting it. Now whatever detail was further necessary to actually implement the program has been attached. It has not been listed detail in this letter because then the letter would become too long. So the attached information has been given as an attachment and it has been referred to in the letter. In the action part, you suggest the action you want your audience to take. These are persuasive messages and with a section that urges specific action but the ending is more than a statement such as institute this program as soon as possible or send me a refund that you need to give much more than that. In fact this section offers a good opportunity for one last reminder of the main benefit that the audience will have from taking the action that you want them to take. This is a good opportunity for you to remind your audience that whatever you want them to take step by step what will be the benefit. This is the closing section of this message. Let's meet early next week in brackets Monday 3pm with a question mark because the writer is not sure if that time is actually convenient to his colleague or not. To see how we might implement a flex time schedule with a little bit of effort now you could soon be concentrating on something more important than scheduling. So here the writer is suggesting action he's suggesting time for a future meeting where they could discuss adopting this procedure because obviously he's trying to persuade the reader to adopt flex time and again he in the end he also gives one last benefit one key benefit that the reader will have more time if he adopts flex time Now many persuasive messages are written to solicit funds, favors, information or cooperation. A lot of times it happens that you need some kind of cooperation or you need funds or favors from the reader and in an organization persuasive techniques are often required to get someone to change policies or procedures to spend money on new equipment for example and service to promote a person or to protect territory of a person within an organization so all these could be different reasons for writing a persuasive message within an organization there's a difference between internal persuasive messages and external persuasive messages internally within an organization personal messages, persuasive messages or external persuasive messages the function will be different or their style or organization will be more formal an external persuasive message is one of the most difficult persuasive tasks you can undertake firstly people are busy so they're reluctant to do something new it takes time and it offers no guarantees, offer reward in return they don't know you, they need to take out a lot of time to actually take the action that you want them to take secondly there are a lot of competing requests a lot of for example if you are trying to persuade a company or somebody who is not part of your organization but somebody outside of your organization to give you funds then that person might have a lot of other people requesting him or her for funds as well so you'll have a lot of competition and in fact public relations departments many large corporations receive so many requests for donations to worthy causes that they sometimes resort to lotteries to decide which one to support they'll just take a pic do a lucky dip and decide which one to give the money to or give the donation to rather than actually looking at each application or each request separately so in that sense when your persuasive message tends to be more difficult to write if it is to solicit funds or favors from an outside organization if you're lucky the company might believe in the project or cause that you're trying to persuade them about and also they might feel that it gives them some benefit to be involved in that or to comply with your request as well and that then is the best use of your persuasive message that then is the best result you can hope from your persuasive message this is more effective in the case of requests for professional favors or information because people may believe that they're obliged to pay their dues by helping others if you can persuade people that by helping you they also have the benefit and they have an obligation then it can be possible that they are ready to help you and you can benefit from it so this is when you're making a persuasive request take special care to highlight direct and indirect benefits to the reader direct benefits might include a reduced workload for a supervisor who institutes flex time or a premium for someone who responds to a survey in the first case someone has a benefit in the second case if you're serving outside of your organization you'll have a survey questionnaire indirect benefits might include better employee morale or the prestige of giving free workshops to small businesses in this case also better employee morale in that case is that you have to persuade someone inside of your company and if you're persuading someone outside of your company to give your business a free workshop what will be the benefit of doing a free workshop so you have to highlight that it will be prestigious to give your company a free workshop when you want to write a persuasive message for action or a persuasive request for action then the attention getting device at the beginning of a persuasive request for action usually shows the reader that you know something about his or her concerns and that you have some reason to do a persuasive request if you're asking for action then you have to show your reader that you know something about his or her concerns and you have to show that you have some reason behind these requests and in this type of a persuasive message more than in most others a flattering comment about the reader is acceptable especially if that comment is sincere the body of the letter or memo covers what you know about the problem you're trying to solve with your reader's help it talks about the facts and figures the benefits of helping the benefits to your reader and also your experience in attacking or tackling the problem the goal is to give you and your request credibility to make the reader believe that helping you will indeed help solve a significant problem the most important thing to remember when writing a persuasive request action is to keep your request within bounds actually nothing is so distressing as a request so generally all encompassing are so inconsiderate that it seems impossible to grant how worthy the cause is whatever your cause is your request should be manageable to grant don't make such big unrealistic requests which cannot be fulfilled because to not do a request even distressing the reader should turn down a request request should be done not to do a request be careful not to doom your request to failure by asking your readers to do all the work for you don't ask your reader to provide all the information that you need just because you are too lazy to seek that information or to spend time to save you from embarrassment or inconvenience or to provide total financial support for a cause that nobody else is supporting because if you're going to make these kind of unrealistic inconsiderate requests then obviously your request is bound to fail another type of persuasive letter is a sales letter by and large sales letters are written by specialized and highly skilled professionals the letter sales letter comes in letter size or larger envelopes with brochures or without brochures and you as a skilled professional letter writer need to know the laws that govern sales letters because this can help you avoid serious legal problems if you do not know the laws of writing sales letter then you need to familiarize yourself with them also you need to be very very clear that making a false statement in a sales letter is fraud if the recipient can prove A that your intent was to deceive or that you made the statement regarding a fact rather than an opinion or speculation the false statement or that the recipient was justified in relying on the statement and also if the recipient was damaged by the statement then all this amounts to fraud or even one of these even one of these can be proven then they amount to fraud also using a person's name or photograph or identity or any other form of identity in a sales letter without permission from that person constitutes invasion of privacy there are some exceptions but generally if you are going to be using any person to promote your product then you need to have their permission written permission to use their name or identity or photograph in your promotional material or your sales letter because without this is illegal there are exceptions for example using the photos of members of a local cricket team or football team in a mailing may be legal if the team members are public figures in the community but otherwise you will need specific permission from people legal problems can also result from publicizing a person's private life in a sales letter so stating that the president of a local bank and if you mention that bank by name serve six months in prison for income tax evasion is a potentially damaging fact to that person and to that bank and this may be considered invasion of privacy even if that bank is your rival and you want to show how much better you are ethically and how much better your organization and the people working in your organization you cannot malign other people what you are talking about is true when you are planning sales letters you need to keep in mind three steps and these are similar to those involved in planning any other persuasive message you need to determine the main idea in sales letters it revolves around a selling point and the related benefits you need to define the audience and you need to choose the approach and format now the main idea is selling points and benefits selling points are the most attractive feature of a product whatever it is that is most attractive about a product is what becomes its selling point obviously whatever is the most attractive thing in a product someone will buy it consumer benefits are the particular advantages that buyers will realize from these features whatever features there will be selling points and the benefits will influence the consumer to buy the product for example one selling point of a personal computer might be its numeric keypad the consumer benefit of this selling point is that the user does not need a separate calculator or the skill to type numbers on the regular keyboard so obviously you cannot write about selling points without a thorough understanding of your subject so whatever you are telling about a selling point there should be some benefit for the consumer because when the consumer sees that benefit then they will be ready to buy your product and to highlight that benefit until you have complete knowledge of your product then you will not be able to explain the selling points and the benefits the first step in writing any sales letter then is to take a good look at the product if you have your own product then you should understand what you are selling ask yourself or someone else if necessary everything you think a potential buyer might want to know about your product what kind of information a potential buyer needs if you are not able to understand then ask yourself if you want to sell this product or if you want to buy this product then you will see what kind of information the audience needs then you will give them information and this defining of the audience's needs is basically defining the audience once you are aware of their needs then you will define the audience in terms of who the audience is who are the type of people who will be buying your product marketers seek to define consumers in terms of demographics which means age, gender, occupation income and education and also in terms of psychographics which means personality, attitude and lifestyles by looking at these things you will classify them as demographics you will categorize your audience or according to psychographics your audience's attitudes personality, beliefs lifestyles you will target them or you will look at their age group or it is possible if you are doing it according to demographics you will see for women of a specific age group if you have designed a product then you will see their psychographics that now in these women in this particular age group generally what type of lifestyle what type of personality is there so you have to look at demographics and psychographics side by side so that you can define your audience in this lecture we learnt to strengthen persuasive messages with the appropriate appeal we learnt how we can gain credibility by supporting our persuasive messages with relevant facts we do not include irrelevant facts because our message gets weak from them we also talked that in our persuasive messages we have to look at interest, desire and action the AIDA plan so that we can organize our persuasive messages according to this plan we also talked about writing a message to persuade your audience to take action or to grant a request or to grant an adjustment and we looked at how to do that what kind of language to use what kind of layout to use and we looked at how to design a sales letter around selling points and benefits of the product we looked at defining the audience and keeping in mind the audience their demographics and their psychographics how we would sell a product to that audience with this we come to the end of this lecture on persuasive messages until next time, Allah Hafiz


We're live. So what we're talking about today are rates and ratios. It's a bit of vocabulary. I don't think, Shay, that I'm going to specifically say to you on a test, define a rate or define a ratio, but I will be using those words in context and expecting you to know what I mean by them. So you are going to need to know this, investigating the difference between rates and ratios. And it starts out, paragraph says, new at a stats agency did a survey of some Canadians and they asked the following question, how many text messages do you send per day on average? You can actually find the survey online if you feel like typing in that huge long HTML link. I don't feel like typing in that huge long HTML link. What they found was between ages of 18 to 34, on average, that age group sent 23 text messages a day. Figure out what page we're on now? Okay. Those little things that make a difference. Page number. Right? Eyes open. Breathing. You'll find the road to success involves all three of those, I'm sure. Okay. So they found on average 23 text messages a day between the ages of 18 to 34. By the way, your age group, do you think more than 23 per day or less than 23 per day on average? Okay. What about an ages 40 to 50? My age group? Not too many. Yeah. We're still mostly emailers if we're going to communicate electronically. I do have a feeling though, I won't be surprised if this number starts to go down because everyone's getting smartphones and you're really limited with the text messages. How many characters are you limited to in a text message? Emily? 140. Why? It's related to a second question. How much does it cost a cell phone company to send a text message? Not how much does it cost you? How much does it cost a cell phone company to send a text message? This was a question that two profs from the University of Kansas asked about three years ago, just when text messages were starting to explode and cell phone companies which used to offer them for free started charging money for them. They asked, well, what's it costing a cell phone company to send a text message? Do you guys know what it costs a cell phone company to send a text message? Sorry? Nothing. And it's related to the 140 characters. Your cell phones, if they were turned on, which I'm sure they're not, if they were in my class, which I'm sure they're not, but your cell phones are constantly sending out a signal looking for the nearest cell phone tower. And when they get a signal from a cell phone tower, this little handshake procedure that goes on, the cell phone tower identifies itself and the cell phone identifies it to the cell phone tower. It's sending those signals out no matter what. But it turns out those signals have a tiny bit of extra memory left over in them. Would you care to guess how many characters of extra memory those signals have? 140. The signal that they built into cell phones when they first brought cell phones in 15 years ago, that they budgeted into your bill back then already, that signal has room for 140 extra characters. They piggyback your text message on there and it costs them nothing because they charged you for it already, except now they're charging most of you for it again, aren't they?  In fact, sue the cell phone companies. Please, it's a ripoff. Should be free because it doesn't cost them anything. You guys know that? Be angry with your cell phone company. Demand better service. I think we get lousy service here in North America. Having said that, end of rant, back to math. Prompted by this survey, Rachel and Sarah decide to record the number of text messages that they sent per day and they do it on Wednesday, Thursday and Friday. It's for a communications technology project. Here's what they find. Rachel sends 46 on Wednesday, 38 on Thursday, 81 on Friday. Sarah sends 23 on Wednesday, 40 on Thursday, 54 on Friday. By the way, why would Friday spike like that? Do you think? Yeah, probably getting ready for the weekend people making plans or whatever, okay? We can interpret some of this data. Here is our vocabulary. Vocabulary number one, Sierra. A comparison of one number to another number with the same units is called a ratio. I would underline the word same units and the word ratio if I was someone who had purchased the book, which most of you have for our planning. Did I say Sierra or Sienna? Did I call you the right name, Sierra? Again, phew. If you're comparing two things and they're the same units, they're the same type of object, we call that a ratio. As compared to the ratio of text Rachel sent on Friday to the number of texts Sarah sent on Friday and write it either as A colon B or A over B. Well, this is meant to be fairly fill in the blank simple, so don't be insulted. How many texts did Rachel send on Friday? Read the chart. How many, 81? So the ratio would be 81 to, how many did Sarah send on Friday? Except traditionally, we will always express a ratio in lowest terms. 81 to 54 is not in lowest terms. What number goes both into 81 and 54? The first thing I thought was nine, and so when I went divide by nine, divide by nine, that got me nine to six, and then I went, oh, actually, apparently, something else still works. In fact, 27, and if you know your 27 times table, some of you may have seen that right away, but the point is you don't need to know your 27 times table. You can't whittle away at these with twos and threes and fives until you get them in lowest terms. Yeah, the ratio is three to two. For every two text messages that Sarah sent, Rachel sent three. You could also write it as a fraction, three over two. I've done a rant about buying a good calculator in this class, yes? Some of you may want to experiment with your fraction button. Now, if you have a fraction button and a good calculator, it looks like this, probably. It looks like a button like that, maybe. Or it may just be a divided by, let me show you what I mean. On my calculator, my fancy schmancy graphing one, if I go 81 over 54, if I hit enter and then I hit the math button twice, it gives me the fraction in lowest terms automatically, which is kind of nice, actually. Let's me know that I haven't made a dumb math mistake on a test or a quiz. Some of you with your fraction button, yours may do that, too. Play around with it, read the manual, not during the lesson, but if you have a fraction button that looks like that or you're wondering later on, call me and I'll see if I can figure out how yours works again. If you paid for the technology, I have no problem if you use the technology. Marcus, 81 over 54, enter, press math and then just go enter, enter. That's the fraction to decimal button is the really quick way to do it. Really handy, actually. Pardon me? Oh, we can fill an ocean with what you did not know, believe me. You ever watch Star Trek? Those things are almost tricorders. You can plug probes and temperature sensors and all sorts of things into those. In fact, technically, those aren't called calculators. They're called handheld computers if you actually look at the specifications for them. B, B says write a ratio in reduced form, comparing the number of texts that Sarah sent on Friday to the number of texts that Rachel sent on Friday. Again, this is meant to be fairly fill in the blankish. If the ratio of Rachel to Sarah was three to two, what is the Rachel of Sarah to Rachel? Two to three. The point of that Devon is the order matters. Write what they said first, first, and what they said second, second. Don't write it the other way around or you'll get marked wrong. C says compare the ratio found on A to the one on B. Is there a difference? Well, the order matters, but otherwise it reduces to the same thing. So ratio, same units to same units, same type of object to same type of object comparison. Then we have our second vocabulary words, a comparison of quantities which cannot be expressed in the same unit is called a rate. What's the speed limit on the low heat highway between pit meadows and the pit bridge? What? Kilometers per hour. That's a rate because kilometers and hours aren't the same units, but the per is like a divided by the diffraction. We use rates all over the place. Any time that you give a speed, that's a rate by definition. Any time you're comparing something to time, you're almost always talking about a rate. So Rachel sent text at a rate of 165 texts in three days. Where the 165 come from, we added Rachel's up. Express the total number of texts Sarah sent over three days as a rate. Again, this is meant to be kind of fill in the blank ish. How many texts did Sarah send grand total? Can someone add that up, please? Well, 54 and 40 is 94 and 20 is 110 and 317, yes? So if we wanted to express that as a rate, we would express it as 117 texts in three days. These we almost always write as a fraction. In fact, in English, we'll often say the word per and that implies a fraction. And you can see Taylor, not the same units. Most people, they'll look at that and they go, well, that's stupid, 117 texts in three days. Most people would express this as a unit rate. A unit rate is how many texts per one day or how many kilometers per hour. That 80 kilometers per hour is a unit rate. You could say, well, it's 160 kilometers every two hours, which is true, but no one says it that way. We always want the unit rate. So part two says a unit rate is a rate expressed with the denominator of one, we know, ins. Express the total number of texts Sarah sent over three days as a rate per day. How would I write this as a rate per day? What would I do with that three? I want to turn it into a one. How can I turn a three into a one? And maybe the answer is too obvious. Divide it by three and same to the top. Anyhow, what's the unit rate? How many texts per day does Sarah send? Thirty-nine texts per. So the next logical question is how many does she send in a month? E. If she continues to text at the same rate, and we have to assume that she is, how many texts would she send in one month, and we'll assume a month has 30 days. I know summer 31, February 28, let's assume a month has 30 days. I want you to notice something. Remember the unit analysis thing that I did last class, where we built this fraction change and we canceled out the units? I want you to notice, it works here too. I can write down 39 texts in one day times three, times three, Mr. Dock, sorry. How many days are we talking about here? Times 30 days, Shania, take a look. Technically, the days would cancel with the days, because one's on the top and one's on the bottom. And what's the only unit that's left kicking around? You're going to get an answer in texts. If you don't know, because the most common question kids have is, so I love the fly or do I divide with a 30? You can actually get the units to tell you. If I divided, the 30 would be on the bottom, and I'd end up with days, days, which doesn't make a days squared, which doesn't really make much sense. If you're not sure, the unit analysis approach can bail you out. Now, I think almost everyone here was saying, Mr. Dock, when you just go 39 times three, yes, 39 times three, 40 times three would be 1200. So 39 times three is going to be 30 less than that, 1,170, someone check my math, yes? Same units, rate different units, turn the page, or next page over. How many of you are planning on buying the book or have already bought it? If you are, this page right here where it says rates and ratio summary would be a good one to either dog here, the corner, or put a little post-it note there or something. When you're studying for this unit test, which is not stuff on Thursday, but when you're studying for this unit test, this would be one of those where you would say, I better read this and make sure I know all this because this is a summary. One of the things I do like about these books is they have summaries fairly frequently. So what I've just talked about for 20 minutes, it's all summarized right there. I'll let you read that on your own time. Then we're going to change gears a tiny bit. It says using proportional reasoning, unit analysis, and unit rates to solve rate problems. Many rate problems can be solved using proportional reasoning, unit analysis, or unit rates. Really a lot of them can be solved with cross-multiplying and building those unit analysis chains. For example, Kim and Cole were given the following problem to solve. Here's the problem. Tommy purchases three bottles of vitamin water for $4.95. After paying, he gets a text message from his wife informing him that some more of his friends are coming to visit. He goes back into the store and he purchases four more bottles. What's the total amount he paid for the seven bottles of vitamin water?    Right? This is somebody somewhere thinking to themselves, I need to give these students an application problem. Oh, here, this is in a store. And so that must mean it's an, I would never do math this way. I really hate these kinds of questions. I'm going to do it because it's here and it's in the notes and it's on the curriculum.  I wouldn't care if I bought three and I bought four and I needed to know how much I'd paid. I'd look at my receipt or I'd see how much money I had left in my wallet. There's a bunch of different ways that I'd answer this question. I guarantee I would not cross multiply and divide. Having said that, rant over, apparently they want us to use algebra to solve this. Fine. Here's what it says. Kim solved this using proportional reasoning. She said this, 4.95 for three bottles is X dollars for seven bottles. And that works. We said that was one approach that you could use last class. I have one fraction equals one fraction. How would I solve this equation when I have one fraction equals one fraction? Two words that you learned from math eight. Do you remember? Yes. Let's all write down so that we're still awake, cross, multiply. And those five of you in the back row that are slouching more and more and more, try setting up because I'm telling you the slouching won't help you pay attention. It'll make it worse. Not that I'm mentioning any names. When I cross multiply, it's this times this equals this times this. But they've actually done two steps at once. Liam, they've gone cross multiply. They knew there was going to be a 3x on the other side, and they knew to get the x by itself. I'm going to divide by the 3. So they went cross multiply and divide. Oh, they would have gone this times this. I think there's a 7 there. They want us to kind of fill in the blanks. How much money was it for seven bottles? X. How much is X? Get your calculators out. Somebody go 495 times 7 divided by 3. 5 times 7 is 35 divided by 3 is 11.6 repeating. I'm going to go with $11.60. Am I close? Alex, I'm close, $11.55. By the way, you can also see Alex. Even if you forced me to do math like that, I'd estimate and do it in my head. I wouldn't re-prick you.  I've gone on a big rant on them in other locations. That's one way to do it. Another way, Emily, is to convert to a unit rate. So Cole said this. Well, look, it was 495 for three bottles. How much for one bottle? Can someone go 495 divided by 3, please? A buck 65, even? And if it's a buck 65 for one bottle, how much for seven bottles? What would you do with this number? And that's what they want us to write here. They went 7 times a buck 65. And you get an answer of also $11.55. Once again, I don't care which method you use, Devin. I do want you to notice here, though, for what it's worth, Aaron, that in both methods, somewhere along the way, you times a 7 and a 495 and divided by a 3. You times the 495, it's on top. And the 7, it's on top. And divided by a 3. It's just that here you divided by 3 first. Which way is the best way? They both are fine. Whichever you like better. Couple more we're done. Turn the page. This one I can at least say is marginally more useful. Sometimes I do like to know if I've spent more or less than the year before. So here's what this one says. Paul hosted an annual wrap-up party for his hockey team last year. This year he's hosting the party again. Woo-hoo! Hopefully not a Game 7 Stanley Cup riot. And like last year, he'll be serving prime rib roast. Last year he bought 8 kilograms for $173.12. This year he paid $10.13 per pound. Says use unit analysis to figure out which rib roast was more expensive at the price to up or down this year. At least I can say that's a bit more of a useful question. And since there's a last year end of this year, I think the first thing I would do is this. Draw a line down the middle of my page. This is going to be last year.  Read the question carefully, please. So last year he spent $173.12 per. And how many kilograms of roast did he get? Let's change that to a unit rate. $173.12 per eight kilograms is how much per kilogram? $21.64, round it off properly? Or did it work out evenly? Worked out evenly? $21.64 per kilogram. What did he pay this year? Matt, what's it say? This year he bought the roast for? What? See it there, kiddo? This year he bought the roast for? Nope. OK. Oh, you got it. For what? Pound. This is in kilograms. Here we're going to do a little bit of math. So I'm going to write down $10.13. Now the abbreviation for pound is still this, LB. But it's falling out of favor. You know what they're using to abbreviate pound with now? Oh, techie people who text message? Oh, you all do. What's the pound key? What's the pound key on your phones, boys and girls? Huh? There is a pound key. What? Matt, that number key is called the pound key. That's why you hear them sometimes say you guys don't drive. If there's a traffic violation called pound 11.30, and that's a free cell caller on your star net or whatever, it's slowly being replaced with the number sign, which I think is better. Anyways, I'll still use LB. How the heck LB? It means pounds. I'll never know. Here's what I'd like to do. I'd like to change this to dollars per kilogram. I need to change pounds to kilograms. And to do that, I'm going to use that dimensional analysis trick. I'm going to multiply it by a conversion factor. I want to end up in what, Adam? Where is pounds right now on the bottom or on the top? So I better put pounds on the top so it'll cancel and kilograms on the bottom. And that'll help me end up with kilograms on the bottom. And they gave me a conversion factor. Read that to me, Adam, my friend. I guess the 2.2 goes next to the LB. And the 1 goes down. And you know what? In fact, I think it's going to be $10.13 times 2.2 divided by 1 divided by 1. But am I going to bother doing the divided by 1? No, if there's a number there, I would divide by whatever number was there, but 1. OK, what's the unit rate per kilo for 10.13 per pound? Courtney, what'd you get? I thought you looked good. So last year was 21.64. I'm going to guess it's going to be close to 21.64, like in the 20s somewhere. What'd you get, kiddo? That times that, 10.13 times 2.2. Let me see what do I get. 10.13 times 2.2. Is that OK? Do you get that? And rounding off properly to, you know what? 22.29. 22.29 per kilo, which was more expensive, Joe, when you're done yawning. Last year or this year? Yep, you awake? Ah, nothing. Wait for it, wait for it. Now you've got the adrenaline rush, right? Ah, I feel good now. The last one.  Most of you will buy a house someday. And for almost all of you, it will be the single biggest purchase you ever make by a long shot. What many of you don't realize is buying the house is only the first part of the fund. As soon as you own it, specifically as soon as you own the land, you get charged tax, property tax. So here's how it works. Property owners are required to pay property tax on an annual basis every year. And there's various ways to calculate the tax. This is the simplest way. Most municipalities don't use a method this simple because they want to charge you more money because governments want to charge more taxes. So the property tax amount is based on something called the mill rate. And it's called the mill rate because the number is expressed in mills where one mill is 1 tenth of a percent. It's sort of like millimeters and milliliters. There's a mill rate. And the assessed value of the property, in fact, this is the basic formula that they use. Property tax equals your assessed value, what your house is worth, divided by 1,000 times the mill rate that year. That's way too much writing, way too much writing. I'm gonna rewrite this as a formula, but I'm gonna use letters. What would be a good letter to use for the phrase property tax? I'll give you a hint.  What would be a good letter to use for the phrase property tax? P or T? Let's use P for property tax. Ah, you know what? It's property tax, let's use T for tax. T, write this down, equals. What would be a good letter to use for assessed value? V, you say? Over 1,000 to still 1,000 times. What would be a good letter to use for the mill rate? So apparently to figure out your taxes, the value of your house divided by 1,000 times whatever the mill rate is that year. Let's look at part A. Charlene paid $1,924.39 in property tax last year when the mill rate was 4.6038. What's her home's assessed value? So take a look at this equation here, this little formula. Are they asking me in part A to find T, V, or M? Read the question carefully. Are they asking me to find T, V, or M? V, that means they told me everything else. So read the question, what's the tax? Can't tell whether you're dead or confused. I think dead. Ah, nothing. Danielle didn't even twitch that time. Okay. Yeah, Danielle, I think the tax is $1,924.39 equals. We're trying to find the value divided by 1,000 times. What's M, the mill rate according to this question, Boston? What's M, the mill rate according to this question? Read, my friend. Yes, 4.6038. Let's get the V by itself. I'd like to do this in one step, so you're ready. What's the 1,000 doing to the V? Adding, subtracting, multiplying, or dividing? Dividing, so how will I move it over? What's the opposite of dividing by 1,000? Timesing. What's the 4.6038 doing to the V? Adding, subtracting, multiplying, or dividing? Timesing. What's the opposite of timesing by 4.6038? How will I move it over to the other side? There's your equation solving very, very quickly. I think you're gonna get this. I think the answer is going to be the value is $1,924.39. Alex, if I'm correct in hearing you, I would times by 1,000 and divide by 4.6038. What was this person's house? What was Cindy Charlene's, sorry, what was Charlene's house assessed at? And by the way, if you want the shock of your life, if you haven't already, if your parents are okay in telling you, ask them how much they pay in property tax, it's stunning, you think. Well, they own the home, how can they tax it? They don't need to have rules that make sense for taxing. They'll still tax you. What'd you get? It's in the hundreds of thousands, I think it's over 400,000, if I'm roughly in my head. What'd you get, Emily? Four, read me the digits, four, so three, five, because we'd go to dollars and cents. Yeah, her house was assessed at a little over $400,000, $418,000 and 35 cents. Is that a reasonable answer? Is that what houses are worth roughly give or take? Yeah, they're in the hundreds of thousands. B, the last question, no cheer. B asks, B asks, how much does her property bill change for the current year? If her property is assessed 10% lower and the mill rate increases to 5.2113, okay. First question is this. What are they asking me to find in this question? I think they're asking me to find T. In fact, I think they want me to find the increase, which means I'll find T and then subtract it from last year's tax. But they want me to find T, which is this equation right here. Let's write it down. T equals V over 1,000 times M. You gonna be okay, Boston? You can deal with the distraction? Sure, okay. Boston, once again, since you did so well last time, what's M, what's the mill rate in this question? 5.2113, and this is gonna be a 1,000 on the bottom here still. The real question is, it says her current property value is 10% lower. If I lose 10%, what do I have left as a percentage? 90, put your pencils down and look up. Don't write this next little bit down. I think what we wanna put here is 90% of, need more room to write, $418,000.35. That's what's going to go there. The real question is math eight review now, how do I find 90% of a number for a candy? Who can remember? What about 0.90? Boston, you just, hang on. You just impress me. Not a boy. First of all, you can't do math with a percent. You always have to make it a decimal, and 90% is 0.9. You learn the trick of dividing by 100 or moving the decimal place over two spots. And if you want a little trick of the trade in math, the word of means times. How much tax this year? 0.9 times that, times that, divided by 1,000, get your calculators out. I'd like to know how much tax we're paying this year. Marcus, what'd you get?  I'm getting $160 and 49 cents, sorry, 1,960 dollars and 49 cents. Okay, 1,960 for, 1,960.49. And I'll add the units dollars. How much more than last year? Go that minus that. We're not gonna bother. What's the whole point of this? Rates and ratios and unit rates and cross-multiplying are your friends. They're handy. Turn the page. What's your homework? Your homework is as follows. Number one, number two, three A, sorry, not number two, three A but not B or C. Number four, number five. With me, Devin. Yeah, I know. That's why I'll come back to it and make fun of you when I do. Okay. Six A and B, seven. Number seven is asking which of these two answers is correct and why? Cause one person got nine minutes and one person got 4.5 minutes. Eight yogis yogurt and nine. You had about a half hour left. You'll get it done easily in class and no homework in theory, except what is your real homework? Make sure you're prepared for the quest on Thursday. I'm gonna hit stop. Then I'm gonna take some, hang on, stop.