- 5-minute read
- 22nd June 2020

# How to Write Fractions in Formal Writing

When using a fraction in a formal document, such as an essay, should you write it as words or numerals? It all depends on the situation! Check out our guide on how to write fractions in formal writing to find out more.

### How to Write Fractions

Fractions represent parts of a whole. They do this with a numerator (i.e. the number of parts present) and a denominator (i.e. the number of parts that make up the whole). We can write them as numerals or words.

Numeral | Word |

1/2 | Half |

3/4 | Three quarters |

5/8 | Five eighths |

17/24 | Seventeen twenty-fourths |

But what are the rules about writing fractions? When should they be numerals and when should they be words? Let’s take a look.

### Fractions as Numerals

To write fractions as numerals, do it with the numerator above the denominator, separated by a line. For instance, if we cut something into three parts, each part would be ‘1/3’, and two parts would be ‘2/3’:

*He ate 2/3 of the pizza by himself!*

There are various ways to write fractions as numerals. In the examples above, we have simply used a forward slash between the two numbers. But we could also use a division slash between superscript and subscript numbers (e.g. ^{1}∕_{2, }^{2}∕_{3}) or a horizontal line known as a vinculum.

The correct format is usually a matter of preference, but you should check your style guide for advice if you are using one.

You can also write fractions as words. Let’s look at how this works.

### Fractions as Words

When writing fractions as words, you need to give:

- The numerator as a cardinal number (e.g. one, two, three).
- The denominator as an ordinal number (e.g. third, fifth, sixth).

For instance, we would write ‘2/3’ as ‘two thirds’:

*He ate two thirds of the pizza by himself!*

This applies for most fractions. But there are two exceptions that have their own words: half (1/2) and quarter (1/4). For instance:

*She spent half the day asleep.*

*We have three quarters of the cake.*

Some do use ‘fourths’ in place of ‘quarters’, but this is quite rare outside of American English, so ‘quarters’ will be correct in most cases.

### Should You Write Fractions as Words or Numerals?

So, when should you write fractions as words and when should you write them as numerals? In less formal writing, as long as your meaning is clear, this is simply a matter of preference. But many style guides suggest writing out simple fractions as words in formal writing:

*The subject completed 2/3 of the exercises.* **✗**

*The subject completed two thirds of the exercises.* **✓**

You can also do this for longer or more complex fractions:

*We received feedback from seventeen twenty-fourths of the participants.*

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But numerals may be clearer in cases like this:

*We received feedback from 17/24 of the participants.*

It ultimately comes down to which style guide you are using, so make sure to check if you have one. However, as a rule, we suggest:

- Writing fractions as words in the main text of a document.
- Using numerals for fractions in measurements, tables of results, equations, and other primarily numerical data.

And in the rest of this post, we will look at cases where you need to be careful about how you write fractions.

### Fractions at the Beginning of a Sentence

Even if you are writing fractions as numerals elsewhere, you should not start a sentence with a numeral. For example, the following would be incorrect:

__22/7__ is a good approximation of pi.**✗**

To avoid this, you would either need to write the fraction as words or rephrase the sentence so that it does not begin with a fraction:

__Twenty-two sevenths__ is a good approximation of pi.**✓**

*The fraction 22/7 is a good approximation for the mathematical value pi.*

**✓**

### Mixed Fractions and Consistency

A mixed fraction is a whole number followed by a fraction. If you use a mixed fraction in your writing, make sure to use a consistent style for the whole number and the fraction:

*The boys ate 5 ½ pizzas.*

**✓**

*The boys ate five and a half pizzas.*

**✓**

Never mix words and numerals in a fraction:

*The hungry boys ate thirty-three and ¾ of the pizzas.*

**✗**

### When to Hyphenate a Fraction

Some people like to add a hyphen between the numerator and denominator when writing fractions as words. For instance, while we’ve written ‘two thirds’ above, we could equally write it as ‘two-thirds’:

*The subject completed two-thirds of the exercises.*

Unless your style guide provides advice on this, it is simply a matter of preference (just remember to be consistent!). However, there are two cases where fractions should include a hyphen:

- When a fractions contains a compound number between twenty-one and ninety-nine (e.g.
*twenty-one thirtieths*). - When a fraction acts as either an adjective or an adverb to modify another word (e.g.
*They got a*).__three-quarter__share

So make sure to look out for these cases, even if you’re not hyphenating fractions elsewhere! And if you would like any extra help to make sure your writing is error free, why not submit a document for proofreading?