What I want to do in thisvideo is really digest the idea that if we have some fraction,as long as we multiply the numerator and thedenominator of the fraction by the same number,then we're going to have an equivalent fraction. So let's think about that. Let's say we multiply thedenominator here by 2. I'm claiming that as long aswe multiply the numerator by 2, we are going to get anequivalent fraction. So here, the denominator was 6. So here, ourdenominator will be 12. If our numerator hereis 4, well, we've got to multiply by 2 again,multiply our numerator by 2, to get 8. So I'm claiming that 8/12is the same fraction as 4/6. And to visualize that,let me redraw this whole. But instead of having6 equal sections, we now have 12 equal sections. So each of the sixwe can turn into 2. That's essentially whatmultiplying by 2 does. We now have twice asmany equal sections. Now that we have twice as manyequal sections-- literally one, two, three, four, five, six,seven, eight, nine, 10, 11 12-- how many of them areactually shaded in yellow? Well, one, two three, fourfive, six, seven, eight-- 8/12. And there's no magic here. If we have twiceas many sections, we're going to have to shadein twice as many of them in order to have the samefraction of the whole. And it goes the other way, too. This isn't just truewith multiplication. It's also true that ifwe divide the numerator and the denominatorby the same quantity, we are going to havean equivalent fraction. So that's anotherway of saying, well, what happens if Iwere to divide by 2? So if I were to divide by2-- so let me divide by 2-- I'm going to have 1/2 thenumber of equal sections. Or I will only havethree equal sections. And I'm claiming if I do thesame thing in the numerator, that this is going torepresent the same fraction. So 4 divided by 2 is 2. So I'm claiming that2/3 is the same fraction as 4/6 is the samefraction as 8/12. Well, let's visualize that. So here, this is6 equal sections. But now, we're going to haveonly three equal sections. So we can merge some ofthese equal sections. So we can merge thesetwo right over here. And we can merge thesetwo right over here. And then, we can mergethese two right over here. So our whole isstill the same whole. But now, we only havethree equal sections. And two of them areactually shaded in. So these are allequivalent fractions. So the big takeaway hereis start with a fraction. If you multiply thenumerator and the denominator by the same quantity,you're going to have an equivalent fraction. If you divide the numeratorand the denominator by the samequantity, you're also going to have anequivalent fraction. So with that in our brains,let's tackle a little bit of an equivalentfractions problem. Let's think about-- ifsomeone says, OK, I have 5/25, and I want to write that as somevalue, let's call that value t, over 100, what would t be? Well, we can seein the denominator to go from 25 to 100,you had to multiply by 4. So if you want anequivalent fraction, you have to multiply thenumerator by 4 as well. So t will need tobe equal to 20. So t is equal to 20. 5/25 is the samething as 20/100. But what if someone says, well,5/25 is equivalent to blank, let's say question mark, over 5? Well now what would you do? Actually, let's doit the other way-- is equal to 1 overquestion mark. Well, you could say, look, toget our numerator from 5 to 1, we have to divide by 5. We have to divide by5 to go from 5 to 1. And so similarly, we have todivide the denominator by 5. So if you divide the denominatorby 5, 25 divided by 5 is going to get you 5.
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So these are allequivalent fractions. 1/5 is equivalent to 5/25,which is equal to 20/100.