There's no denying that mathematics is a subject many of us hope we won't have to encounter much outside the classroom. But while most of us won't have to deal with the more complicated areas regularly, simple mathematical concepts such as fractions often crop up in daily life.

Fractions are incredibly useful for visualising and quantifying values and percentages. But in formal writing, it's important that you write them out correctly. Depending on the situation, how you do this will differ. For this reason, we decided to create this handy guide. Regardless of what you're working on, we've got you covered.

Here, we'll walk you through everything you need to know when writing out the different kinds of fractions in formal writing, including the rules to follow. So, to kick things off, let us explain the basic terminology that will help you understand this guide.

Basic terminology for fractions

Mathematics is a subject that contains many technical terms. When it comes to working with fractions, that's no different. Thankfully, however, they often sound more complicated than they actually are. To help you get to grips with things, here are the key terms you'll need to know that will come up later:

Numerator:

Fractions represent parts of a whole quantity or collection of objects. A numerator is a number that represents the number of parts of the whole amount. It is the top value if a fraction is written in numerals. For example, if you have a pizza cut into ten equal slices and leave three slices, you'd have 3/10 of the pizza in the box. In this case, the numerator is the number three.

Denominator:

The denominator is the bottom number in the fraction. It represents the number of parts that the whole quantity has been divided into. So, take the earlier example of a pizza. The pizza was cut into ten slices, and only three remain. The denominator is ten because that's how many slices the pizza was cut into originally. Even though parts of the pizza have been eaten, the denominator remains the same because it shows how many parts the whole pizza was split into.

Cardinal number:

Cardinal numbers, sometimes referred to as "cardinals" or "counting numbers", are numbers used for counting quantities of things. For example, if you were counting marbles in a jar, you'd use cardinal numbers such as one, two, three, and so on. The key thing to note with cardinal numbers is that they don't denote order.

Ordinal number:

Ordinal numbers are numbers used to denote positions in a sequence, such as first, second, third, and fourth. So, say you ran a race and won; you'd receive an award for first place. The next person who crossed the finish line would be second, and so on.

Quantifier:

Quantifiers are words, expressions, or phrases that signify the number of objects that a statement denotes. In mathematics, fractions can be used to signify a reduction or increase in quantity. For example, you could say there has been a 1/3 reduction in the population of a town. In this case, the fraction is referred to as a quantifier as it denotes reduction.

Now we've got the basics covered, let's walk through the rules for writing fractions. We'll then move on to explain how to write different types of fractions.

Rules for writing fractions in words

When it comes to switching fractions from numerals into words, there are some rules to follow:

  • Do hyphenate fractions: it's common practice to hyphenate worded fractions, so it's clear that they should be considered one grammatical unit. For example, 2/5 would be written "two-fifths", with the hyphen placed in the middle. That said, this may differ depending on your institution's style guide for grammar and preferences. Regardless of whether you decide to hyphenate fractions, ensure that you are consistent.
  • Don't double hyphenate long fractions: the only exception to the previous rule is when you write out larger fractions — such as 45/83. Instead of hyphenating between the numerator and the denominator, hyphenate between the two separate numbers for clarity. In this case, you'd write "forty-five eighty-thirds".
  • Don't mix words and numerals: When writing out fractions as words, don't mix numerals in with the wording. For example, for the fraction 3/5, writing "3 fifths" is incorrect. Instead, it should be "three-fifths".

How to write proper and Improper fractions

A proper fraction is a fraction where the numerator is smaller than the denominator. An improper fraction is simply the opposite, where the numerator is larger than the denominator. This means that 2/3, 1/4, and 7/15 are all proper fractions, while 12/5, 5/3, and 12/9 are all improper fractions.

The general rules for writing out both proper and improper fractions are the same. The numerator should be a cardinal number, and the denominator should be an ordinal number. Additionally, you should pluralize ordinal numbers from three onwards if the numerator is three or more — thirds, fourths, fifths, and so on.

So, if you were writing out the fraction 2/3, you'd write "two-thirds". Similarly, if you wanted to spell out the improper fraction 12/5, you'd write it as "twelve-fifths".

There are a couple of exceptions to these rules. The first is that when you write out the fraction 1/2, it should be written as "one-half". The second exception is that if you are writing out a fraction where the denominator is four, you can either write "fourths" "or quarters". So the fraction 3/4 could be written as "three-fourths" or "three-quarters". Depending on what you're writing and where you're based, you may choose one over the other. Regardless, ensure consistency across your work.

How to write mixed fractions

There may be times when you need to write out a number adjoined to a fraction — E.g. 3 2/5.

This is what's known as a mixed fraction or mixed number. To write these kinds of fractions out, you'd write the whole number as a cardinal number, the word "and", then follow it with the written-out fraction using the standard rules. In this case, the written form of the fraction would be "three and two-fifths".

How to write fractions as quantifiers

The rules for writing out fractions differ depending on whether the fraction is being used as a quantifier. If you are using a fraction as a standalone unit, you don't need to hyphenate it. For example, if you said the population was reduced by 2/3, then you'd write the fraction as "two thirds". However, if you use the fraction as a quantifier, you'd write: "There was a two-thirds reduction in the population". The reason is that the fraction denotes a reduction, making it a quantifier.

Frequently Asked Questions

When should you write fractions as words instead of numerals?

You should always write fractions as words if you are writing a formal document such as a newspaper article, essay, or similar. Also, if your institute requires you to comply with their preference for written fractions.

You should also never start a sentence with a numeral fraction, even if you have used then elsewhere. In this case, the best thing to do is to rearrange the sentence so that it doesn't start with a fraction — it's better for continuity.

Should you always hyphenate fractions?

There are some cases where you don't need to hyphenate written fractions. These include:

When the fraction stands alone and is not used as a quantifier.
In the middle of a larger fraction. For example, the fraction 45/83 should be written "forty-five eighty-thirds".

Overall, though, it's common practice to hyphenate fractions. But this is also up to the preference of the institution, such as your company or educational establishment. If you cannot identify or have not been told whether you should hyphenate, choose one and ensure to be consistent throughout your writing.

Writing fractions in words is nowhere near as complicated as some of the mathematical terms make it out to be. When you are faced with a numeral fraction, simply write out the top number (numerator) as a cardinal number, such as one, two, or three. Then insert a hyphen, followed by the bottom number (denominator). The denominator should be written as a pluralized ordinal number if it is the number three or more. So, the fraction 2/3 would be written "two-thirds".

If you have a mixed fraction, such as 3 2/5, write the first number separately, followed by "and", then the fraction. In this case, that's "three and two-fifths". Finally, remember not to mix numerals and words together. Once you find your or your institution's preference, keep your writing of fractions consistent.