# Integer and fractional part: propfrac propFrac

### 5.7.2 Integer and fractional part: propfrac propFrac

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 command writes a fraction as an integer plus a proper fraction.
propFrac is a synonym for propfrac.

- propfrac takes one argument:
  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=bq+r.

(For rational expressions, see Section 5.32.8.)

#### Examples.

- Input:
  propfrac(42/15)
  Output:

  2+

  4
  5

- Input:
  propfrac(43/12)
  Output:

  3+

  7
  12