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Mathematics 64 Online
OpenStudy (anonymous):

Typically, 5.7% of students in one district do not graduate. If there are 15,000 students, how many won't graduate?

OpenStudy (jamesj):

So if 100% did not graduate, how much would that be?

OpenStudy (anonymous):

idk

OpenStudy (jamesj):

100% of something is all of something. Hence, if 100% of 15,000 did not graduate, how much is that?

OpenStudy (anonymous):

all of them???

OpenStudy (jamesj):

100% of 15,000 = 15,000. Alternatively, \[ \frac{100}{100} \times 15,000 = 1 \times 15,000 = 15,000 \] So far so good?

OpenStudy (anonymous):

thats the answer??

OpenStudy (jamesj):

Nope. We want 5.7% of 15,000. So one or two more steps and we'll get there. In general, x% of 15,000 is \[ \frac{x}{100} \times 15,000 \] For example, what is 10% of 15,000? Well, using the formula we just wrote down, it must be \[ \frac{10}{100} \times 15,000 \] Now, what is that equal to?

OpenStudy (anonymous):

14,145???

OpenStudy (jamesj):

No, \[ \frac{10}{100} \times 15,000 = \frac{1}{10} \times 15,000 \] by dividing top and bottom by 10. So far so good? Is so, what is \[ \frac{1}{10} \times 15,000 \] ?

OpenStudy (anonymous):

I really dont get it

OpenStudy (jamesj):

x% of 15,000 is a way of expressing how much of 15,000 we have. 100% of 15,000 is all of 15,000. That is, 100% of 15,000 = 15,000 0% of 15,000 on the other hand is zero. That is 0% of 15,000 = 0. Therefore, 5.7% of 15,000 is asking for a portion of fraction of 15,000. To answer the question exactly, we need to know what x% of 15,000 means for any value of x. By definition x% of 15,000 is \[ \frac{x}{100} \times 15,000 \]

OpenStudy (jamesj):

This is the definition of what x% of a quantity means. In your question 5.7% of 15,000 means precisely, \[ \frac{5.7}{100} \times 15,000 \] Can you calculate that?

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