Percent word problem: recycling cans

in the United States 13 out of every 20 cans are recycled what percent of cans are recycled so 13 out of every 20 are recycled so 13 20 it's or 13 over 20 could also be viewed as 13 13 divided by 20 or 13 divided by divided by 20 and if we do this we'll get a decimal and it's fairly straightforward to convert that decimal into a percentage so 13/20 we have the smaller number in this case being divided by the larger number so we're going to get a value less than one since we're going to get a let value less than one let's put a decimal right over here and let's add a couple of zeros as many zeros as we would need and we could say hey look 20 goes into 13 zero times zero times 20 is zero and then 13 minus zero is 13 now you bring down a zero 20 goes into 130 let's see it goes in five times 20 is 100 so 6 times 20 is 120 this is going to go 6 times 6 times 20 is 120 you subtract you get a 10 let's bring down another zero 20 goes into 100 five times 5 times 20 is 100 and we are we are done so this written as a decimal this written as a decimal is 0.65 so as a decimal it's 0.65 and if you want to write it as a percentage you essentially multiply this by 100 or another way you could say is you shift the decimal over two spots to the right so this is going to be equal to 65 65 percent now there's another way you could have done it is you could have said look percent literally means per hundred so 13 out of 20 13 out of 20 is going to be equal to what over is going to be equal to what over 100 well to go from 20 to 100 you forget the denominator to go from 20 to 100 you would multiply by five so let's multiply the numerator by five as well and thirteen times five let's see that's 15 plus 50 which is 65 so this would have been a little bit of fat a faster way to do it especially if you recognize it's pretty easy to go from 20 to 100 you multiply by 5 so we do the same thing with the 13 and so you'd get 65 over 100 which is the same thing as 65 / let me write this percent symbol 65% and it's a reminder percent literally means per hundred sixty-five per hundred sixty-five percent