 So the topic is percents. So let's start first with a definition. A percent is simply means out of 100. So for example, if I have 37%, it really means 37 over 100. That's simple. Percent. Alright, we're going to go through a lot of different rules where percents, decimals, fractions. The first one is how to change a percent to a decimal. So I have 25%. I'm going to first off drop the percent, and I'm going to figure out where the decimal currently is since there's not a decimal. I know that the decimal follows right after the last value, which is the five. And then to change that percent to a decimal, I'm simply going to move that decimal two places to the left. So it now becomes 0.25. So 25% is the same thing as 0.25. So how do we change a percent to a decimal? You move the decimal two places to the left. Second example, or second rule. How do we change a decimal to a percent? So we have 0.95. We're just going to go backwards from what we just did. So we're going to take the decimal point and move it two places to the right this time. So it now becomes 95%. So I moved it two places to the right, and I added a percent sign. So to change a decimal to a percent, move the decimal two places to the right. All right. Now what if you want to change a percent to a fraction? This one is really simple. All you have to do is remember what percent stands for. It means out of 100. So 20% is really 20 over 100. And that particular fraction is fine. That is acceptable unless your instructor needs you to reduce that, and that fraction will reduce. So if you're asked to put that fraction in simplest form, you would want to reduce it. The largest number that will go into both 20 and 100 is 20. So divide the numerator and denominator by the 20. 20 divided by 20 is 1, and 100 divided by 20 is 5. So two possible answers, 20 over 100 or 1 over 5. So how do we change a percent to a fraction? It's simple. Just remember that a percent means out of 100. Now to change a fraction to a percent, there are two methods. The first method I'm going to use deals with proportions. So I'm going to take 10 over 30, the original problem, and I'm going to set up a proportion remembering what percent means. Percent means something over 100. So something is what I'm looking for over 100. And then I'm going to just cross-multiply. So 10 times 100 would give me 1,000, and set it equal to 30 times x, which is 30x. Now to solve this, of course we're wanting to solve this equation for x, 30 and x are being multiplied. So to undo that process, I'm going to divide both sides by 30. I'm going to grab my calculator and 1,000 divided by 30 will give us approximately 33.3. I'm going to use the wavy lines for approximately. And this other side of course just becomes x. So x is 33.3 percent. So 10 over 30 changes to 33.3 percent. So to change a fraction to a percent, you can just set up a proportion. Well there's another method. The other method isn't the method I really prefer, it's a little bit easier. You're going to start by taking the 10 over 30 and changing it to a decimal. So 10 divided by 30 would be approximately 0.333. And now that I have a decimal, I can easily change that decimal to a percent. If you remember from the previous rule, to change it to a percent, I'm going to move that decimal two places to the right. So this becomes 33.3 percent. So 10 over 30 again is 33.3 percent. And we get exactly the same answer we did in the previous slide. So to change a fraction to a percent, change the fraction to a decimal first, which is what we did here using the calculator. And then you can change that decimal to a percent by moving it two places to the right. Now the final rule is what if you're dealing with the percent of a number. And this is also really simple. So 20 percent of 16. The first thing, focus on the 20 percent and changing that 20 percent to a decimal. So currently the decimal is after the zero. To change a percent to a decimal, you move it two places to the left. So we now have 0.20. Alright, second thing, the word of typically with percents, the word of implies multiplication. And then the last thing, just drop down the 16. So we're going to do 0.20 times 16, which will give us 3.2. So 20 percent of 16 is 3.2. So what did we do? So to find the percent of a number, change the percent to a decimal, which is what we did here, and then you're simply going to multiply. And one other thing to remember, when working with percents, the word of implies multiplication. So you now have all the rules. Let's take a minute and look at two possible examples. So there are 55 students in a class. 25 of them work 20 hours a week or more at jobs outside of school. What percent of the students work 20 hours or more per week at jobs? So we're looking for the percent of students. So what do we know? We know that there are a total of 55 students in this class. And we know that 25 of them are working 20 hours or more a week. So first we can set up just a fraction to represent this or a ratio to represent this. So 25 out of 55 students are working. So 25 students are working 20 hours a week or more out of 55 students that are the total number of students in the class. So again, you have two options of how you can do this. First, I could change this fraction to a decimal. So 25 divided by 55 would give me approximately 0.45. And then remember, we can then change that decimal to a percent by moving the decimal point two places to the right. So that would give me 45 percent. So this is method one. And this means that 45 percent of the students in this particular class work 20 hours a week or more. Now let's look at method two. The other option would be to take the same 25 out of 55 students and set up a proportion. And remember, because we're talking about a percent, it's going to be something, which I don't know, out of 100. Again, to solve this, we just cross multiply. So 25 times 100 would be 2500. Set it equal to 55 times x, which is 55x. And again, to solve, we're just going to divide both sides by 55. So 2500 divided by 55 will give us again about 45 percent is equal to our value. So in both cases, we end up with 45 percent. One more example. Osteoporosis is a disease that leads to brittle bones and is partially caused by a lack of calcium. Each year, 250,000 people suffer osteoporosis-related hip fractures, about 15 percent of whom die after sustaining such fractures. How many people die each year after fracturing their hip? So there are two numbers that we need to focus on. The first one, we're talking about a total of 250,000 people who suffer from hip fractures. And then we're given that 15 percent of those die. So let's see if we can write this into a problem that makes a little more sense written out in words. So it's really 15 percent of how many die? Well, out of a total of 250,000. So 15 percent of the total is going to be the number that die. And this goes back to one of our rules. First thing, you want to take the 15 percent and change it to a decimal. So remember, right now, 15 the decimal places here, move it two places to the left, and we end up with 0.15. Then remember the word of implies multiplication. And then finally just drop down the 250,000. So it becomes a very simple multiplication problem. So 0.15 times 250,000 will give us a total of 37,500 of those who suffer from a hip fracture that will die. So that sums up her sense.