A fraction compares a part (numerator) to a whole (denominator). Believe it or not, that’s exactly what percentages do as well, but in a different format. Percent means ‘per 100’. Therefore, percentages are simply a part expressed as a fraction of 100.

However, instead of having a numerator and denominator – which can be visually cluttered and messy – the part is expressed using the percentage symbol ‘%’. This slight change can make it far less daunting to look at and, thus, easier to understand and interpret.

As such, fractions and percentages are often used interchangeably. As we’ll explain in this article, there are real-life scenarios where you must know how to convert a fraction to a percent. Doing so can be tricky if you don’t know what to look out for, but it’s not as hard as it seems.

This article will explain the various methods in which this can be done and the steps involved with each, all without using a percent calculator.

Converting fractions to a percent can be done in two ways: dividing the numerator by the denominator and multiplying the result by 100 or by creating an equivalent fraction with 100 as the denominator and calculating the numerator accordingly.

The first method – called the multiplying by 100 method – is by far the easiest one and can be applied to any fraction. The second method – called the equivalent fraction method – is slightly more difficult and is typically reserved for fractions where the denominator is a factor of 100. In any case, let’s explain the steps involved in both methods.

### Steps to convert fractions to percentage

#### Multiplying by 100

The multiplying by 100 method uses the following formula:

- Percentage = (numerator / denominator) * 100

This can be rearranged as follows:

- Numerator / denominator = percentage / 100

Therefore, this method actually has two methods in itself, both of which will provide you with the same answer but take a different approach. We’ll distinguish between them using the letters ‘A’ and ‘B’.

**Multiplying by 100 A** – the steps are as follows:

- Divide the numerator by the denominator to create a decimal
- Multiply the decimal by 100 to convert it into a percentage

**Multiplying by 100 B **– the steps are as follows:

- Multiply the numerator by 100
- Divide the result by the denominator to convert it into a percentage

As you can see, both methods have the exact same steps, but they are just completed in reverse order. Most people tend to choose method A since it asks you to convert fractions to decimals and then to percentages which is an important relationship in mathematics. However, method B is equally effective, and your choice depends entirely on your personal preference.

When it comes to the division steps, this can be done with either long division, short division, or even a calculator. It may be best to practice with all three so that you are comfortable with all scenarios.

#### Equivalent fractions

The steps involved in this method are as follows:

- Create an equivalent fraction with 100 as the denominator.
- Find the number you must multiply the original denominator by to achieve 100.
- Multiply the original numerator by the same number to find its equivalent numerator. The equivalent numerator is your percentage.

As mentioned earlier, this method is typically reserved for fractions where the original denominator is a factor of 100 since it means the multiplying number will be an integer. This can be applied to denominators that aren’t a factor of 100, but it does result in a more difficult calculation.

### Practice converting fractions to percent

You’ve just learned the methods and theory behind converting a fraction to a percent, but let’s look at some examples to see these in action.

#### Multiplying by 100 – example 1

What is 4/6 as a percent?

Method A

- Divide the numerator by the denominator to create a decimal

4 ÷ 6 = 0.66666

- Multiply the decimal by 100 to convert it into a percentage

One thing to note when multiplying a decimal by 100 is that you need to move the decimal point to the right by two place value. Therefore: 0.66666 x 100 = 66.67. All you need to do from here is add the percent sign to the answer.

This means that 4/6 as a percent is **66.67%**.

Method B

- Multiply the numerator by 100

4 x 100 = 400

- Divide the result by the denominator to convert it into a percentage

400 / 6 = 66.67.

Adding the percent sign gives us our final answer of **66.67%**. This example proves both methods provide you with the same answer.

#### Multiplying by 100 – example 2

What is the fraction 40/110 as a percent?

Method A

- Divide the numerator by the denominator to create a decimal

40 ÷ 110 = 0.363636

- Multiply the decimal by 100 to convert it into a percentage

0.363636 x 100 = 36.36%

This means that the percent value of 40/110 is **36.36%**.

Method B

- Multiply the numerator by 100

40 x 100 = 4000

- Divide the result by the denominator to convert it into a percentage

4000 / 110 = **36.36%**

#### Multiplying by 100 – example 3

What is the percent value of 2/5?

Method A

- Divide the numerator by the denominator to create a decimal

2 ÷ 5 = 0.4

- Multiply the decimal by 100 to convert it into a percentage

0.4 x 100 = 40%

This means that the percent value of 2/5 is **40%**.

Method B

- Multiply the numerator by 100

2 x 100 = 200

- Divide the result by the denominator to convert it into a percentage

200 / 5 = **40%**

#### Equivalent fraction – example 1

To show that this method works just as well as the multiplying by 100 method, let’s use the above fraction of 2/5 and convert this to a percentage.

- Create an equivalent fraction with 100 as the denominator

2/5 = ?/100

- Find the number you must multiply the original denominator by to achieve 100

100 ÷ 5 = 20

- Multiply the original numerator by the same number to find its equivalent numerator. The equivalent numerator is your percentage

2 x 20 = 40

This means that 3/7 as a percentage is **40%**.

Clearly, we have reached the same answer. But that was fairly easy since the denominator 5 is a factor of 100. What happens when this isn’t the case?

#### Equivalent fraction – example 2

What is 3/7 as a percentage?

- Create an equivalent fraction with 100 as the denominator

3/7 = ?/100

- Find the number you must multiply the original denominator by to achieve 100

100 ÷ 7 = 14.2857

- Multiply the original numerator by the same number to find its equivalent numerator. The equivalent numerator is your percentage

3 x 14.2857 = 42.86

This means that 3/7 as a percentage is **42.86%**.

Since 7 is not a factor of 100, the resulting calculations involve many decimal points, which can be tricky to multiply and divide accurately without a calculator. Of course, that doesn't mean it's impossible, only that doing it by hand will take more time and may be more challenging.

#### Equivalent fraction – example 3

What is the percent value of 6/8?

- Create an equivalent fraction with 100 as the denominator

6/8 = ?/100

- Find the number you must multiply the original denominator by to achieve 100

100 ÷ 8 = 12.5

- Multiply the original numerator by the same number to find its equivalent numerator. The equivalent numerator is your percentage

6 x 12.5 = 75

This means that the percent value of 6/8 is **75%**.

### Fraction to percentage conversion table

We’ve just explained how to convert any fraction to a percent, but you’ll often encounter certain fractions more than others. Instead of having to convert them every time, it may make sense to remember them by heart. Therefore, below is a table highlighting some of the most popular fractions you’ll come across.

Fraction | Percent |

1/2 | 50% |

1/3 | 33.33% |

2/3 | 66.67% |

1/4 | 25% |

2/4 | 50% |

3/4 | 75% |

1/5 | 20% |

2/5 | 40% |

3/5 | 60% |

4/5 | 80% |

1/6 | 16.67% |

2/6 | 33.33% |

3/6 | 50% |

4/6 | 66.67% |

5/6 | 83.33% |

1/7 | 14.29% |

2/7 | 28.57% |

3/7 | 42.86% |

4/7 | 57.14% |

5/7 | 71.43% |

6/7 | 85.71% |

1/8 | 12.5% |

2/8 | 25% |

3/8 | 37.5% |

4/8 | 50% |

5/8 | 62.5% |

6/8 | 75% |

7/8 | 87.5% |

1/9 | 11.11% |

2/9 | 22.22% |

3/9 | 33.33% |

4/9 | 44.44% |

5/9 | 55.56% |

6/9 | 66.67% |

7/9 | 77.78% |

8/9 | 88.89% |

1/10 | 10% |

2/10 | 20% |

3/10 | 30% |

4/10 | 40% |

5/10 | 50% |

6/10 | 60% |

7/10 | 70% |

8/10 | 80% |

9/10 | 90% |

### When will I need to convert a fraction to a percent?

This conversion has various real-world applications and is often necessary when comparing, calculating, or presenting data since percentages are much easier to understand and interpret. Examples include tests and scores, accounting, surveys, etc.

For instance, suppose you are a student taking an exam. Your score will be represented as a fraction, with your score being the numerator and the total available score being the denominator. This will then be used to calculate a percentage of how well you performed.

Another example is when crunching numbers for accounting purposes. Suppose you are calculating the profit margin of a business. The business's net profit is the fraction's numerator, and the total revenue earned will be the denominator. You can then calculate the profit margin using the methods outlined in this article.

Also, a fraction to percent calculation is used when conducting surveys and questionnaires. For instance, suppose 4 out of 20 people answered ‘No’ and 16 answered ‘Yes’ to a particular question. Instead of saying 4 out of 20 people answered no, often this will be represented as a percentage, and the same applies to people who answered yes.

Simply place the percent value as the numerator, add the denominator ‘100’, and simplify if possible. And that’s it; that’s all you have to do to successfully convert a percent to a fraction.

Converting a percent to a fraction is far easier than converting a fraction to a percent, mainly because percentages are essentially expressed as a fraction already – percent / 100. The only thing you have to do is show the fraction in its simplest form. Let’s see some examples.

### Practice converting percents to fractions

#### Example 1

What is 30% as a fraction?

To do this conversion, you must:

- Place the percent value as the numerator and add the denominator 100

This gives you the fraction 30/100.

- Check if this can be simplified

Both the top and bottom number can be divided by 10, giving you the fraction: 3/10.

Therefore, 30% as a fraction is **3/10**.

#### Example 2

What is 64% as a fraction?

- Place the percent value as the numerator and add the denominator 100

This results in the fraction 64/100.

- Check if this can be simplified

Both the numerator and denominator can be divided by 4, giving you the fraction: 16/25

Therefore, 64% as a fraction is **16/25**.

#### Example 3

Express 80% as a fraction

- Place the percent value as the numerator and add the denominator 100

This results in the fraction 80/100.

- Check if this can be simplified

Both the numerator and denominator can be divided by 10, giving you the fraction: 8/10.

8/10 can be further simplified by dividing both numbers by 2, giving you the fraction 4/5.

Therefore, 80% as a fraction is **4/5**.

There are two methods to convert a fraction to a percent. The multiplying by 100 method is the most common, but there’s also the equivalent fraction method which is useful if the fraction denominator is a factor of 100.

Both methods will achieve the same final answer but take slightly different approaches. Therefore, it’s important to learn both and choose the one you are most comfortable using.

### How do I convert a fraction to a percentage?

Divide the numerator by the denominator and multiply by 100. Or you can multiply the numerator by 100 and divide by the denominator.

For example, 3/10 as a percentage:

- 3 ÷ 10 = 0.3
- 0.3 x 100 = 30%

### How do I convert a percentage to a fraction?

Place the percentage as the numerator, place ‘100’ as the denominator, and simplify the fraction to its simplest form.

For example, 60% as a fraction:

- 60/100
- Simplify by dividing by 20 = ⅗

### How do you turn 1/4 into a percent?

1/4 as a percentage is 25%:

- 1 ÷ 4 = 0.25
- 0.25 x 100 = 25%

### How do you turn 3/4 into a percent?

3/4 as a percentage is 75%:

- 3 ÷ 4 = 0.75
- 0.75 x 100 = 75%

### How do you turn 3/5 into a percent?

3/5 as a percentage is 60%:

- 3 ÷ 5 = 0.60
- 0.60 x 100 = 60%

### How do you turn 5/8 into a percent?

5/8 as a percentage is 62.5%:

- 5 ÷ 8 = 0.625
- 0.625 x 100 = 62.5%