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PROBLEM: In the United States,

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13 out of every 20 cans are recycled.

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What percent (%) of cans are recycled?

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So 13 out of every 20 are recycled.

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So 13 20ths … or 13 over 20 (13/20) …

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could also be viewed as

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13 ÷ 20, or 13/20.

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And if we do this, we’ll get a decimal.

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And it’s fairly straightforward

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to convert that decimal into a percentage.

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So 13 ÷ 20 (or 13/20) …

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We have the smaller number, in this case,

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being divided by the larger number.

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So, we’re going to get a value less than 1.

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Since we’re going to get a value less than 1,

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let’s put a decimal point right over here.

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And let’s add couple of 0s –

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as many 0s as we would need.

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And we could say,

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“Hey, look, 20 goes into 13 zero (0) times.”

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0 х 20 is 0. (0 х 20 = 0).

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And then 13 - 0 = 13.

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Now you bring down a 0.

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20 goes into 130 –

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Let’s see, it goes in –

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5 × 20 = 100.

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So, 6 × 20 = 120.

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So it’s going to go 6 times –

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6 × 20 = 120.

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You subtract.

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You get a 10.

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Let’s bring down another 0.

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20 goes into 100 five (5) times.

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5 × 20 = 100.

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And we are done.

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So this, written as a decimal, is 0.65.

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So, as a decimal, it’s 0.65.

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And if you want to write it as a percentage (%),

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you essentially multiply this number by 100.

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Or another way you could say it is

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you shift the decimal point over

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two spots to the right.

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So, this is going to be equal to 65 percent (or 65%).

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Now. There’s another way you could have done it.

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You could have said,

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“Look, ‘percent’ literally means ‘per hundred’

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So, 13 out of 20 is going to be equal to what over –

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is going to be equal to what over 100?

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Well, to go from 20 to a 100 –

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(Forget the denominator.)

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To go from 20 to 100, you would multiply by 5.

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So let’s multiply the numerator by 5, as well.

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And 13 × 5 –

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Let’s see.

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That’s 15 + 50, which is 65.

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So this would have been a faster way to do it,

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especially if you recognize that

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it’s pretty easy to go from 20 to 100.

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You multiply 20 by 5.

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So we would do the same thing with the 13.

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And so, you would get 65 over 100 (65/100),

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which is the same thing as 65 percent (65%) –

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(Let me write this percent symbol.)

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65 percent. (65%.)

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And just a reminder:

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‘Percent’ literally means ‘per hundred.’

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65 per hundred.

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65 percent. (65%.)