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Simplify a ratio from a tape diagram

In this problem, we have a mixture of yellow and red paint. There are 12 parts yellow and 8 parts red. We want to find the ratio of red paint to the total paint in the mixture. To do this, we add the parts of red and yellow paint together (8 + 12 = 20). The ratio of red paint to total paint is 8:20.  Created by Sal Khan.

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  • marcimus purple style avatar for user jamacker
    I don't get this
    (3 votes)
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  • aqualine ultimate style avatar for user Jem-Jem
    We're told that the following diagram describes the volume of yellow and red paint in an orange mixture. So we can see that for every 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 parts of yellow, we have 1, 2, 3, 4, 5, 6, 7, 8 parts of red. They ask us, "What is the ratio of red paint to total paint in the mixture?" So, pause this video and see if you can have a go at that before we do it together. All right, so if we wanna think about red paint, it looks like we have every, we have eight parts red paint, and if we think about the ratio of that towards total paint, you might be tempted to put a 12 there. But that's not the total paint, that's just the yellow paint. The total paint for every eight parts red, would be the eight parts red plus the 12 parts yellow. So, it'd be eight plus 12, which is 20. And this is true, the ratio of red paint to the total paint in the mixture is . Now, you might not always see it expressed this way, because there's other ways of writing an equivalent ratio. Some that people would argue are actually simpler. Another way to think about it is this diagram where we see the red paint, it has eight parts right over here, but we could also describe it as four groups of two. Just like that, because eight is divisible by four. And if you divide the 12 parts of yellow into four groups, it's four groups of three. And you'll see in a second why this is really interesting, because we were able to break down both of these into four groups. And when you do that, you see very clearly, hopefully, that for every two parts of red you have three parts of yellow. For every two parts of red, you have three parts of yellow. Two parts of red, three parts of yellow, and then last but not least, these two parts of red and then those three parts of yellow. So, for every two parts of red you have three parts yellow. Now once again, the ratio that they're asking isn't the ratio of red to yellow, which is two to three, but you could just take one of these groups and say, all right, for every two parts of red I have 1, 2, 3, 4, 5 parts of total paint. So, you could say that the ratio is also, for every two parts of red, I have five parts of total paint. And hopefully, this makes intuitive sense right here. Why these two things are equivalent. If for every eight you have 20 total, well, if you divide that by four for every two of red, you're going to have five.
    (2 votes)
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  • blobby green style avatar for user Joshua
    Why are they called "tape" diagrams
    (1 vote)
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  • blobby green style avatar for user 639958
    Why do we need ratios?
    (1 vote)
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  • blobby blue style avatar for user Anna
    i dont get how you add the fractions up to make the whole number.
    (1 vote)
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  • male robot hal style avatar for user kedar kekunnaya
    Are there simplifying ratios like in fractions?
    (1 vote)
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  • blobby blue style avatar for user Kitty
    simplifying is finding a common factor and dividing it by it right?pls confirm?!
    (1 vote)
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  • blobby green style avatar for user JordanB
    why do we have use tape diagrams
    (1 vote)
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  • piceratops seedling style avatar for user PΩRTER
    are these videos required
    (0 votes)
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  • duskpin tree style avatar for user adisonhittdd
    How do ratios work?
    (1 vote)
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    • duskpin ultimate style avatar for user Alexa
      Ratios compare two numbers, usually by dividing them. If you are comparing one data point (A) to another data point (B), your formula would be A:B. This means you are dividing information A by information B. For example, if A is 5 and B is 10, your ratio will be or 5 to 10.
      (0 votes)

Video transcript

- [Instructor] We're told that the following diagram describes the volume of yellow and red paint in an orange mixture. So we can see that for every 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 parts of yellow, we have 1, 2, 3, 4, 5, 6, 7, 8 parts of red. They ask us, "What is the ratio of red paint to total paint in the mixture?" So, pause this video and see if you can have a go at that before we do it together. All right, so if we wanna think about red paint, it looks like we have every, we have eight parts red paint, and if we think about the ratio of that towards total paint, you might be tempted to put a 12 there. But that's not the total paint, that's just the yellow paint. The total paint for every eight parts red, would be the eight parts red plus the 12 parts yellow. So, it'd be eight plus 12, which is 20. And this is true, the ratio of red paint to the total paint in the mixture is 8:20. Now, you might not always see it expressed this way, because there's other ways of writing an equivalent ratio. Some that people would argue are actually simpler. Another way to think about it is this diagram where we see the red paint, it has eight parts right over here, but we could also describe it as four groups of two. Just like that, because eight is divisible by four. And if you divide the 12 parts of yellow into four groups, it's four groups of three. And you'll see in a second why this is really interesting, because we were able to break down both of these into four groups. And when you do that, you see very clearly, hopefully, that for every two parts of red you have three parts of yellow. For every two parts of red, you have three parts of yellow. Two parts of red, three parts of yellow, and then last but not least, these two parts of red and then those three parts of yellow. So, for every two parts of red you have three parts yellow. Now once again, the ratio that they're asking isn't the ratio of red to yellow, which is two to three, but you could just take one of these groups and say, all right, for every two parts of red I have 1, 2, 3, 4, 5 parts of total paint. So, you could say that the ratio is also, for every two parts of red, I have five parts of total paint. And hopefully, this makes intuitive sense right here. Why these two things are equivalent. If for every eight you have 20 total, well, if you divide that by four for every two of red, you're going to have five.