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Part:whole ratios

In this video, we explore ratios using apples and oranges. We find the simplified ratio of apples to total fruit (2:5) and learn to represent ratios as fractions (2/5). The fraction indicates that 2/5 of the fruit are apples. Key definitions include ratio, simplified ratio, and fraction notation. Created by Sal Khan.

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Video transcript

Voiceover:Let's think about another scenario involving ratios. In this case, let's think about the ratio of the number of apples. Number of apples to ... Instead of taking the ratio of the number of apples to the number of oranges, let's take the number of apples to the number of fruit. The number of fruit that we have over here. And I encourage you to pause the video and think about that on your own. Well, how many total apples do we have? We have 2, 4, 6, 8 apples. So we're going to have 8 apples. And then how much total fruit do we have? Well we have 8 apples and we have 3, 6, 9, 12 oranges. So our total fruit is 8 plus 12. We have 20 pieces of fruit. So this ratio is going to be 8 to ... 8 to 20. Or, if we want to write this in a more reduced form, we can divide both of these by 4. 4 is their greatest common divisor. And so this is the same thing as a ratio. 8 divided by 4 is 2 and 20 divided by 4 is 5. So 2 to 5. Now, does this make sense? Well, if we divide ... If we divide everything into groups of 4. So ... Or if we divide into 4 groups, I should say. So 1 group, 2 groups, 3 groups, and 4 groups. That's the largest number of groups that we can divide these into so that we don't have to cut up the apples or the oranges. We see that in each group, for every 2 apples we have 1, 2, 3, 4, 5 pieces of fruit. For every 2 apples we have 5 pieces of fruit. This is actually a good opportunity for us to introduce another way of representing ... Another way of representing ratios, and that's using fraction notation. So we could also represent this ratio as 2 over 5. As the fraction 2 over 5. Whenever we put it in the fraction it's very important to recognize what this represents. This is telling us the fraction of fruit that are apples. So we could say 2/5 of the fruit ... Of the fruit ... Of the number of fruit, I guess I could say. Of number of fruit ... Of fruit is equal to the number of apples. Right, I'm just going to say 2/5 of fruit if we're just speaking in more typical terms. 2/5 of fruit are apples. Are, are apples. So, once again, this is introducing another way of representing ratios. We could say that the ratio of apples to fruit, once again, it could be 2 to 5 like that. It could be 2, instead of putting this little colon there we could literally write out the word to. 2 to 5. Or we could say it's 2/5, the fraction 2/5, which would sometimes be read as 2 to 5. This is also, when it's written this way, you could also read that as a ratio, depending on the context. In a sentence like this I would read this as 2/5 of the fruit are apples.