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Relating fractions to 1

Sal uses 1 as a benchmark for identifying fractions greater than or less than 1.

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Video transcript

- [Instructor] We are told, "Select the two fractions "that are greater than one." So pause this video and see if you can figure out which two of these fractions are greater than one. All right, now let's work on this together. And so, the main realization here, the main thing to pay attention to is how the numerator relates to the denominator. When we are at one, they're equal to each other. For example, one is equal to one whole. I guess you could write it that way, one oneths. Or you could also write it as two halves, is also equal to three thirds, is also equal to four fourths. We could go on and on. If you want it in terms of sixths, one would be equal to six sixths. And so, if whatever we have up here is larger than the denominator, so if we have seven sixths or if we were to have maybe five fourths. Notice, the numerator is larger than denominator. These are all situations when we are greater than one. And all the situations where the numerator is less than the denominator, so example one half or nine 11ths, or 10 11ths, these are all situations where we are less than one. All of this is less than one. So let's look over here. Four is less than six. Four sixths is less than six sixths. Remember is the same thing as six sixths. So this is not greater than one, so I would not select that. Nine fourths, well that's definitely larger than four fourths. That is greater than one and once again our numerator is larger than our denominator, so we know that we are greater than one. So I will select that one. And then we see again five halves. Two halves is equal to one, so five halves is definitely greater than one. So I like that one as well. And notice, five is greater than two and then we are already know we picked our two choices, but we can look at the other ones. Seven is less than eight, so seven eighths is less than eight eighths, so this is less than one. And three thirds, we've already talked about it, that's equal to one. So I like those two choices. Let's do another example that tackles it a little bit of a different way. It says, "What, which fraction could represent "Point A on the number line?" And Point A is here. They don't tell us a lot about Point A, but all they do tell us by looking at the number line is that Point A is less than one. So which of these, another way to think about it, is less than one? All right, in order for it to be less than one the numerator has to be less than the denominator. Here our numerator is greater than the denominator. Seven fourths is definitely larger than four fourths. Remember, four fourths is equal to one. This right over here I could rewrite as four fourths. And so, seven fourths is going to be someplace, seven fourths is going to be someplace over there. So this is definitely not our choice. Two halves, well once again that's the same thing as one. That's right over there. So that's not our choice. What about five eighths? Well, five eighths, the numerator is less than the denominator. Eight eighths is equal to one, so that's that point again. So five eighths would be to the left of that. So that could be Point A. So I like that choice.