diff --git a/src/dask_awkward/lib/core.py b/src/dask_awkward/lib/core.py
index e52e43af..98b03e63 100644
--- a/src/dask_awkward/lib/core.py
+++ b/src/dask_awkward/lib/core.py
@@ -500,19 +500,17 @@ def f(self, other):
             deps = [self]
             plns = [self.name]
             if is_dask_collection(other):
-                task = (op, self.key, *other.__dask_keys__())
                 deps.append(other)
+                plns.append(other.name)
                 if inv:
-                    plns.insert(0, other.name)
+                    task = (op, *other.__dask_keys__(), self.key)
                 else:
-                    plns.append(other.name)
+                    task = (op, self.key, *other.__dask_keys__())
             else:
                 if inv:
                     task = (op, other, self.key)
                 else:
                     task = (op, self.key, other)
-            if inv:
-                plns.reverse()
             graph = HighLevelGraph.from_collections(
                 name,
                 layer=AwkwardMaterializedLayer(
@@ -532,6 +530,11 @@ def f(self, other):
                     meta = op(other, self._meta)
                 else:
                     meta = op(self._meta, other)
+            if meta.ndim:
+                divisions = other.divisions if is_dask_collection(other) else [0, 1]
+                return new_array_object(
+                    graph, name, meta=ak.Array(meta), divisions=divisions
+                )
             return new_scalar_object(graph, name, meta=meta)
 
         return f
@@ -570,6 +573,15 @@ def f(*args):
         args = tuple(
             ak.Array(arg.content) if isinstance(arg, MaybeNone) else arg for arg in args
         )
+        args = tuple(
+            (
+                ak.Array(arg)
+                if isinstance(arg, ak._nplikes.typetracer.TypeTracerArray)
+                else arg
+            )
+            for arg in args
+        )
+
         result = op(*args)
         return result
 
@@ -2598,6 +2610,8 @@ def typetracer_array(a: ak.Array | Array) -> ak.Array:
             behavior=a._behavior,
             attrs=a._attrs,
         )
+    elif isinstance(a, numbers.Number):
+        return ak.Array([a]).layout.to_typetracer()
     else:
         msg = (
             "`a` should be an awkward array or a Dask awkward collection.\n"
diff --git a/tests/test_core.py b/tests/test_core.py
index 8dd82b9f..e679c051 100644
--- a/tests/test_core.py
+++ b/tests/test_core.py
@@ -440,8 +440,6 @@ def test_typetracer_function(daa: Array) -> None:
     tta = typetracer_array(aa)
     assert tta is not None
     assert tta.layout.form == aa.layout.form
-    with pytest.raises(TypeError, match="Got type <class 'int'>"):
-        typetracer_array(3)
 
 
 def test_single_partition(ndjson_points_file: str) -> None: