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## Equivalent representations of percent problems

## Video transcript

- [Instructor] So let's
assume that this entire square represents a whole. And we can see that part
of it is shaded in in blue. What we're going to do in this video is try to represent the
part that is shaded in blue as a fraction, as a decimal, and as a percent. So pause the video and
see if you can do that. Well, let's first think
about it as a fraction. So, the whole is split
into one, two, three, four, five, six, seven, eight,
nine, 10 equal sections, and six of them are filled in. So the blue represents 6/10 of a whole, or it represents, you
could just say, 6/10. And you could also rewrite that. If you divide the numerator
and the denominator by two, that's the same thing as three over five. Fair enough. Now let's represent it as a decimal. What decimal would it be? Pause the video again and
see if you can do that. Well, 6/10, we could literally
just go to our place value. So that's the ones
place, we have a decimal. And then you have your tenths place. And so we have 6/10, so you could just put it right over there. We are putting a six in the
tenths place to represent 6/10. Now, what about a percentage? Well, percent means per 100, so one way to think
about it is six over 10 is the same thing as what per 100? That is equal to, if we
multiply the numerator and the denominator by 10, that's the same thing as 60 per 100. Or another way of thinking about it, 60 per, instead of 100 you could say cent. And so this would be equal to 60%. Let's do another example. So here, once again, our entire
square represents a whole. So see if you can represent this as the part that's shaded
in blue as a fraction. Pause the video and do that. Well, you can see that
this is a 10 by 10 grid, so there's 100 equal sections here. 100 equal sections. Each of these squares represents 1/100. And how many of them are there? Well, let's see, this
row is 10, 20, 30, 40, and then one, two, three, four. So this is 44 over 100, 44/100. And we could actually
represent this in other ways. We could divide the numerator
and the denominator by four, in which case you would get 11 over 25. That's another way to
represent this same fraction. Now, what about as a decimal? Well, 44/100, you could say, well, you have your ones place, and then this is the same thing. You could literally
just say this is 44/100. This is another way of
representing 44/100. It's 4/10 and 4/100 is 44/100. And then if you were to do a percent, well, this is 44 per 100, or 44/100, but even here I like look
at it as 44 per 100 or 44%. So this is going to be 44%. And we're done.