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# Converting Fractions to Percent

The first step in converting a fraction into a percentage is remembering what a percentage is. Percent simply means expressing the figure as a number out of 100. To convert a fraction into a percent, begin by dividing the numerator by the denominator. Then, multiply the resulting decimal by 100.

For example, the fraction $\frac{4}{8}$ can be converted into a decimal by dividing 4 by 8 and getting 0.5. Then, we multiply 0.5 by 100 to get 50%. This tells us that 4 is 50% of 8. Let's try some more practice problems:

## Converting fractions to percent (numerator less than or equal to denominator)

For a fraction such as $\frac{2}{25}$ , the denominator of 25 is substantially higher than the numerator of 2. This means that when we do long division, we'll need to add extra zeros until we have something that 25 goes into. We'll need two zeros in this case since 25 goes into 200 8 times. Since we added two zeros, we also added two zeros and a decimal point to our answer to get 0.08.

Now that we have a decimal, we simply multiply it by 100. $0.08×100=8$ , meaning the fraction $\frac{2}{25}$ is equivalent to 8% or 8 out of 100. Here is an illustration proving the two values are equivalent:

## Converting fractions to percent (numerator greater than or equal to denominator)

If you were asked to write $\frac{7}{4}$ as a percent, you would notice that the numerator is greater than the denominator. Fortunately, that doesn't change the procedure at all. We still divide 7 by 4 to get 1.75 and then multiply the decimal by 100 to get 175%. Really, the only thing that changes when the numerator is greater is that your answer should be above 100%, whereas we should expect something below 100% when the denominator is greater.

## Tricks for converting fractions to percent

Everyone loves when there's a shortcut that can get them to the correct answer, and the fact that percentages are out of 100 means that there are several ways to speed things up based on the numbers you're given. First, any fraction with 100 as the denominator is the numerator percent. For example, $\frac{50}{100}$ is 50% while $\frac{175}{100}$ is 175%.

Second, any fraction with a multiple of 100 as the denominator can be converted to a fraction with 100 as the denominator. For instance, $\frac{5}{25}$ is the same as $\frac{20}{100}$ since we multiplied both the numerator and denominator by 4. $\frac{20}{100}$ is 20%, and since $\frac{5}{25}$ is an equivalent fraction, it is also equal to 20%.

Third, you can simplify fractions to get numbers that are easier to work with. For example, the fraction $\frac{18}{27}$ might be a bit unwieldy. However, expressing the fraction in simplest form gives you $\frac{2}{3}$ , a common fraction that you probably know is equivalent to about 66.7% offhand.

You can't always take advantage of tricks like this, but it feels really good when you can!

## Converting fractions to percent practice questions

a. Express $\frac{1}{8}$ as a percent.

$\frac{1}{8}=0.125$

$0.125×100$

$12.5%$

b. Express $\frac{5}{3}$ as a percent.

$\frac{1}{3}=0.333\text{...}$

$0.333\text{...}×5=1.6666\text{...}$

$1.6666×100%$

Approximately 167%

c. Express $\frac{30}{25}$ as a percent.

$\frac{30}{25}=\frac{6}{5}$

$\frac{1}{5}=0.2$

$0.2×6=1.2$

$1.2×100%$

$120%$

d. Express $\frac{8}{10}$ as a percent.

$\frac{8}{10}=0.8$

$0.8×100=80%$

$80%$

Percent

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