Why is the numpad on a keyboard not designed to print typographically correct symbols?

Question

As Wikipedia states, the numeric keypad, number pad or short numpad

provides calculator-style efficiency for entering numbers. The numpad’s keys are digits from 0 to 9, addition (+), subtraction (−), multiplication (×) and division (÷) symbols, …

I wonder now why for instance when we press the − key on our numpad a hyphen-minus (Unicode character U+002D and HTML symbol &#45) gets displayed rather than the “correct” minus sign (Unicode character U+2212 and HTML symbol −).

The same thing applies also to the +, × and ÷ keys;

• the + yields not a full-width plus (＋), but rather a standard + sign,
• the × prints an asterisk (*) and no multiplication sign (×)
• and the ÷ displays a slash (/) rather than the suspected obelus (÷)

… although all of this symbols are shown on the keyboard keys as you can see in the following German computer keyboard illustration from commons.wikimedia.org:

Is there any technical reason for this behavior – as @CAI mentions in his answer about the correct minus sign – or a is this only because of historical reason?

Answer 1

Historical reasons only – plus a side dish of "backward compatibility".

The original PC keyboards were very much 'typewriter-like'. Also, in the original ASCII set there were no 'fullwidth plus', 'minus', and 'multiply' symbols. The common MS-DOS 'extended ASCII' set contained a proper 'divide' – but only in certain codepages. (Only a guess, but it can be assumed the asterisk was chosen for 'multiplication' rather than × because it would look too close to the lowercase character x.)

Since lots of computers were used for administrative purposes only, the calculator-like keypad addition appeared later on. Initially it doubled for use with the arrow, page up/down, and home/end keys; later on, these in turn appeared as extra extra keys. The labeling on the keypad keys duplicated those of calculators at that time, but the character they typed had to be the same as the original ones used, for compatibility with existing software and for keyboards without the extra keys.

The key caps reflect what the keys insert into programs to do the function they describe. It’s quite similar to pressing a key labelled "Backspace" and expecting that literal text to turn up.

I know of no software at all that allows to use the Unicode character × for multiplication. The same goes for the Unicode characters Mathematical Minus and Divide (come to think of it, neither do other function/characters such as the Square glyph "²" – entering "5²" into a calculator does not make it show "25" – and the Square Root character).

It’s not the only peculiarity of standard keyboards. Most have All Caps letters printed on the keys, but all of the computers I know start up in lowercase mode, and it takes an extra key (Shift) or software mode (Caps Lock) to actually enter uppercase characters.