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# Percents from fraction models

## Video transcript

so we're told the square below represents one hole so this entire square as a hole and then they ask us what percent is represented by the shaded area so why don't you pause this video and see if you can figure that out so let's see the hole is divided into 1 2 3 4 5 6 7 8 9 10 equal sections of which 1 2 3 4 5 6 7 are actually filled in that's the shaded area so one way to think about it is 7 tenths are shaded in but how do we express this fraction as a percent they're asking for a percent well remember percent it literally means per hundred cent same root as the word hundred you see it in cents or century and so can we write this as per hundred instead of per ten well 7 / 10 is the same thing as 70 per hundred or 70 percent and how did I go from 7/10 to 70 over 100 well I just multiply both the numerator and the denominator by 10 and once you do more and more percentage you'll get a hang of it you say Oh 7/10 that's the same thing as 70 400 which is 70 percent let's do another example here we're told 100 percent is shown on the following tape diagram so just this amount right over here is 100 percent and then they asked us what percent is represented by the entire tape diagram so by this entire thing right over here pause this video and see if you can answer that well one way to think about a hundred percent 100 percent is equivalent to a whole and now we have three times as much of that for the entire tape diagram so you could view this as three wholes or you could say that's a hundred percent we have another hundred percent right over here and then we have another 100 percent right over here so the whole tape diagram that would be three hundred percent let's do another example this is strangely fun alright okay and I'll see it says the large rectangle below represents one hole all right so that's this whole thing is one hole what percentage is represented by the percent shaded area so pause the video and see if you can figure that out again so let's just express it as a fraction first so we have a total of 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 squares so out of those 20 squares we see that 6 of them are actually shaded in so 6 twentieths can rewrite that as per hundred well let's see to go from 20 to 100 I multiply by 5 and so if I multiply so if I multiply the numerator by 5 I'll get the same value 6 times 5 is 30 so 6 / 20 is the same thing as 30 per hundred which is the same thing as 30% which literally means per hundred so this is 30% let's do one last example here we are told each large rectangle below represents one hole so this is a hole and then this whole thing right over here is another hole what percentage is represented by the shaded area again pause the video see if you could answer that so this one we have shaded in a hole so that is 100% and then over here we have shaded in 1 2 3 4 fifths of the hole so 4/5 if I want to express it as per hundred what would it be well five times 20 is a hundred so 4 times 20 is 80 so 4/5 or 80 hundredths is filled out here or you can say 80 / hundred which is the same thing as 80% so this right over here is 80% so what percent is represented by the shaded area well we have a hundred percent and then we have 80 percent so we have one hundred and eighty percent it's more than a whole if you have a percentage that is larger than 100 percent you're talking about something that is more than a hole and then we see that we have a hole right over here and then we have 80 percent more than that