Welcome to mine presentationon indistinguishable fractions. So identical fractionsare, essentially what they sound like. They're 2 fractions thatalthough lock use different numbers, they actuallyrepresent the exact same thing. Permit me show you an example. Let's say i hadthe portion 1/2. Why isn't the writing. Permit me make certain I getthe right color here. Let's say i hadthe fraction 1/2. For this reason graphically, if us to drawthat, if I had actually a pie and also I would have cut itinto two pieces. That's the denominatorthere, 2. And then if ns were come eat1 the the 2 piece I would have consumed 1/2 of this pie. Renders sense. Nothing too facility there. Well, what if instead ofdividing the pie into two pieces, allow me simply drawthat exact same pie again. Rather of splitting it in twopieces, what if I split that pie into 4 pieces? So right here in the denominator Ihave a opportunity of-- total of 4 piece in the pie. And also instead of eat onepiece, this time I actually ate 2 of the 4 pieces. Or i ate 2/4 of the pie. Fine if we look at this twopictures, we can see that I've consumed the sameamount of the pie. So this fractionsare the same thing. If who told you the theyate 1/2 that a pie or if lock told you that they ate 2/4 that apie, it transforms out of that they ate the very same amount of pie. For this reason that's why we're sayingthose two fractions room equivalent. One more way, if us actuallyhad-- let's do an additional one. Let's say-- and that pie isquite ugly, however let's i think it's the same form of pie. Let's say us dividedthat pie into 8 pieces. And now, rather of eating 2we ate 4 of those 8 pieces. So we ate 4 the end of 8 pieces. Well, us still finished up eatingthe exact same amount that the pie. Us ate half of the pie. Therefore we watch that 1/2 will certainly equal2/4, and that amounts to 4/8. Now do you watch a pattern hereif we just look at the number relationshipsbetween 1/2, 2/4, and also 4/8? Well, to go from 1/2 come 2/4 wemultiply the denominator-- the denominator simply as evaluation isthe number on the bottom the the fraction. Us multiply thedenominator by 2. And also when you main point thedenominator by 2, we also multiply the numerator by 2. Us did the exact same thing here. And that renders sense becausewell, if I double the number of pieces in the pie, then ns haveto eat double as numerous pieces come eat the very same amount the pie. Let's carry out some much more examplesof tantamount fractions and hopefully it'llhit the allude home. Allow me erase this. Why isn't the letting me erase? permit me use the constant mouse. OK, good. Sorry for that. Therefore let's say ns hadthe fraction 3/5. Well, by the exact same principle,as lengthy as we multiply the numerator and also the denominatorby the same numbers, we'll gain an indistinguishable fraction. So if we multiply the numeratortimes 7 and the denominator times 7, we'll acquire 21-- because3 time 7 is 21-- end 35. And so 3/5 and 21/35 areequivalent fractions. And we essentially, and I don'tknow if you already know just how to multiply fractions, yet all wedid is us multiplied 3/5 times 7/7 to obtain 21/35. And also if you look in ~ this, whatwe're doing here isn't magic. 7/7, well what's 7/7? If I had 7 pieces in a pieand i were come eat 7 that them; i ate the whole pie. So 7/7, this is thesame point as 1. So every we've essentiallysaid is well, 3/5 and we multiplied it time 1. I beg your pardon is the same thing as 7/7. Oh boy, this thingis messing up. And that's how we obtained 21/35. So it's interesting. All we did is multiply thenumber by 1 and also we know that any number times 1is still that number. And also all we did is we figuredout a different method of creating 21/35. Let's start witha portion 5/12. And also I wanted to compose that withthe denominator-- let's to speak I want to write that withthe denominator 36. Well, to go from 12 come 36, whatdo we have to multiply by? well 12 goes into36 three times. So if we multiply thedenominator by 3, we additionally have to main point the molecule by 3. Time 3. We get 15. Therefore we gain 15/36 is thesame point as 5/12. And just going come our originalexample, every that's speak is, if I had a pie through 12pieces and also I ate 5 of them. Let's say ns did that.

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And also then you had actually a pie, thesame size pie, you had actually a pie with 36 piece andyou ate 15 of them. Climate we in reality ate thesame amount of pie.