“Fractions” are naturally difficult for children to understand, which is why it is only given more careful attention in the second half of primary school.

While this is the case in the educational setting, adults meanwhile find it hard to master the concept of fractions particularly in the context of formal writing.

So, this post focuses on the details of writing fractions as well as knowing their common types to help you write more accurately and efficiently.

Without further ado, let’s get right into it.

**How should we write fractions in formal writing?**

**In formal writing, simple and common fractions like “one-third,” “two-thirds,” and “three-fourths” are generally written in words. However, complex ones like improper and mixed fractions (i.e., fractions greater than 1) are typically written either in numeral or decimal form.**

**A general guide to writing fractions in formal writing**

A lot of symbols tend to be intimidating for many of us because we do not necessarily have to use them on a daily basis.

For instance, the **meaning of the symbol “॥**”** in math** which suggests parallelism or norm value is foreign to those who are not engaged in the field of mathematics.

But, other mathematical concepts are relatively easier to grasp because we are often exposed to elements as such.

In particular, fractions are meanwhile much easier to understand than parallelism and norm value because fractions are, by and large, applicable in our daily lives.

Writing fractions means representing the idea of having “parts of a whole” through understandable symbols such as words, numbers, as well as punctuation marks.

Even if fractions are predominatly used and discussed in maths, they may also be needed in formal writing scenarios from time to time.

In general, formal writing entails learning **how to properly start formal letters** and formatting all the necessary parts according to widely-accepted writing guidelines.

However, writing fractions formally specifically means methodically referring to specific writing style guidelines prescribed by different institutions and organizations.

As there are numerous guidelines available, the rules recommended by the most popular writing manuals are only highlighted later in this post.

But before we get to that intricate part, first, let us try to learn the different types of fractions to really understand what’s going on here.

**Types of fractions**

Fractions are a type of numerals used to represent the idea that a part, as well as other several equal parts, of a whole exists.

To put it simply, fractions can be used to teach a child that a whole pizza or cake can actually be shared with other people like friends and family.

In less technical language, a fraction may also be referred to as a “portion,” “segment,” “piece,” or “fragment” depending on the context of the language use.

Two major parts make up a fraction: the “numerator” or the number above the fractional bar and the “denominator” or the number below the fractional bar.

The numerator indicates the number of “taken or used parts” based on the value of the denominator, just like the number “1” in the examples below:

Examples:

*1/2, 1/3, 1/4, 1/5, 1/6*

Moreover, fractions can be divided into three basic types according to the relationship between their numerators and denominators.

A fraction whose numerator value is smaller than the denominator belongs to the type called “proper fractions.”

Examples:

*1/4, 2/3, 2/5, 3/8, 5/6*

On the contrary, “improper fractions” are those fractions whose numerators are larger than the denominators.

Examples:

*6/3, 5/2, 8/3, 7/4, 9/6*

Meanwhile, when a fraction is made up of **a whole number** and a fractional part, it belongs to the third type called “mixed fractions.”

Examples:

*2 ⅜, 1 ½, 4 ⅜, 3 ⅖, 1 ¾*

Although fractions are generally classified and written as explained above, they may also be represented in decimal forms after doing conversions.

When this is the case, fractions are more specifically called “decimal fractions.”

Examples:

*0.70, 0.48, 0.25, 0.33, 0.96*

**Writing fractions as numerals**

In general, fractions can be written as numerical figures that represent portions or quantities not equal to 1 or a whole.

There are different ways of representing fractions as numerals in your word processor; the choice is a matter of preference if and when you are not strictly adhering to a style guide.

The first way of writing fractions is done using a horizontal fractional bar, also known as a “vinculum,” between the numerator and denominator.

Examples:

*2*

*3*

*,*

*4*

*3*

*,*

*1*

*5*

*,*

*12*

*7*

*,*

*3*

*4*

Another is using the forward-slash between the numerator and the denominator like the following:

Examples:

*3/5, 2/3, 7/10, 1/6, 4/5*

Or, fractions may also be written using a superscript and a subscript together with a division or forward slash between the numerator and the denominator.

Example:

*⅝, ½, ⅖, ⅜, ⅓*

All the variations above are applicable in math-related contexts. Sometimes, though, we might get confused with fraction-like symbols that appear in other language contexts.

An example of this is **the usage of “v/r” in emails and letters** which rather stands for the expression “very respectfully” instead of a fractional concept.

Another example that may likely cause misinterpretation is **the usage of “/j” in emails** which implies that the sender is trying to convey a message jokingly.

Tricky symbolic expressions like “v/r” and “/j” should be avoided in most formal writing cases to prevent misinformation.

At the same time, we also have to be aware of these nuances to avoid miscommunication, especially with those people whose first language is not English.

**Writing fractions as words**

Now that we’re done with the easy part, let us also learn how to represent fractions in words in case your style guide specifically suggests doing so.

The general rule in writing fractions as words is to write the numerator as a cardinal number and the denominator as an ordinal number in its plural form.

A cardinal number is also known as a “counting number” or the way we say “one, two, three, for, five, six,” etc. in conversations.

Meanwhile, the manner of writing or speaking “in order” or “in sequence” such as when we say “first, second, third, fourth” makes use of ordinal numbers.

Writing ordinal numbers in their plural form means applying pluralization rules, thereby making the ordinals “thirds, fourths, fifths, sixths, or sevenths” instead.

Therefore, to write fractions as words, we have to say “three-fourths” or “two-thirds,” for instance.

Example:

*The president won the election by garnering*

*two-thirds**of the citizens’ votes.*

*The plague was responsible for wiping out about **three-fourths** of the entire population.*

Until now, there is still controversy as to whether a hyphen should come between the numerator and denominator; hence, the hyphen is optional.

But, the more popular choice to date, at least over the internet, is to use a hyphen so as to assist the readability of written texts.

If there are rules, there are also exceptions – this is also true among fractions. The first exception is related to writing fractions with “1” as the numerator.

Logically speaking, the number “1” is considered grammatically singular in number; therefore, the word representing the denominator should not be pluralized if the numerator is “1.”

This means that we have to say “one-third,” “one-fifth,” “one-sixth,” or “one-eighth” instead.”

Example:

*One-third**of the class has been late due to the heavy rains.*

Also, remember that this rule is also related to the agreement between the subject and the verb used in the sentence.

A singular subject that follows the fractional element must be paired with a singular verb as well.

Example:

*One-third**of the*

*population*

*has*

*been**diagnosed with chronic diseases.*

Clearly enough, a plural subject must also make use of a plural verb.

Example:

*Two-thirds**of the*

*participants*

*are**adult male students.*

**Writing fractions in formal writing according to style guides**

When dealing with written fractions in formal writing, the first thing to do is to refer to the writing style manual prescribed or suggested by your organization.

Fields like social and behavioral sciences mainly follow the formatting suggested by the American Psychological Association or APA.

Journalists and newswriters adhere to the Associated Press writing guidelines; whereas writers, editors, and publishers alike follow the Chicago Manual of Style or CMS (also CMoS).

Let us get into the nitty-gritty of fractions according to each of these writing style giants.

**Writing fractions in ****APA style**

The general rule in writing numerals including common fractions according the the APA manual is to use numbers in expressing anything 10 and higher.

Example:

*The study showed that 11/25 of the participants are unaware of the program.*

This also means that numerals below 10, particularly zero to nine, are to be expressed in words rather than numbers.

Example:

*Two-thirds of the interviewees did not disclose their real names.*

In the last example sentence above, you may also notice that no hyphen is used in expressing the fractional phrase; this is done according to the APA format.

But, a hyphen must be used when the fractional element is specifically used as an adjective or adverb modifier for other words.

Example;

*A two-thirds vote is necessary to pass bills in congress.*

Also, the APA strongly suggests not using numerals as the first element in a sentence; hence, the best practice is to paraphrase the sentence to avoid beginning with a number.

Moreover, certain rules also apply to decimal fractions in APA format. It recommends using a zero before the decimal point if the statistical data can be greater than 1.

Examples:

*t*(35) = 0.67

Cohen’s *d = *0.81

However, no zero should be placed before a decimal fraction if a piece of statistical data is unable to go beyond 1.

Example:

*r*(24) = -.28

*p =*.0413

**Writing fractions in ****AP style**

Meanwhile, the AP style specifically suggests writing fractions that are not greater than one in words, particularly with the help of a hyphen.

Example:

*The paunchy kid gobbled on two-thirds of the cake.*

However, fractions larger than 1 must be written in numerical figures to represent them more clearly; this rule includes mixed numbers in particular.

A single space between the whole number and the fraction is also to be used when writing mixed fractions.

Example:

*The final contender finished 3 ½ whole roasted chickens in seven minutes.*

But, more importantly, the AP suggests converting larger and more complicated fractions to decimals for practical reasons.

Example:

*Eating 3.5 whole chickens in a single meal is unbelievable.*

The rule above also means that while using one or two “four-thirteenths” in a single text is okay, having too many of them would be considered unruly.

**Writing fractions in CMS style**

Writing according the CMS is more or less the same with the APA and AP styles, particularly writing simple and common fractions like one-half and two-thirds in words.

Example:

*One-fourth of the class did not pass the final exam.*

But, more complex fractions like “twelve-nineteenths” or “seven-thirteenths” need to be converted into “0.63” and “0.54” instead.

Example:

*The final exam was quite difficult, which resulted in the failure of 0.63 of the class.*

In writing mixed fractions, the CMS also prescribes not putting a space between the whole number and the fractional element, unlike the AP style.

Example:

*You’ve already eaten 4½ apples. Aren’t you full yet?*

**When not to use fractions in formal writing**

As you can see, general and specific rules apply when using fractions in formal writing. But, when do we have to avoid them?

There are two easy-to-remember answers to the question above. The first one is that a numeral fraction – fractions written using numbers – should never begin a sentence.

As the human mind is conditioned to recognize capital letters at the beginning of a sentence, it becomes naturally hard to distinguish where sentences start and end if we see numerals instead.

The second thing to remember is that expressing fractions in words meanwhile has to be avoided if and when it makes reading a more difficult activity.

Reading is inarguably a complex process that entails so much time and effort to get done; so, it is always better to find more practical alternatives to make it less taxing.

But, above all, consistency is always key in making writing more readable and therefore remarkable for all types of audiences.

**Frequently Asked Questions on “Writing Fractions in Formal Writing”**

**What is the difference between a “ratio” and a “fraction”?**

While ratios are used to represent the idea that a number can contain another number once or more, fractions are used to represent the idea that a part or parts of a whole exists.

**What are the different ways of writing fractions?**

Fractions can be written using a horizontal fractional bar or forward slash between the numerator and denominator. A superscript and subscript may also be used to represent fractions as well as decimals.

**How do we write “¾” in words?**

The expression** “**three-fourths” is used to represent the fractional part “¾.” Another way of representing this value in words is by using the phrase “seventy-five percent.”

**Conclusion**

Although children and adults have different struggles regarding fractions, it is clear that there is a gap as to how both groups learn math and language skills.

This gap likely implies that more emphasis should be also be given in teaching children how to convert numerals into words at school.

Hey fellow Linguaholics! It’s me, Marcel. I am the proud owner of linguaholic.com. Languages have always been my passion and I have studied Linguistics, Computational Linguistics and Sinology at the University of Zurich. It is my utmost pleasure to share with all of you guys what I know about languages and linguistics in general.