The Percent Proportion

Today's lesson will be on the percent proportion. The key to remembering how to set these up and solve them is this big main idea of the fraction is over of equals percent over 100. The 100 never changes. And the percent is labeled by your symbol here. There is is your part. So if you hear parts and holes, this is where that comes into play. Divided by the whole. So when you're reading these examples, you want to identify these keywords is of percent and be able to highlight and organize the information. So number one says what percent of 15 is 12. There's a couple key things here. What percent that's our unknown. So if you're looking at your setup here, is over of equals percent over 100, the 100 always goes down. And it says what percent. So that's our X this is where you want to pay special attention to the of 15. And that is 12. So the word that's on the left hand side of the number is what tells you where it goes. So of 15, we'll meet the 15, go on the bottom. And is 12. It goes up top. Now, this looks like something that we worked with before. A proportion. So we are going to cross multiply to solve this proportion. So we have 12 times 100, which is 1200. Is equal to 15 times X, which is 15 X and then we divide by 15 to get the X alone. So our missing percentage, which is 1200 divided by 15, makes our unknown X 80. And we're talking about a percent. So we want to make sure we include the percent sign. That is the key to these problems, is making sure that our information makes sense. Now, for example, too, finding a part. So they want to know what number is 36% of 50. So again, the 100 doesn't change. But the pieces of information that we have this time are different. So we have 36%. So we put our 36 here. We chop off the percent sign. It's really not necessary. And we have this of 50. So of goes on the bottom or on the denominator. And we don't know what number is. So X would go where the is normally would go. So now that we have our proportion, we are going to cross multiply. And find out what the X could be. So X times 100 is a hundred X and 50 times 36 is 1800. Divide by 100. And make sure along the way that you were showing these steps. It's a big thing to get used to this. And when we divide that out, we get 18. Those are your first two examples. All right, let's look at example three. Finding a hole. So we have a 150% of what number is 24. So very much like how we read it is how we're going to set it up. So the 100th stays the same. And the percentage this time is one 50. It goes right above where the percentage would be. There is is 24, so is over of. Oh, wait. Of what number that is our X this time? So now we can cross multiply. 24 times 100 is 2400. Is equal to a 150 X now you can show that if you need to. That's fine. Divide by the one 50. To each side. And our X is equal to 16. Which makes sense because 24 divided by 16 is more than a hundred just like one 50 divided by 100. It's a little more than a 100% there. So our summary. So the key things that you have to make sure that you pay attention to is highlighting keywords. These keywords are your is. Of in percent. Okay, our last example today is a real-life application. The bar graph shows the strengths of tornadoes that occurred in Alabama in 2011. What percent of the tornadoes were EF ones. So if you look at your table here, we have a number of tornadoes on the Y axis and the strength on the X axis. And I'm looking for the EF one. So there are 50 EF one tornadoes. And I want to find out how many tornadoes occurred as a whole for this whole year. So this is our part. And all of these tornado numbers added together will be our whole. Okay, once we have identified our partner hole, the part is your is. And the whole is your of. So I'm going to set up my proportion. So my part for EF ones means I have 58 over those tornadoes in the year. And the total number would be 36. Plus 58. Plus 29. Plus the 13 plus the 7 plus the two. And when you add those all together in your calculator, you will get a 145. Let's put that in. So 50 out of a 145. Is equal to what person. Of 100. And we have our proportion. So we are going to cross multiply. And then solve for the X, just like we've been doing before. The key to these is making sure that you understand which is your part in which is your whole and taking your time and labeling everything that you need to label. So when we solve for that, we get X equals 40 and remember we're talking about percent. So 40% of the tornadoes. Are EF ones. Okay. That is the end of your examples for this section of our unit. What I want you to do is go to the next page in your packet. It complete number one to 7. When you're done with that, come see myself or the co teacher and then we will see how you did.