SICP 2.1: Rational numbers

From SICP section 2.1.1 Example: Arithmetic Operations for Rational Numbers

Exercise 2.1 asks us to define a better version of make-rat that handles both positive and negative arguments. Here's the last version from the text, along with several example cases to show how it works:

(define (make-rat n d)
  (let ((g (gcd n d)))
    (cons (/ n g) (/ d g))))

> (define x (make-rat 1 2))
> (print-rat x)

1/2
> (define x (make-rat -1 -2))
> (print-rat x)

-1/-2
> (define x (make-rat 1 -2))
> (print-rat x)

1/-2
> (define x (make-rat -1 2))
> (print-rat x)

-1/2

The new version of make-rat should normalize the sign so that if the resulting rational number is positive, both the numerator and denominator are positive. If the rational number is negative, only the numerator should be negative.

We can correct make-rat by checking to see if the denominator is negative. If it is, we need to multiply both the numerator and denominator by -1 to normalize the result. If not, we just pass the arguments bare to cons.

(define (make-rat n d)
  (let ((g (gcd n d)))
    (if (< d 0)
        (cons (/ (* n -1) g) (/ (* d -1) g))
        (cons (/ n g) (/ d g)))))

We can use the same definitions as before to see the results from the new make-rat procedure.

> (define x (make-rat 1 2))
> (print-rat x)

1/2
> (define x (make-rat -1 -2))
> (print-rat x)

1/2
> (define x (make-rat 1 -2))
> (print-rat x)

-1/2
> (define x (make-rat -1 2))
> (print-rat x)

-1/2

Related:

For links to all of the SICP lecture notes and exercises that I've done so far, see The SICP Challenge.