diff --git a/fixedcal/core/date.py b/fixedcal/core/date.py
index 73cc1cf..f4ea0ef 100644
--- a/fixedcal/core/date.py
+++ b/fixedcal/core/date.py
@@ -108,5 +108,13 @@ class FixedDate:
             return 4
         return ((self.day_of_year-1) // 91) + 1
 
-    # TODO: plus and minus operations
-    # TODO: equatable
+    def __eq__(self, o: "FixedDate") -> bool:
+        return self._day_of_year == o.day_of_year and self._year == o.year
+
+    def __gt__(self, o: "FixedDate") -> bool:
+        if self._year == o.year:
+            return self._day_of_year > o.day_of_year
+        return self._year > o.year
+
+    def __sub__(self, o: "FixedDate") -> timedelta:
+        return self.datetime - o.datetime
diff --git a/tests/operations_test.py b/tests/operations_test.py
new file mode 100644
index 0000000..02e70e2
--- /dev/null
+++ b/tests/operations_test.py
@@ -0,0 +1,35 @@
+import unittest
+from datetime import datetime, timedelta
+from fixedcal.core.date import FixedDate
+
+class TestOperations(unittest.TestCase):
+    def setUp(self):
+        self.fixed1 = FixedDate(date=datetime(2022, 12, 5))
+        self.fixed2 = FixedDate(date=datetime(2022, 12, 6))
+
+    def test_equal_with_two_same(self):
+        self.assertTrue(self.fixed1 == self.fixed1)
+
+    def test_equal_with_two_different(self):
+        self.assertFalse(self.fixed1 == self.fixed2)
+
+    def test_greather_than_with_true_expected(self):
+        self.assertTrue(self.fixed2 > self.fixed1)
+
+    def test_greather_than_with_false_expected(self):
+        self.assertFalse(self.fixed1 > self.fixed2)
+
+    def test_greather_than_with_two_same(self):
+        self.assertFalse(self.fixed1 > self.fixed1)
+
+    def test_less_than_with_true_expected(self):
+        self.assertTrue(self.fixed1 < self.fixed2)
+
+    def test_subtration_with_two_different(self):
+        self.assertEqual(self.fixed2-self.fixed1, timedelta(1))
+
+    def test_subtration_with_smaller_first(self):
+        self.assertEqual(self.fixed1-self.fixed2, timedelta(-1))
+
+    def test_subtration_with_two_same(self):
+        self.assertEqual(self.fixed1-self.fixed1, timedelta(0))