Construct a better rational number representation

Piece of cake! (Which means there's a really steep slope coming up
pretty soon! :D)

chapter1/ex2-1-1-better-rational-math.scm

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+; Ex. 2.1 A better implementation of rational arithmetic
+
+; Construct rational number as a pair object. 
+; ; This improves upon the make-rat procedure of Section 2.1.2.
+(define (make-rat n d) 
+    (let ((norm-n (abs (/ n (gcd n d))))
+          (norm-d (abs (/ d (gcd n d))))
+          (same-sign? (or (and (< n 0) (< d 0)) 
+                          (and (> n 0) (> d 0)))))
+      (cond ((= n 0) 
+             (cons 0 1))
+            ((= d 0) 
+             (error "The denominator must be non-zero! " d))
+            (same-sign?
+             (cons norm-n norm-d))
+            (else
+             (cons (- norm-n) norm-d)))))
+
+
+; Extract the numerator and/or denominator of a rational number, 
+; assuming it is represented as a pair object.
+(define (numer x) (car x))
+
+(define (denom x) (cdr x))
+
+
+; Perform rational number arithmetic operations
+(define (add-rat x y)
+    (make-rat (+ (* (numer x) (denom y))
+                 (* (numer y) (denom x)))
+              (* (denom x) (denom y))))
+
+(define (sub-rat x y)
+    (make-rat (- (* (numer x) (denom y))
+                 (* (numer y) (denom x)))
+              (* (denom x) (denom y))))
+
+(define (mul-rat x y)
+    (make-rat (* (numer x) (numer y))
+              (* (numer x) (numer y))))
+
+(define (div-rat x y)
+    (make-rat (* (numer x) (denom y))
+              (* (denom x) (numer y))))
+
+(define (equal-rat? x y)
+    (= (* (numer x) (denom y))
+       (* (numer y) (denom x))))
+
+
+; Display a pair object using the conventional rational number 
+; notation.
+(define (print-rat x)
+    (newline)
+    (display (numer x))
+    (display "/")
+    (display (denom x)))