The short answer is that Tcl (like most comuter languages) doesn't do
fractions; it only knows about integers and floating-point numbers. 
Hence [expr] doesn't "evaluate" fractions, but the way you would ask it to
compute a quotient may look like as it evaluates a fraction.

[[Explain idioms of "computer arithmetic".]]

Sometimes, [Tcl]'s [expr]ession handling can be a little bit unexpected to newcomers:
 % expr 1/2
 0

This is because the above code asks for ''integer'' division (this is true in many other languages too) and that (conceptually) contains a round-down-to-int of the result. (The remainder operation, %, is often useful when you're working with integer division).
 % puts "1/2 is [expr 1/2] remainder [expr 1%2]"
 1/2 is 0 remainder 1

If you really want to end up with a half, force one of the arguments to the division operation to be a floating-point value:
 % expr double(1)/2
 0.5

See [expr problems with int] for more on integer division and how to avoid it.

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rdt : 2005-01-27 : This is a property of integers that can take on values of 0,1,2,... and therefore have no values between 0 and 1.  However:
 % expr 1.0 / 2
 0.5
show the expected value.  Whereas in a calculator, most math is done
in floating point, in Tcl, floating point math is only performed when
you explicitly say to do so.

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[GWM] A quaint gotcha to beware of:

expr 225/119/84. => 0.0119047619048

while

expr 225./119/84 => 0.0225090036014

In the the first case the division (225/119) is performed as integer division (giving 1) then divided by the real 84. In the second case 225./119 is floating point and divided by 84 gives the correct answer.

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[Category Mathematics]