Line plot distribution: trail mix

- [Voiceover] The plot below shows the amount of trail mix in each of four camper's bags. So let's look at this. We see there's a dot for each camper's bag, and it tells us that there's one bag that has this much trail mix, one bag that has this much trail mix, two bags that have this much trail mix. If the total amount of trail mix in all of the bags were redistributed so that each bag contained an equal amount of trail mix, how much trail mix would be in each bag? All measurements are rounded to the nearest eighth of an ounce. So right now the bags, there's different amounts depending on which bag you look at. But they want us to redistribute it. So what we really wanna do is think about let's take all of the trail mix in the four bags together, and then divide it by four so that they all have an even amount. So let's just think about how much trail mix we have in these four bags together. So we have this bag right over here, and it has this amount. And let's see, it says rounded to the nearest eighth of an ounce. Are these eighths? Let's see, this is one, two, three, four, five, six, seven, eight. Yep, so between two and three is divided into eight sections. So each of these hash marks are an eighth. So this is 2 1/8, 2 2/8. So this is 2 2/8. Now 2/8 is the same thing as 1/4. You can divide two by two and eight by two, and you would get 1/4. So 2 2/8 is the same thing as 2 1/4. Now you have this bag right over here, and how much is in this bag? Well let's see, that is 1/8, 2/8, 3/8, 4/8, 5/8, 6/8. So that's going to be 2 6/8. Now 6/8, six and eight are both divisible by two, so if you divide them both by two, that's the same thing as 3/4. So that's the same thing as 2 3/4. 2 3/4. And now you have two dots right over at this point over here. So there's two dots that have this many ounces of trail mix. Well how many ounces is this? 3 1/8, 2/8, 3/8, 4/8. So that's 3 4/8. Well 4/8 is the same thing, they're both divisible by four. Four divided by four is one, eight divided by four is two. This is the same thing as 3 1/2. 3 1/2. And you see that this dot right over here, it is halfway between three and four. And so let's think about, let's list the amount of ounces in each of the bags. So you have 2 1/4 ounces. That's one of the bags. You have another bag that's 2 3/4 ounces. Then you have two bags, remember there's two bags here, that's what the dot plot does for us. We have two bags here that are 3 1/2 ounces. So 3 1/2 and 3 1/2. Now let me make sure that doesn't look like an exponent to you. 3 1/2. Now what was our strategy? What we wanted to do is redistribute all of the trail mix so that we have the same amount in each bag. So one way that you could imagine this is imagine everyone pouring their trail mix into a big pile and then dividing that pile into four, and then putting exactly 1/4 of the total into each bag. Then you would redistribute it so that you have the same amount in each bag. So let's add it all together. Let's create our pile. Let's add 2 1/4 plus 2 3/4 plus 3 1/2 plus 3 1/2. Well what is, let's see, two plus two is four. 1/4 plus 3/4 is going to be 4/4. So this right over here is going to equal to five. Another way to think about it, you could rewrite these. You could say 2 1/4, two is the same thing as 8/4, so this would be 9/4 plus, let's see, four times two is eight plus three is 11. Plus 11/4. Then you would have 3 1/2 plus 3 1/2, you might be able to say three plus three is six, 1/2 plus 1/2 is one, so it's going to be seven. But if you wanted to write it like this, you could write 3 1/2, that's two times three is six, plus one is seven. Plus 7/2 plus 7/2. So these are sometimes called improper fractions, although some people disagree with calling them improper fractions. These are just fractions where the numerator is greater than the denominator. But anyway, let's add all of this up. So 9/11, let me see what color I haven't used yet. Sorry, not 9/11, 9/4 plus 11/4 is going to be equal to what? This part is going to be equal to 20/4, which is the same thing as five. 20 divided by four is five, or you could say 20/4 is going to be five wholes. Then 7/2 plus 7/2, that's going to be 14/2, plus 14/2, that's this part right over here. 14/2 is the same thing as seven. Five plus seven. So in total, you have 12 ounces. Once again, I just did this as another way to do it, but you could have just said, look, two plus two is four, 1/4 plus 3/4 is another whole. So four plus one is five. Then 3 1/2 plus 3 1/2, three plus three is six, 1/2 plus 1/2 is one, six plus one is seven. So in total, you have 12 ounces. Now that's if you combine everything together, but now we wanna redistribute it into the four bags. We wanna divide it equally into four bags. So you just take your 12 ounces, let me do this in a new color, you just wanna take your 12 ounces and divide it by four. Divide it into four equal groups. Then you're gonna get three ounces per bag. So that's our answer. How much trail mix would be in each bag? Three ounces. And we are done.