Shodor > Interactivate > Discussions > Percents

Student: How are fractions and percents related to each other?

Mentor: Both fractions and percents represent parts of a whole. Where a fraction is a part of the amount of the denominator, a percent is always some part of 100. The word "percent" comes from Latin and means, "part of one hundred".

Student: So if I have fifty parts of one hundred, that is fifty percent, or 50%, right?

Mentor: Yes, and to express 50% as a fraction, think of it this way; it is fifty parts out of one hundred or 50/100.

Student: OK, that makes sense. And it looks like I can reduce that fraction by dividing both numbers by 50.

50÷50=1 and 100÷50=2 so the reduced fraction is 1/2

Mentor: Good work! Fifty percent is one half. Now let's try another. Suppose I have a fraction of 1/5. How would I convert that to a percent?

Student: Well, if a percent is some part of 100, then I will multiply 1/5 by 100.

1/5 x 100 is the same as 1/5 x 100/1, and I multiply across: 1*100=100 in the numerator and 5*1=5 in the denominator to show that 100/5 = 20

Mentor: Yes. So 1/5 is the same as 20%.

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