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Picture it: you and a group of friends decide to go to the new restaurant in town for lunch. You all decide before you get there that, to make the math easier, you will just split the bill 5 ways instead of having to worry about separate checks or trying to calculate what everyone owes. When the bill comes, Ted, the math nerd of the group, says, 'The total bill is $70. Remember, we are each paying 20%.' You reach for your wallet thinking, 'It sure would be easier to calculate what I owe if I knew what fraction 20% was.'
The word percent means 'per 100,' so any number written as a percent really is a fraction meaning that number over 100. So 50% really is 50 per 100, or 50/100. 127% is 127 per 100, or 127/100.
Since percent is just a different way to write a fraction, converting from percent notation to fraction notation is really quite easy. Just take the percent, write it as the numerator of a fraction with 100 as the denominator, simplify the fraction and remove the percent symbol.
Let's try an example. Convert 42% to a fraction.
First we write the number 42 as the numerator of a fraction. Numerator means the top number of a fraction. We place the number 100 in the denominator of the same fraction. The denominator is the bottom number of the fraction.
Now we have a fraction 42/100, which can be reduced to 21/50. This means that 42% written as a fraction is 21/50.
Now why don't we go back and figure out what you owe for lunch. 20% written as a fraction is 20/100, which can be reduced to 10/50 and then again to 1/5. So your portion of the bill is 1/5 of $70, which is 70/5, or $14.
How about another example, this one with a twist. Convert 66.6% to a fraction.
Percents that include numbers after the decimal point have one extra step in the conversion process. You start the same way, by creating a fraction with the percent on top and 100 on bottom - in this case, 66.6/100.
Because there is a decimal in the numerator, you need to multiply it by 10 to remove that decimal. In order to keep the fraction balanced, you then need to also multiply the denominator by 10. That way, the fraction becomes 666/1000, which can be reduced to 333/500.
Converting a percent to a fraction is a simple two-step process. First, turn the number into a fraction with 100 as the denominator. Second, reduce the fraction.
After studying this video lesson's contents, you could remember how to perform the two-step conversion of fractions to percents and vice versa.
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Algebra I: High School20 chapters | 168 lessons | 1 flashcard set
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