The meaning of percent (Khan Academy)

[One speaker] 

[The video opens to a black screen with a square of graphing paper, and the title “Shade 20% of the square below.”]

Narrator: We’re asked to shade twenty percent of the square below [Uses the cursor to underline the “20%”]. Before doing that, let’s just even think about what percent means. Let me even just rewrite it. Twenty percent is equal to, I’m just writing it out as a word, twenty per cent [writes on the screen “20%= 20 percent”], which literally means twenty per cent. Let me break it out. Which is the same thing as twenty per cent [writes on the screen “= 20 per cent”], and if you are familiar with the word century, you might already know that cent comes from Latin for the word hundreds. This literally means you can take cent [draws a box around the word “cent”], and that literally means one hundred. So this is the same thing as twenty per hundred. Twenty per hundred [writes on the screen “= 20 per 100”]. Twenty percent means you are really going to, if we want to shade twenty percent, that means, if you break up the square into one hundred pieces, we want to shade twenty of them. Twenty per hundred.

So how many squares have they drawn here? Let’s see, if we go horizontally right here, we have one, two, three, four, five, six, seven, eight, nine, ten squares. If we go vertically, we have one, two, three, four, five, six, seven, eight, nine, ten [Draws a tick mark by each square as it is counted]. So this is a ten by ten square. So it has one hundred squares here. So if we want to shade this, or another way to say it is that this larger square, i guess that’s the square that they’re talking about. This larger square is broken up into one hundred smaller squares, so it’s already broken up into the hundred. So if we want to shade twenty percent of that, we need to shade twenty of every hundred squares that it is broken into. So, with this, we’ll just literally shade in twenty squares. So let me just do one. So if I just do one square [shades in one square], just like that, I have just shaded one per hundred of the squares. One hundred out of the hundred would be the whole, I’ve shaded one of them, this would be that one square by itself would be one percent of the entire square [labels the shaded square as “1%”]. If I were to shade another one, if I were to shade that and that [shades two squares], then those two combined, that’s two percent of the entire square, it’s literally two per hundred, where one hundred would be the entire square. So if we wanted to do twenty, we do one, two, three, four, actually if we shave this, not shave, if we shade this entire row, that will be ten percent, right? One, two, three, four, five, six, seven, eight, nine, ten [Shades each square as it is counted], and we want to do twenty, so that’ll be one more row. So I can shade in this whole other row right here [shades the row below]. And then I would have shaded in twenty of the hundred squares. Or another way of thinking about it, if you take this larger square, divide it into one hundred equal pieces, I’ve shaded twenty per hundred, or twenty percent, of the entire larger square. Hopefully that makes sense.

[Video ends]