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# Percent word problem: recycling cans

It's nice to practice conversion problems, but how about applying our new knowledge of percentages to a real life problem like recycling? Hint: don't forget your long division! Created by Sal Khan.

Video transcript

PROBLEM: 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 20ths … or 13 over 20 (13/20) … could also be viewed as 13 ÷ 20, or 13/20. 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 (or 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 1. Since we’re going to get a value less than 1, let’s put a decimal point right over here. And let’s add couple of 0s – as many 0s as we would need. And we could say, “Hey, look, 20 goes into 13 zero (0) times.” 0 х 20 is 0. (0 х 20 = 0). And then 13 - 0 = 13. Now you bring down a 0. 20 goes into 130 – Let’s see, it goes in – 5 × 20 = 100. So, 6 × 20 = 120. So it’s going to go 6 times – 6 × 20 = 120. You subtract. You get a 10. Let’s bring down another 0. 20 goes into 100 five (5) times. 5 × 20 = 100. And we are done. So 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 number by 100. Or another way you could say it is you shift the decimal point over two spots to the right. So, this is going to be equal to 65 percent (or 65%). Now. There’s another way you could have done it. You could have said, “Look, ‘percent’ literally means ‘per hundred’ So, 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 a 100 – (Forget the denominator.) To go from 20 to 100, you would multiply by 5. So let’s multiply the numerator by 5, as well. And 13 × 5 – Let’s see. That’s 15 + 50, which is 65. So this would have been a faster way to do it, especially if you recognize that it’s pretty easy to go from 20 to 100. You multiply 20 by 5. So we would do the same thing with the 13. And so, you would get 65 over 100 (65/100), which is the same thing as 65 percent (65%) – (Let me write this percent symbol.) 65 percent. (65%.) And just a reminder: ‘Percent’ literally means ‘per hundred.’ 65 per hundred. 65 percent. (65%.)