How to find percentage from a fraction a1 - ACT Math

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Question

$\frac{5.5}{10}$ is equivalent to what percentage?

Answer

Divide the fraction out to get the decimal

5.5 / 10 = 0.55

To find the percentage, shift the decimal point two to the right = 55%

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Question

Write $\frac{27}{25}$ as a percent

Answer

To find a percent from a fraction you can either divide the number on your calculator and multiply by 100:

$100\cdot\frac{27}{25}=108$

or you can just multiply the numerator and denominator by the same number that makes the denominator equal to 100 (because a % is just #/100):

$\frac{27}{25}\cdot\frac{4}{4}=\frac{108}{100}$

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Question

One half of a group of professors is made up of mathematicians, and one fourth of the remaining portion is made up of philosophers. The remaining portion is made up of sociologists. If there are professors in the room, how many are sociologists?

Answer

To begin, remember with percentages that "of" means multiplication and "is" means "equals." Now, we know that one fourth of the remaining half are philosophers. This means that he philosophers really are:

$\frac{1}{4}\frac{1}{2}=\frac{1}{8}$

So, there are $1-\frac{1}{2}-\frac{1}{8}$ sociologists as a percentage. This is:

$1-\frac{1}{2}-\frac{1}{8}=\frac{8}{8}-\frac{4}{8}-\frac{1}{8}=\frac{3}{8}$

Therefore, $\frac{3}{8}$ of the are sociologists, or:

$\frac{3}{8}464=174$ are sociologists.

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Question

Convert the following fraction into a percent.

$\frac{2}{5}$

Answer

To convert a fraction into a percent, make the denominator 100 and then the numerator will be the percent. Thus,

$\frac{2}{5}*\frac{20}{20}=\frac{40}{100}=40%$

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