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Lesson 55: Introduction to Percentages
Percentages come up again and again, both in math, as well as in everyday life. It's important to fully understand how they work, and how they relate to decimals. This lesson explains the basics.
Many students don't realize that percent just means "out of 100." That is all it means. The symbol % just means to put the number over a denominator of 100. Percent is really "per cent." Per means "of," and cent is a prefix that means 100, such as in century, or even one cent being 1/100 of a dollar.
In real life, it is not that common that we break a whole into 100 equal parts. For example, we are not likely to cut a pizza pie into 100 equal pieces, and then eat 23 of them. But if we did, we could say that we ate 23% of the pie. Thinking back to the lessons on fractions and decimals, we could also say that we ate 0.23, or twenty-three hundredths of the pie, or we could say that we ate 23/100 of the pie, if we wanted to represent it as a fraction. It's important to understand that these are all different ways of staying the exact same thing, and describing the same portion of a whole.
Let's practice converting some simple fractions to percentages. Let's say you ate 1/2 (half) of your candy. To convert it to a percent, we need to convert 1/2 to a fraction that has a denominator of 100. How many parts of 100 do we need to represent half of them? You probably realize that it's 50. 50/100 is equivalent to 1/2. 50/100 is 50%, so we can say that you ate 50% of your candy.
How about if you ate two out of 8 pieces of candy. This is a bit trickier. It would be best to first reduce the fraction, which we learned how to do. 2/8 is the same as 1/4 (one-fourth). If we want a fraction with a denominator of 100, what portion of 100 is one-fourth of it? You can probably figure out that it is 25. So 2/8 is the same as 1/4, which is the same as 25/100, which is 25%. You ate 25% of your candy.
It's quite common to divide things into 10 parts. For example, you might have driven 7/10 (seven-tenths) of a mile. What percent is that? All we have to do is multiply the numerator and denominator by 10. That will give us a denominator of 100, and numerator of 70, so we have 70/100. Now it's easy to see that you drove 70% of a mile.
This is just a basic introduction to percentages. Make sure that you memorize the fact that the word percent, or the % symbol just means "out of 100," or "over a denominator of 100."
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