7.2.2  Integral and fractional part of a rational number

Rational numbers are often broken up into integer and fractional parts, where the fractional part has absolute value less than 1; i.e., the absolute value of the top integer is smaller than that of the bottom integer. Such a fraction is called a proper fraction. The propfrac or propFrac command writes a fraction as an integer plus a proper fraction.

• propfrac takes r, a rational number.
• propfrac(r) returns

  q+

  r b

  with   0≤ r<b

  where r=a/b is in lowest terms and and a=b q+r.

(For rational expressions, see Section 11.6.8.)

Examples