Added modulus/remainder note (#5008)

* Added modulus/remainder note

* Addressed feedback

* Addressed feedback

Author: Ron Petrusha

docs/visual-basic/language-reference/operators/mod-operator.md

@@ -1,9 +1,7 @@
 ---
 title: "Mod Operator (Visual Basic)"
-ms.date: 07/20/2015
+ms.date: 04/24/2018
 ms.prod: .net
-ms.reviewer: ""
-ms.suite: ""
 ms.technology: 
   - "devlang-visual-basic"
 ms.topic: "article"
@@ -18,11 +16,10 @@ helpviewer_keywords:
   - "arithmetic operators [Visual Basic], Mod"
   - "math operators [Visual Basic]"
 ms.assetid: 6ff7e40e-cec8-4c77-bff6-8ddd2791c25b
-caps.latest.revision: 22
-author: dotnet-bot
-ms.author: dotnetcontent
+author: rpetrusha
+ms.author: ronpet
 ---
-# Mod Operator (Visual Basic)
+# Mod operator (Visual Basic)
 Divides two numbers and returns only the remainder.  
 
 ## Syntax  
@@ -38,12 +35,34 @@ number1 Mod number2
  `number2`  
  Required. Any numeric expression.  
 
-## Supported Types  
+## Supported types  
  All numeric types. This includes the unsigned and floating-point types and `Decimal`.  
 
-## Result  
- The result is the remainder after `number1` is divided by `number2`. For example, the expression `14 Mod 4` evaluates to 2.  
-  
+## Result
+
+The result is the remainder after `number1` is divided by `number2`. For example, the expression `14 Mod 4` evaluates to 2.  
+
+> [!NOTE]
+> There is a difference between *remainder* and *modulus* in mathematics, with different results for negative numbers. The `Mod` operator in Visual Basic, the .NET Framework `op_Modulus` operator, and the underlying [rem]<xref:System.Reflection.Emit.OpCodes.Rem> IL instruction all perform a remainder operation.
+
+The result of a `Mod` operation retains the sign of the dividend, `number1`, and so it may be positive or negative. The result is always in the range (-`number2`, `number2`), exclusive. For example:
+
+```vb
+Public Module Example
+   Public Sub Main()
+      Console.WriteLine($" 8 Mod  3 = {8 Mod 3}")
+      Console.WriteLine($"-8 Mod  3 = {-8 Mod 3}")
+      Console.WriteLine($" 8 Mod -3 = {8 Mod -3}")
+      Console.WriteLine($"-8 Mod -3 = {-8 Mod -3}")
+   End Sub
+End Module
+' The example displays the following output:
+'       8 Mod  3 = 2
+'      -8 Mod  3 = -2
+'       8 Mod -3 = 2
+'      -8 Mod -3 = -2
+```
+
 ## Remarks  
  If either `number1` or `number2` is a floating-point value, the floating-point remainder of the division is returned. The data type of the result is the smallest data type that can hold all possible values that result from division with the data types of `number1` and `number2`.  
 
@@ -55,18 +74,18 @@ number1 Mod number2
 
 -   The [/ Operator (Visual Basic)](../../../visual-basic/language-reference/operators/floating-point-division-operator.md) returns the full quotient, including the remainder, as a floating-point number. For example, the expression `14 / 4` evaluates to 3.5.  
 
-## Attempted Division by Zero  
+## Attempted division by zero  
  If `number2` evaluates to zero, the behavior of the `Mod` operator depends on the data type of the operands. An integral division throws a <xref:System.DivideByZeroException> exception. A floating-point division returns <xref:System.Double.NaN>.  
 
-## Equivalent Formula  
+## Equivalent formula  
  The expression `a Mod b` is equivalent to either of the following formulas:  
 
  `a - (b * (a \ b))`  
 
  `a - (b * Fix(a / b))`  
 
-## Floating-Point Imprecision  
- When you work with floating-point numbers, remember that they do not always have a precise representation in memory. This could lead to unexpected results from certain operations, such as value comparison and the `Mod` operator. For more information, see [Troubleshooting Data Types](../../../visual-basic/programming-guide/language-features/data-types/troubleshooting-data-types.md).  
+## Floating-point imprecision  
+ When you work with floating-point numbers, remember that they do not always have a precise decimal representation in memory. This can lead to unexpected results from certain operations, such as value comparison and the `Mod` operator. For more information, see [Troubleshooting Data Types](../../../visual-basic/programming-guide/language-features/data-types/troubleshooting-data-types.md).  
 
 ## Overloading  
  The `Mod` operator can be *overloaded*, which means that a class or structure can redefine its behavior. If your code applies `Mod` to an instance of a class or structure that includes such an overload, be sure you understand its redefined behavior. For more information, see [Operator Procedures](../../../visual-basic/programming-guide/language-features/procedures/operator-procedures.md).  
@@ -81,7 +100,7 @@ number1 Mod number2
 
  [!code-vb[VbVbalrOperators#32](../../../visual-basic/language-reference/operators/codesnippet/VisualBasic/mod-operator_2.vb)]  
 
-## See Also  
+## See also  
  <xref:Microsoft.VisualBasic.Conversion.Int%2A>  
  <xref:Microsoft.VisualBasic.Conversion.Fix%2A>  
  [Arithmetic Operators](../../../visual-basic/language-reference/operators/arithmetic-operators.md)