Percent from fraction models

So we're told the square below represents one whole. So, this entire square is a whole. Then they ask us, what percent is represented by the shaded area? So why don't you pause this video and see if you can figure that out?

So, let's see. The whole is divided into 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 equal sections, of which 1, 2, 3, 4, 5, 6, 7 are actually filled in. That's the shaded area.

So, one way to think about it is seven tenths are shaded in. But how do we express this fraction as a percent? They're asking for a percent. Well, remember, percent literally means per hundred. Cent has the same root as the word hundred; you see it in cents or century.

So, can we write this as per hundred instead of per ten? Well, seven per ten is the same thing as seventy per hundred or 70 percent. How did I go from 7 tenths to 70 over 100? Well, I just multiply both the numerator and the denominator by 10.

And once you do more and more percents, you'll get the hang of you say, "Oh, seven tenths, that's the same thing as 70 per 100," which is 70 percent.

Let's do another example. Here, we're told 100 percent is shown on the following tape diagram. So, just this amount right over here is 100, and then they ask us, what percent is represented by the entire tape diagram? So, by this entire thing right over here, pause this video and see if you can answer that.

Well, one way to think about a hundred percent: 100 is equivalent to a whole. And now we have three times as much of that for the entire tape diagram. So, you could view this as three wholes, or you could say that's a hundred percent. We have another hundred percent right over here, and then we have another 100 percent right over here.

So, the whole tape diagram, that would be 300 percent.

Let's do another example. This is strangely fun! All right? Okay. It says the large rectangle below represents one whole. All right, so this whole thing is one whole. What percentage is represented by the shaded area? So pause the video and see if you can figure that out again.

So, let's just express it as a fraction first. So, we have a total of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 squares. So, out of those 20 squares, we see that six of them are actually shaded in.

So, six twentieths. Can we write that as per hundred? Well, let's see. To go from twenty to a hundred, I multiply by five. And so, if I multiply the numerator by 5, I'll get the same value: 6 times 5 is 30.

So, 6 per 20 is the same thing as 30 per 100, which is also the same thing as 30 percent, which literally means per hundred. So, this is thirty percent.

Let's do one last example here. We are told each large rectangle below represents one whole. So, this is a whole, and then this whole thing right over here is another whole. What percentage is represented by the shaded area? Again, pause the video; see if you can answer that.

So, this one we have shaded in a whole. So, that is 100 percent. And then over here, we have shaded in one, two, three, four fifths of the whole.

So, four fifths, if I want to express it as per hundred, what would it be? Well, five times twenty is a hundred, so 4 times 20 is 80.

So, four-fifths or 80 hundredths is filled out here, or you could say 80 per 100, which is the same thing as 80 percent.

So, this right over here is 80 percent. So, what percent is represented by the shaded area? Well, we have a hundred percent, and then we have eighty percent, so we have one hundred and eighty percent.

It's more than a whole. If you have a percentage that is larger than a hundred percent, you're talking about something that is more than a whole. And then we see that we have a whole right over here, and then we have eighty percent more than that.