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How to read and write fractions

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To read a fraction, say the numerator as a number and the denominator with the name of the part. 5/7 is “five sevenths”: five parts, each one a seventh of the whole. When the numerator is 1 the name is singular, “one seventh,” and with any other numerator it is plural.

How each denominator is named

In English the denominator is read as an ordinal number, and it is made plural when the numerator is not 1. Two denominators are special: 2 is read half (halves in the plural) and 4 can be read fourth or quarter. This follows the English Wikipedia article on fractions, cited at the bottom.

How a fraction is read, by denominator
DenominatorName of the partExample
2half1/2, "one half" or "a half"
3third1/3, "one third"
4fourth or quarter3/4, "three fourths" or "three quarters"
5 to 7fifth, sixth, seventh2/5, "two fifths"
8 and 9eighth, ninth3/8, "three eighths"
10tenth7/10, "seven tenths"
11, 12, 20eleventh, twelfth, twentieth7/11, "seven elevenths"
100hundredth1/100, "one hundredth"
1000thousandth1/1000, "one thousandth"

The table reads from top to bottom like a staircase: the larger the denominator, the smaller each part. That is why a hundredth is much less than a half, even though both are “one part.”

Singular, plural and denominators over 10

Agreement follows the numerator: “one fourth” but “three fourths.” It works the same way past 10: 1/12 is “one twelfth” and 5/12 is “five twelfths.” Compound denominators are built from the whole number, for example 9/20 “nine twentieths” and 4/25 “four twenty-fifths.”

The denominators 100 and 1000 are read hundredths and thousandths. That is why 13/100 is “thirteen hundredths” and is also 0.13 as a decimal.

“One half” and “half” are not always interchangeable. “One half” names the number, as in “one half plus one fourth”; “half” is used for part of something concrete, like half of 18. For 1/11 there is a similar distinction between “an eleventh” and the position “the eleventh,” which the post Eleventh or one eleventh? explains.

How to read a mixed number

A mixed number adds a whole number and a fraction, and it is read with the word “and” between the two: 4 5/6 is “four and five sixths.” The fraction alone, 29/6, is read “twenty-nine sixths,” and the two ways of writing name the same amount.

Worked example: reading a mixed number and writing it as a fraction

A stretch of trail is four and five sixths miles long. How is it read, and how is it written with a single fraction?

  1. Read the mixed number. “Four and five sixths,” that is, 4 plus five sixths.
  2. Turn the wholes into sixths. Each whole has 6 sixths, so 4 wholes are 4 × 6 = 24 sixths.
  3. Add the parts. 24/6 + 5/6 = 29/6.
  4. Read the result. 29/6 is “twenty-nine sixths.”

Result: 29/6 of a mile.

Check: 29 ÷ 6 is 4 with 5 left over, which is the mixed number you started with.

How to write a fraction said in words

The first number in the phrase is the numerator, and the name of the part gives the denominator. “Five ninths of a gallon” is written 5/9 gal: the gallon is the whole and each part is 1/9 of a gallon. “Seven of twelve equal parts” is 7/12.

The order matters. “Three fourths” is 3/4 and “four thirds” is 4/3, which already exceeds one whole. The denominator does not count objects or units of measure: in “three fifths of a pizza” the 5 counts the equal parts of one pizza, not five pizzas.

If you do not remember the name, say “numerator parts of denominator,” for example “eleven parts of fifteen,” and show the written fraction. The steps for writing fractions in a document are in the guide to fractions in Word and Google Docs.

Practice

  1. Read 11/15.
  2. Write “thirteen hundredths” with numbers.
  3. Write “four and two thirds” as a mixed number and as an improper fraction.
Show the answers
  1. “Eleven fifteenths.”
  2. 13/100.
  3. 4 2/3 = (4 × 3 + 2)/3 = 14/3.

Where to go next

To know what each number in the fraction counts, the guide to numerator and denominator explains it with figures. If a reading makes you doubt between proper, improper or mixed, the guide to types of fractions tells them apart. The mixed number to fraction tool checks the conversion of any mixed number, and visual fractions draws the fraction you just read.

Sources

Frequently asked questions

Can a fraction be read as “numerator over denominator”?

Yes. “Five over nine” identifies 5/9 without doubt and is heard a lot in class. “Five ninths” also tells the size of each part. Always keep the order: “nine over five” would be 9/5, a quantity greater than 1. If you do not know the name of the denominator, this reading works.

How is a negative fraction read?

Put “negative” (or “minus”) in front: −4/9 is “negative four ninths.” With a mixed number, the sign applies to the whole number: −1 2/3 is read “negative one and two thirds” and equals −(1 + 2/3) = −5/3. Writing −1 + 2/3 would give a different number, −1/3.

Is a fraction read the same as its equivalent?

Not necessarily. 6/8 is “six eighths” and 3/4 is “three fourths” (or “three quarters”), even though they are worth the same. The reading tells how the whole was divided and how many parts are taken. To go from one to the other, see equivalent fractions and the simplify calculator.

How is a fraction read as a division?

The bar also means ÷, so 7/4 can be read “seven divided by four” and equals 1.75. This reading explains why a fraction can exceed 1: seven divided by four gives 1 with 3/4 left over. It works as long as the denominator is not zero.

Next step

Fraction Guides Find the guide that answers your question: what a fraction is, why 1/2 + 1/3 = 5/6, GCF or LCM, repeating decimals or sharing a total.
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