# ## Fractions to Percents

When you are asked to convert fractions to percentages, there are two different methods you can use.

1. Convert the fraction to a decimal and then convert the decimal to a percentage.
2. Set up a proportion and solve it with cross-multiplication.

I personally prefer the first method, but you can choose whichever method makes the most sense to you. If you need to know how to convert a percentage to a fraction or how to convert a decimal to a fraction, check out the linked pages.

## How to Convert Fractions to Percentages

### Decimal Conversion Method

1. Convert the fraction to a decimal by dividing the numerator by the denominator.
2. Multiply the decimal by 100 (click here for a shortcut to do it in your head).
3. Write your answer with a percentage sign and check if it is reasonable.

It is much easier to convert fractions to percentages if you use a calculator to do the division and multiplication. Just remember that integrity is always more important than math. So, if your teacher does not allow calculators, then use long division and decimal multiplication.

#### Examples

Convert this fraction to a percentage: $\frac{3}{4}$

What is the decimal form of $$\frac{3}{4}$$?

I need to divide the numerator by the denominator to convert the fraction to a decimal.

$3 \div 4 = 0.75$

What is the product of 0.75 and 100?

$0.75 \times 100 = 75$

Is it reasonable that $$\frac{3}{4}=75\%$$?

Yes, it is reasonable that they are equivalent because $$\frac{3}{4}$$ is between a half and a whole and $$75\%$$ is between $$50\%$$ and $$100\%$$.

$\frac{3}{4}=75\%$

Convert this fraction to a percentage: $\frac{9}{5}$

What is the decimal form of $$\frac{9}{5}$$?

I need to divide the numerator by the denominator to convert the fraction to a decimal.

$9 \div 5 = 1.8$

What is the product of 1.8 and 100?

$1.8 \times 100 = 180$

Is it reasonable that $$\frac{9}{5}=180\%$$?

Yes, it is reasonable that they are equivalent because $$\frac{9}{5}$$ is an improper fraction that is just a little bit less than 2 wholes and $$180\%$$ is just a little bit less than $$200\%$$.

$\frac{9}{5}=180\%$

Convert this fraction to a percentage: $\frac{5}{11}$

What is the decimal form of $$\frac{5}{11}$$?

I need to divide the numerator by the denominator to convert the fraction to a decimal.

$5 \div 11 = 0.45454545…$

If I want to, I can write the repeating decimal with a vinculum over the repeating digits.

$0.45454545…=0.\overline{45}$

What is the product of $$0.\overline{45}$$ and 100?

$0.\overline{45} \times 100= 45.454545…$

Is it reasonable that $$\frac{5}{11}=45.\overline{45}\%$$?

Yes, it is reasonable that they are equivalent because $$\frac{5}{11}$$ is just a little bit less than a half and $$45.\overline{45}\%$$ is just a little less than $$50\%$$.

$\frac{5}{11}=45.\overline{45}\%$

### Cross Multiplication Method

1. Set up a proportion by making your fraction equal to $$\frac{x}{100}$$.
2. Use cross multiplication to solve the proportion for x.
3. Write your answer with a percentage sign and check if it is reasonable.

#### Examples

Convert this fraction to a percentage: $\frac{3}{4}$

What proportion will help me find the percentage that is equivalent to $$\frac{3}{4}$$?

$\frac{3}{4}=\frac{x}{100}$

What is x?

$\frac{\red 3}{\yellow 4}=\frac{\yellow x}{\red 100}$

To solve for x, I need to cross multiply the proportion.

${\yellow 4x}={\red 300}$

Then I will divide both sides of the equation by 4 to get x by itself.

${\yellow x}={\red 75}$

Is it reasonable that $$\frac{3}{4}=75\%$$?

Yes, it is reasonable that they are equivalent because $$\frac{3}{4}$$ is between a half and a whole and $$75\%$$ is between $$50\%$$ and $$100\%$$.

$\frac{3}{4}=75\%$

Convert this fraction to a percentage: $\frac{9}{5}$

What proportion will help me find the percentage that is equivalent to $$\frac{9}{5}$$?

$\frac{9}{5}=\frac{x}{100}$

What is x?

$\frac{\red 9}{\yellow 5}=\frac{\yellow x}{\red 100}$

To solve for x, I need to cross multiply the proportion.

${\yellow 5x}={\red 900}$

Then I will divide both sides of the equation by 5 to get x by itself.

${\yellow x}={\red 180}$

Is it reasonable that $$\frac{9}{5}=180\%$$?

Yes, it is reasonable that they are equivalent because $$\frac{9}{5}$$ is an improper fraction that is just a little bit less than 2 wholes and $$180\%$$ is just a little bit less than $$200\%$$.

$\frac{9}{5}=180\%$

What proportion will help me find the percentage that is equivalent to $$\frac{5}{11}$$?

$\frac{5}{11}=\frac{x}{100}$

What is x?

$\frac{\red 5}{\yellow 11}=\frac{\yellow x}{\red 100}$

To solve for x, I need to cross multiply the proportion.

${\yellow 11x}={\red 500}$

Then I will divide both sides of the equation by 11 to get x by itself.

${\yellow x}={\red 45.45454545…}$

Is it reasonable that $$\frac{5}{11}=45.\overline{45}\%$$?

Yes, it is reasonable that they are equivalent because $$\frac{5}{11}$$ is just a little bit less than a half and $$45.\overline{45}\%$$ is just a little less than $$50\%$$.

$\frac{5}{11}=45.\overline{45}\%$

## Why It Works

The cross multiplication method works because percentages can be written as fractions with denominators of 100.

We connect the unknown percentage $$\frac{x}{100}$$ to the fraction with an equal sign because we want to find the percentage that is equivalent to the fraction.

The decimal conversion method works because it is a two-step process of converting fractions to decimals and converting decimals to percentages. To see why each of these sub-steps work, check out the “Why It Works” sections on the linked pages.