 We're going to go over some examples of solving proportions, and we're going to start with a simpler example and move to an example that seems more complicated. But you'll see that if you approach it the same way we approach this simple problem, you'll have an easier time with it. So if you buy a 5-pound bag of apples and it contains 11 apples, how much does one apple weigh? So if we look at 11 apples in 5 pounds and we want to know how much one apple weighs, we can set up this proportion. So we don't know how many pounds one apple is, but we can cross-multiply to solve. So we have 5 pounds apples equals 11x pounds. And we're going to divide both sides by 11 apples so that we're left with the x pounds. And we're going to be able to solve that and determine divided by 11 equals 1 apple weighs 0.45 pounds. OK, so if we know one apple weighs 0.45 pounds, we can solve this second part of the problem. If one apple has 95 calories, how many calories are there per pound? So we want to know x number of calories in 1 pound. And we know that there are 95 calories in 0.45 pounds. And we get that number because we just solved for one apple and knew that it was 0.45 pounds. So we're going to cross-multiply. 0.4 equals 95. Divide both sides by 0.45. 95 divided by 0.45 is 211 calories per pound. So you can see that we can use previous information that we had from the first part of the problem to solve the second part of the problem. But we're still just setting up proportions and cross-multiplying in order to solve them. So this is an example of something that's going to look a lot more complicated. You're going to look at a problem like this and not know where to start. But if you think back to your apples and your proportions, it's going to be not as complicated as it looks. So let's read through this problem. Transgenic animals are animals that have deliberately had a gene from another organism inserted into their genome. So these animals can then produce foreign proteins. The first medicine that was produced by transgenic animals is called antithrubbin. Antithrubbin is an anticoagulate protein. So it makes it so that your blood doesn't clot. The antithrumbin is used to treat an antithrumbin deficiency. So if people are born without this anticoagulant protein and they need it, they can take antithrumbin the drug. And it's produced by goats in their milk. And in a year, 150 goats can produce 100 kilograms of antithrumbin. So we know 150 goats can produce 100 kilograms of antithrumbin. So how much is produced in a year by a single goat? So we want to know if 150 goats are producing 100 kilograms in a year, how much is one goat producing? And so that big, long problem, you had to read it because you had to understand that the antithrumbin was being produced by goats. And it's important to know what you're dealing with. But really, when you get down to it, it's very similar to our apples. We can know that we have a certain amount and a certain number of goats. And we need to determine what amount is in one goat. It's produced by one goat. It's not really in a goat. So then you have 150 x goat is equal to 100 goat kg. You're going to divide both sides by 150 goats. And so this is going to cancel. So you're going to have 0.66 kilograms produced by one goat. You may want to convert that into grams. If you want to convert that into grams, we just use our 1,000 grams. Sorry, our conversion factor here. 1,000 grams is 1 kilogram. Get rid of the kilograms. And that will give you 660 because this is 0.7 grams of antithrumbin produced by each goat. So just like with the apple problem, if we have a second part of the problem, we may need to use that information to solve our second part of our problem. And in this case, we do. If a goat can produce 1,100 liters of milk in a year, how many grams of antithrumbin are they producing per liter? So we know that they have 667 grams of antithrumbin per year. And we've just been told in this problem is in 1,100 liters. And we want to solve to determine how many grams are being produced in one liter. So again, we're just cross multiplying the same as with the apples and the calories. It's just that we're using grams and liters and goats and transgenic animals to determine what proportions to set up. So we have 667 gram liters equals 1,100 x gram liters. We're going to divide both sides by 1,100 liters. Grams is equal to, and let me get my calculator, 667 divided by 1,00.606 grams. So in one liter of milk, each goat is producing 0.606 grams of antithrumbin. So you can see that even though you might be intimidated by the length of a word problem or some of the content of the word problem, oftentimes, if you just think back to your simple proportion solving, you'll be able to set up a proportion that can give you the answer.