### 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

propfrac(42/15)

2+

4
5

propfrac(43/12)

3+

7
12