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CCSS.Math:

the plot below shows the amount of trail mix in each of four campers bags so let's look at this and we see there's a dot for each campers 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 the bags there's different amounts depending on which bag you look at but they want us to redistribute it so what we really want to 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 this is it says rounded to the nearest eighth of an ounce and are these eight let's see this is this is one two three four five six seven eight yep so this the the the between two and three is divided into eight sections so each of these hash marks are 1/8 so this is 2 and 1/8 2 and 2 8 so this is two and two eighths now two eighths is the same thing as 1/4 you can divide two by two and eight by two and you would get 1/4 so two and two eighths is the same thing as 2 and 1/4 and now you have 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 two and 6/8 now 6/8 six and eight are both divisible by two so if you divide them both by 2 that's the same thing as 3/4 so that's the same thing as 2 and 3/4 it's 2 and 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 and 1/8 2/8 3/8 4/8 so that's three and four eight well 4/8 is the same thing they're both divisible by 4 4 divided by 4 is 1 8 divided by 4 is 2 this is the same thing as 3 and 1/2 3 and 1/2 and you see that this dot right over here it is halfway between 3 & 4 and so let's think about let's let's list the the amount of ounces in each of the bags so you have 2 and 1/4 ounces that's one of the bags you have another bag that's 2 and 3/4 ounces and then you have 2 bags remember there's two bags here that's what the dot plot does for us we have two bags here that are three and a half ounces so three and a half and three and a half now let me make sure that doesn't look like an exponent to you three and a half 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 I'm everyone pouring their trail mix into a big pile and then dividing that pile into four and then putting exactly one-fourth of the total in 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 and 1/4 plus 2 and 3/4 plus 3 and 1/2 plus 3 and 1/2 well what is what is let's see 2 2 plus 2 is 4 1/4 plus 3/4 is going to be 4 fourths so this right over here is going to be equal to this is going to be equal to 5 another way to think about it you could rewrite these you could say 2 and 1/4 2 is the same thing as 8 fourths so this would be 9 fourths plus plus you could plus let's see 4 times 2 is 8 plus 3 is 11 plus 11 fourths and then then you would have three and a half three and a half plus three and a half you might be saying it 3 plus 3 is 6 1/2 plus 1/2 is 1 so it's going to be 7 but if you wanted to write it like this you could write let's see 3 and 1/2 that's 2 times 3 is 6 plus 1 is 7 plus 7 halves plus seven halves so these are sometimes called improper fractions 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 not let me just in a color I haven't used yet so nine sorry not nine eleven nine fourths plus eleven fourths is going to be equal to what this part is going to be equal to twenty-four it's which is the same thing as five twenty divided by four is five or you can say twenty four it's going to be five holes and then seven halves plus seven halves that's going to be fourteen abs plus fourteen halves that's this part right over here fourteen halves is the same thing as seven five plus seven so in total you have twelve ounces and 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 hole so 4 plus 1 is 5 and then three and a half plus three and a half three plus three is six half plus half is one six plus one is seven so in total you have 12 ounces now that's that's if you combine everything together but now we want to redistribute it into the into the four bag so we want to divide it equally into four bags so you just take your 12 ounces let me do this in a new color you just want to take your 12 ounces you just want to take your 12 ounces and divide it by 4 divide it into four equal groups and then you're going to get three ounces / 3 ounces per bag so that's our answer how many how much trail mix would be in each bag three ounces and we are done