Very simple calculator with four basic operations using only if/else statements
You need to check for input validity and have a mechanism for retry. Users can enter all sorts of things
Your variable names aren't consistent. number and secondNumber. I would go with firstNumber and secondNumber in your scheme, but I would not use your scheme.
Your variable names are too verbose: secondNumberConversion. How about n1 and n2?
A simple, elegant, maintainable and extensible solution is to use a Dictionary.


Not addressing 1. here is my version:

Console.WriteLine("Welcome to the simple calculator!"
                  + " The four operators of this calculator are "
                  + "+, -, *(multiply), and /(divide)");

Console.Write("First Number: ");
Int64 n1 = Int64.Parse(Console.ReadLine());

Console.Write("Second Number: ");
Int64 n2 = Int64.Parse(Console.ReadLine());

Console.Write("Operator: ");
string operatorType = Console.ReadLine();

var operatorsFuncMap = new Dictionary&lt;string, Func&lt;Int64, Int64, Int64&gt;&gt; 
{
    {"+", (a, b) =&gt; a + b},
    {"-", (a, b) =&gt; a - b},
    {"*", (a, b) =&gt; a * b},
    {"/", (a, b) =&gt; a / b},
};

Console.WriteLine(operatorsFuncMap[operatorType](n1, n2));