diff --git a/collects/tests/typed-scheme/optimizer/generic/one-arg-arith.rkt b/collects/tests/typed-scheme/optimizer/generic/one-arg-arith.rkt
new file mode 100644
index 00000000..990036e4
--- /dev/null
+++ b/collects/tests/typed-scheme/optimizer/generic/one-arg-arith.rkt
@@ -0,0 +1,20 @@
+#lang typed/scheme #:optimize
+
+(require racket/unsafe/ops)
+
+(- 12)
+(- 12.0)
+(/ 4.2)
+
+(+ 1)
+(+ 1.0)
+(+ (expt 2 100))
+(* 1)
+(* 1.0)
+(* (expt 2 100))
+(min 1)
+(min 1.0)
+(min (expt 2 100))
+(max 1)
+(max 1.0)
+(max (expt 2 100))
diff --git a/collects/typed-scheme/optimizer/fixnum.rkt b/collects/typed-scheme/optimizer/fixnum.rkt
index 17044a15..fbe684c1 100644
--- a/collects/typed-scheme/optimizer/fixnum.rkt
+++ b/collects/typed-scheme/optimizer/fixnum.rkt
@@ -71,6 +71,12 @@
            #:with opt
            (begin (log-optimization "binary nonzero fixnum" #'op)
                   #'(op.unsafe n1.opt n2.opt)))
+
+  (pattern (#%plain-app (~and op (~literal -)) f:fixnum-expr)
+           #:with opt
+           (begin (log-optimization "unary fixnum" #'op)
+                  #'(unsafe-fx- 0 f.opt)))
+
   (pattern (#%plain-app (~and op (~literal exact->inexact)) n:fixnum-expr)
            #:with opt
            (begin (log-optimization "fixnum to float" #'op)
diff --git a/collects/typed-scheme/optimizer/float.rkt b/collects/typed-scheme/optimizer/float.rkt
index 9890d7b3..b7970212 100644
--- a/collects/typed-scheme/optimizer/float.rkt
+++ b/collects/typed-scheme/optimizer/float.rkt
@@ -68,13 +68,22 @@
            #:with opt
            (begin (log-optimization "binary float" #'op)
                   (n-ary->binary #'op.unsafe #'f1.opt #'f2.opt #'(fs.opt ...))))
-  (pattern (~and res (#%plain-app (~var op (float-op binary-float-comps))
-                                  f1:float-expr
-                                  f2:float-expr
-                                  fs:float-expr ...))
+  (pattern (#%plain-app (~var op (float-op binary-float-comps))
+                        f1:float-expr
+                        f2:float-expr
+                        fs:float-expr ...)
            #:with opt
            (begin (log-optimization "binary float comp" #'op)
                   (n-ary->binary #'op.unsafe #'f1.opt #'f2.opt #'(fs.opt ...))))
+
+  (pattern (#%plain-app (~and op (~literal -)) f:float-expr)
+           #:with opt
+           (begin (log-optimization "unary float" #'op)
+                  #'(unsafe-fl- 0.0 f.opt)))
+  (pattern (#%plain-app (~and op (~literal /)) f:float-expr)
+           #:with opt
+           (begin (log-optimization "unary float" #'op)
+                  #'(unsafe-fl/ 1.0 f.opt)))
   
   ;; we can optimize exact->inexact if we know we're giving it an Integer
   (pattern (#%plain-app (~and op (~literal exact->inexact)) n:int-expr)
diff --git a/collects/typed-scheme/optimizer/number.rkt b/collects/typed-scheme/optimizer/number.rkt
new file mode 100644
index 00000000..81acd094
--- /dev/null
+++ b/collects/typed-scheme/optimizer/number.rkt
@@ -0,0 +1,16 @@
+#lang scheme/base
+
+(require syntax/parse
+         (for-template scheme/base scheme/flonum scheme/unsafe/ops)
+         "../utils/utils.rkt"
+         (optimizer utils))
+
+(provide number-opt-expr)
+
+(define-syntax-class number-opt-expr
+  ;; these cases are all identity
+  (pattern (#%plain-app (~and op (~or (~literal +) (~literal *) (~literal min) (~literal max)))
+                        f:expr)
+           #:with opt
+           (begin (log-optimization "unary number" #'op)
+                  ((optimize) #'f))))
diff --git a/collects/typed-scheme/optimizer/optimizer.rkt b/collects/typed-scheme/optimizer/optimizer.rkt
index eae6d01e..a3a93ea8 100644
--- a/collects/typed-scheme/optimizer/optimizer.rkt
+++ b/collects/typed-scheme/optimizer/optimizer.rkt
@@ -7,7 +7,7 @@
                        racket/private/for)
          "../utils/utils.rkt"
          (types abbrev type-table utils subtype)
-         (optimizer utils fixnum float inexact-complex vector string
+         (optimizer utils number fixnum float inexact-complex vector string
                     pair sequence box struct dead-code))
 
 (provide optimize-top)
@@ -21,6 +21,7 @@
   #:literal-sets (kernel-literals)
 
   ;; interesting cases, where something is optimized
+  (pattern e:number-opt-expr          #:with opt #'e.opt)
   (pattern e:fixnum-opt-expr          #:with opt #'e.opt)
   (pattern e:float-opt-expr           #:with opt #'e.opt)
   (pattern e:inexact-complex-opt-expr #:with opt #'e.opt)