Notation Stifles Arithmetic Intuition Building

There are a multitude of ways to represent additive and multiplicative operations. Typically students will learn something like the following for addition, subtraction, multiplication and division respectively. Where a,b are real numbers.

a+ b, a - b, a \times b, a \div b

Here I am just going to enumerate the problems with these basic notations and why similar notations do not work either, and then conclude with modern notations that are well suited to these operations.

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