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CCSS.Math:

what I hope to do in this fraction is be able to rewrite the fraction 8/10 as being something over a hundred so I could put a question mark here or I could put a star over here star over a hundred and what I care about is figure out what is this star equal to 8 over 10 is equal to what over 100 and I encourage you to pause the video to think about it now to help us work through this I have I have set up a little diagram you're actually two diagrams to think about what eight tenths looks like and then I have the same hole instead of being split into tenths I have it split up into hundredths I have it split up to a hundred equal sections and we have to figure out how many of these hundred equal sections are equivalent to the eight out of the ten equal sections right over here so let's think about that a little bit so once again we have 10 equal sections here and we have colored in one let me mark them all if we've colored in one two three four five six seven eight of them this this that this diagram this picture represents eight tenths 10 equal sections I have colored in eight of them now how do I do that if I'm talking about a hundredths well it's the same hole right over here now if I want to fill up the same amount of that hole so let me get a little paintbrush here so it would be the equivalent of 1/10 would be filling in ten hundredths so that's ten hundredths right over there then two tenths or that second tenth every time I fill in the tenth that's the same thing as filling in ten hundredths let me write that down because that's interesting so we see here that 1/10 is equal to 10 over 100 every time I fill in 1/10 every time I fill in a tenth that's 1/10 right over there if you look at this diagram that's equivalent to 10 hundredths it's equivalent to 10 of those hundred equal sections so if I want to figure out fill out eight tenths that's going to be eight times ten hundredths or 8000s and let's just see that right over here so we already did ten hundreds 20 hundredths 20 hundredths this is going to be 30 hundredths 40 hundredths 50 hundredths 60 hundredths 70 hundredths and 80 hundreds notice I've filled in the same amount and I could fill it in just to make it a little bit clearer but I filled in the same amount of both of these equal holes but over here how many of these squares have I filled in I have filled in 80 now let me get my pen going I have over here I have filled in 80 out of my hundred squares while over here I filled in eight out of my ten equal rectangles but there's the same amount of area there the same fraction of the hole so eight over 10 is going to be the same thing as 80 over 100 you see it's the exact same thing we've just divided the one on the right here into ten times as many sections and you could even see it mathematically that look if we divide it into ten times as many sections so if we multiply a denominator by 10 to go from 10 to 100 well that means that each of these eight sections in this one are going to represent ten times as many in this one so we would say well eight is going to represent ten times as many of the hundredths so eight times 10 is 80 10 times 10 is 100 eight tenths is the same thing as 8000s and in general if you're trying to rewrite a fraction but and and and not change its value so you want an equivalent fraction as long as you multiply the denominator or as long as you multiply the numerator and the denominator by the same thing you will not be changing the value of the fraction it's also true if you divide the numerator and the denominator by the same thing you also will not be changing the value of the fraction in this case we have multiplied both the numerator and the denominator by 10 and you see why we did it