One-character fractions
Unicode has 18 everyday fractions as single characters: ½, the thirds, the quarters, the fifths, the sixths, ⅐, the eighths, ⅑ and ⅒. Their official names start with "vulgar fraction", where vulgar simply means common. There is also ↉ (zero thirds) and ⅟, a "one over" piece you can put in front of any digit.
½, ¼ and ¾ are the oldest. They sit in the Latin-1 block, have Windows Alt codes and work in practically every font. The rest are in the Number Forms block; they are well supported on modern phones and computers, but ⅐, ⅑ and ⅒ were added later and can be missing from older fonts.
How to write any other fraction
There is no single character for 5/12 or 1/16, but you can build one: a superscript numerator, the fraction slash ⁄ (U+2044) and a subscript denominator, as in ⁵⁄₁₂ and ¹⁄₁₆. The pieces are in the building blocks above, or on the superscript symbols and subscript symbols pages.
The fraction slash is not the ordinary slash /. It is more slanted and tells software that the digits around it form one fraction. For mixed numbers, put the whole number right before the fraction: 1½, 2¾. In recipes and measurements this reads better than 1 1/2, where the space is easy to miss.
How to type fractions
On Windows, use Alt + 0189 for ½, Alt + 0188 for ¼ and Alt + 0190 for ¾. Other fractions have no Alt code. Word turns 1/2, 1/4 and 3/4 into ½, ¼ and ¾ as you type; for the others, type the code, such as 2153 for ⅓, and press Alt + X.
A Mac and an iPhone have no default fraction keys, so use the Character Viewer (Control + Command + Space), copy from this page, or set up text replacements. On Android, Gboard shows fractions such as ½, ⅓ and ¾ when you long-press the number keys on the symbols keyboard.
In HTML, use ½, ¼ and ¾. In LaTeX, write \frac{1}{2}. For the single most used fraction, see the 1/2 symbol page.