diff --git a/yarn-project/foundation/src/fields/fields.test.ts b/yarn-project/foundation/src/fields/fields.test.ts
index 02f08f0e319..c2673ff86e9 100644
--- a/yarn-project/foundation/src/fields/fields.test.ts
+++ b/yarn-project/foundation/src/fields/fields.test.ts
@@ -1,4 +1,4 @@
-import { GrumpkinScalar } from './fields.js';
+import { Fr, GrumpkinScalar } from './fields.js';
 
 describe('GrumpkinScalar Serialization', () => {
   // Test case for GrumpkinScalar.fromHighLow
@@ -53,3 +53,122 @@ describe('GrumpkinScalar Serialization', () => {
     expect(deserialized).toEqual(original);
   });
 });
+
+describe('Bn254 arithmetic', () => {
+  describe('Addition', () => {
+    it('Low Boundary', () => {
+      // 0 + -1 = -1
+      const a = Fr.ZERO;
+      const b = new Fr(Fr.MODULUS - 1n);
+      const expected = new Fr(Fr.MODULUS - 1n);
+
+      const actual = a.add(b);
+      expect(actual).toEqual(expected);
+    });
+
+    it('High Boundary', () => {
+      // -1 + 1 = 0
+      const a = new Fr(Fr.MODULUS - 1n);
+      const b = new Fr(1);
+      const expected = Fr.ZERO;
+
+      const actual = a.add(b);
+      expect(actual).toEqual(expected);
+    });
+
+    it('Performs addition correctly', () => {
+      const a = new Fr(2);
+      const b = new Fr(3);
+      const expected = new Fr(5);
+
+      const actual = a.add(b);
+      expect(actual).toEqual(expected);
+    });
+  });
+
+  describe('Subtraction', () => {
+    it('Low Boundary', () => {
+      // 0 - 1 = -1
+      const a = new Fr(0);
+      const b = new Fr(1);
+      const expected = new Fr(Fr.MODULUS - 1n);
+
+      const actual = a.sub(b);
+      expect(actual).toEqual(expected);
+    });
+
+    it('High Bonudary', () => {
+      // -1 - (-1) = 0
+      const a = new Fr(Fr.MODULUS - 1n);
+      const b = new Fr(Fr.MODULUS - 1n);
+
+      const actual = a.sub(b);
+      expect(actual).toEqual(Fr.ZERO);
+    });
+
+    it('Performs subtraction correctly', () => {
+      const a = new Fr(10);
+      const b = new Fr(5);
+      const expected = new Fr(5);
+
+      const actual = a.sub(b);
+      expect(actual).toEqual(expected);
+    });
+  });
+
+  describe('Multiplication', () => {
+    it('Identity', () => {
+      const a = new Fr(Fr.MODULUS - 1n);
+      const b = new Fr(1);
+      const expected = new Fr(Fr.MODULUS - 1n);
+
+      const actual = a.mul(b);
+      expect(actual).toEqual(expected);
+    });
+
+    it('Performs multiplication correctly', () => {
+      const a = new Fr(2);
+      const b = new Fr(3);
+      const expected = new Fr(6);
+
+      const actual = a.mul(b);
+      expect(actual).toEqual(expected);
+    });
+
+    it('High Boundary', () => {
+      const a = new Fr(Fr.MODULUS - 1n);
+      const b = new Fr(Fr.MODULUS / 2n);
+      const expected = new Fr(10944121435919637611123202872628637544274182200208017171849102093287904247809n);
+
+      const actual = a.mul(b);
+      expect(actual).toEqual(expected);
+    });
+  });
+
+  describe('Division', () => {
+    it('Should succeed when mod inverse is -ve', () => {
+      const a = new Fr(2);
+      const b = new Fr(3);
+
+      const actual = a.div(b);
+      expect(actual.mul(b)).toEqual(a);
+    });
+
+    it('Should succeed when mod inverse is +ve', () => {
+      const a = new Fr(10);
+      const b = new Fr(5);
+      const expected = new Fr(2);
+
+      const actual = a.div(b);
+      expect(actual.mul(b)).toEqual(a);
+      expect(actual).toEqual(expected);
+    });
+
+    it('Should not allow a division by 0', () => {
+      const a = new Fr(10);
+      const b = Fr.ZERO;
+
+      expect(() => a.div(b)).toThrowError();
+    });
+  });
+});
diff --git a/yarn-project/foundation/src/fields/fields.ts b/yarn-project/foundation/src/fields/fields.ts
index 28e0a64dad8..1f23f5473f5 100644
--- a/yarn-project/foundation/src/fields/fields.ts
+++ b/yarn-project/foundation/src/fields/fields.ts
@@ -302,8 +302,8 @@ function modInverse(b: bigint) {
   if (gcd != 1n) {
     throw Error('Inverse does not exist');
   }
-  // Add modulus to ensure positive
-  return new Fr(x + Fr.MODULUS);
+  // Add modulus if -ve to ensure positive
+  return new Fr(x > 0 ? x : x + Fr.MODULUS);
 }
 
 /**
diff --git a/yarn-project/simulator/src/avm/avm_context.test.ts b/yarn-project/simulator/src/avm/avm_context.test.ts
index f54fe99a358..240de5eb14f 100644
--- a/yarn-project/simulator/src/avm/avm_context.test.ts
+++ b/yarn-project/simulator/src/avm/avm_context.test.ts
@@ -24,8 +24,9 @@ describe('Avm Context', () => {
         pc: 0,
       }),
     );
-    // FIXME: I can't get this to work.
-    // expect(newContext.worldState).toEqual(context.worldState.fork());
+
+    // We stringify to remove circular references (parentJournal)
+    expect(JSON.stringify(newContext.worldState)).toEqual(JSON.stringify(context.worldState.fork()));
   });
 
   it('New static call should fork context correctly', () => {
@@ -49,7 +50,8 @@ describe('Avm Context', () => {
         pc: 0,
       }),
     );
-    // FIXME: I can't get this to work.
-    // expect(newContext.worldState).toEqual(context.worldState.fork());
+
+    // We stringify to remove circular references (parentJournal)
+    expect(JSON.stringify(newContext.worldState)).toEqual(JSON.stringify(context.worldState.fork()));
   });
 });
diff --git a/yarn-project/simulator/src/avm/avm_memory_types.test.ts b/yarn-project/simulator/src/avm/avm_memory_types.test.ts
index c5701c54d93..9aeccaa73b9 100644
--- a/yarn-project/simulator/src/avm/avm_memory_types.test.ts
+++ b/yarn-project/simulator/src/avm/avm_memory_types.test.ts
@@ -160,8 +160,7 @@ describe('Field', () => {
     expect(result).toStrictEqual(new Field(50n));
   });
 
-  // FIXME: field division is wrong
-  it.skip(`Should divide two Fields correctly`, () => {
+  it(`Should divide two Fields correctly`, () => {
     const field1 = new Field(10);
     const field2 = new Field(5);
     const result = field1.div(field2);
diff --git a/yarn-project/simulator/src/avm/opcodes/arithmetic.test.ts b/yarn-project/simulator/src/avm/opcodes/arithmetic.test.ts
index 1475ef1a7c4..e08fe4bcb8e 100644
--- a/yarn-project/simulator/src/avm/opcodes/arithmetic.test.ts
+++ b/yarn-project/simulator/src/avm/opcodes/arithmetic.test.ts
@@ -201,8 +201,7 @@ describe('Arithmetic Instructions', () => {
       expect(inst.serialize()).toEqual(buf);
     });
 
-    // FIXME: field division is wrong
-    it.skip('Should perform field division', async () => {
+    it('Should perform field division', async () => {
       const a = new Field(10n);
       const b = new Field(5n);