# Convert Fractions to Percents

Divide the top of the fraction by the bottom, multiply by 100 and add a "%" sign.

## The Simplest Method is to Use a Calculator

- Divide the top of the fraction by the bottom,
- Then multiply the result by 100 and read off the answer !

### Example: What is \frac{5}{8} as a percent?

Get your calculator and type in "5 ÷ 8 =", the calculator should show **0.625**

Then multiply by 100 and your answer is: **62.5%**

(Remember to put the "%" sign so people know it is "per 100")

OR you can multiply the top by 100 first then divide by the bottom number:

### Example: What is \frac{5}{8} as a percent?

Multiply 5 by 100 first, then divide by 8

500 ÷ 8 = 62.5%

(Remember that "%" sign!)

## Or Move the Decimal 2 Places

After dividing, instead of multiplying by 100 we can just **move the decimal point 2 places to the right**, then add the %

### Example: Convert ^{1}/_{8} to a percentage

Divide 1 by 8:

1 ÷ 8 = 0.125

Move the decimal point **2 places to the right**

Remember to add the "%" sign: **12.5%**

## Another (Harder) Method

Percent means "per 100", so try to change the fraction to \frac{?}{100} form.

### Follow these steps:

- Step 1: Find a number you can multiply the
**bottom of the fraction**by to get 100. - Step 2: Multiply both top and bottom of the fraction by that number.
- Step 3. Then write down just the top number with the "%" sign.

### Example 1: Convert \frac{3}{4} to a Percent

Step 1: We can multiply 4 by **25** to become 100

*(why 25? because 100 divided by 4 is 25)*

Step 2: Multiply top and bottom by 25:

×25 |
||

\frac{3}{4} | = | \frac{75}{100} |

×25 |

Step 3: Write down 75 with the percent sign:

### Answer = 75%

### Example 2: Convert \frac{3}{16} to a Percent

Step 1: We have to multiply 16 by 6.25 to become 100

*(why 6.25? because 100 divided by 16 is 6.25)*

Step 2: Multiply top and bottom by 6.25:

×6.25 |
||

\frac{3}{16} | = | \frac{18.75}{100} |

×6.25 |

Step 3: Write down 18.75 with the percentage sign:

### Answer = 18.75%

## Yet Another Method: Proportions

Because a percent is actually a ratio (parts per 100) we can also use Proportions to do the conversion.

First, put what you know into this form:

\frac{Top of Fraction}{Bottom of Fraction} = \frac{Percent}{100}

Then solve using **"multiply across the known corners, divide by the third number"**:

### Example: Convert \frac{3}{16} to percent

Fill in what you know:

\frac{3}{16} = \frac{Percent}{100}

Multiply across the known corners, then divide by the third number. The "known corners" are top left and bottom right:

Percent = (3 × 100) / 16

= 300 / 16

= **18.75**

### Answer: \frac{3}{16} is **18.75%** (same answer as the previous example!)