Select Translators... from the Preferences menu.
Select the translator Mathematica -- MathML. Make sure the two checkboxes Include translator name in translation and Include MathType data in translation are not checked. You do not need to perform this step for every equation. Once you select the appropriate translator, future equations will be translated using this translator until you select a different one.
Select the equation or equation fragment you want to insert into Mathematica, and copy it to the clipboard (Ctrl+C).
Paste the equation into a Mathematica notebook (Ctrl+V). The equation may now be used just like any other Mathematica equation.

Inserting a Mathematica equation into MathType

If you have an equation in a Mathematica notebook that you want to use in MathType, follow these steps:

Select the equation.
Right-click the equation, and choose Copy as -> MathML from the contextual menu.
Paste the equation into MathType. The equation may now be edited and used just like any other MathType equation.

Tips for Best Results

Following the steps above, one can easily cut and paste mathematical expressions between Mathematica and MathType. However, in order to evaluate or symbolically manipulate a MathType expressions in Mathematica, it may be necessary to further edit the expression once you have pasted it into Mathematica.

Mathematica uses a number of syntax conventions for mathematical expressions that allow it to maintain an internal representation suitable for calculation. By contrast, MathType is an equation editor, concerned primarily with giving authors an easy way to create nicely styled and well-typeset notations, and doesn't impose any restrictions on the notations created. As a result, it will often be necessary to "fix up" a MathType expression you have pasted into Mathematica to ensure it conforms to Mathematica conventions. There are two areas in particular that are worth highlighting, since they arise frequently:

Special Symbols. Mathematica uses three special symbols to eliminate ambiguities from expressions. Specifically, Mathematica uses a special DifferentialD character for the d in a differential (e.g. dx), an ExponentialE character for Euler's constant, and an ImaginaryI character for the square root of -1. Since Mathematica relies on these characters, you will need to edit your expressions to use them as well. Typically, you would do this after pasting into Mathematica, but before evaluation.

These characters can be used directly in MathType, if you have Mathematica's fonts installed on your system. Use the Edit | Insert Symbol command on the MathType window to open the Insert Symbol dialog. Choose View by Description from the pull down menu at the top, and then click the "New Search" button. Search for "differential" (or "exponential" or "imaginary" as appropriate). The relevant Mathematica characters will appear among the results. Choose the one appropriate for your expression.
Explicit Grouping. In many mathematical expressions, the proper grouping of terms is not explicit, and instead relies on the reader's understanding of notational conventions. For calculation, however, underspecified grouping is a common source of errors. Both Mathematica and MathType employ algorithms to infer the proper grouping in underspecified expressions. However, for best results, we recommend adding parentheses to make grouping explicit in the following situations:
- Add parentheses around function arguments. This is particularly important for trigonometric functions where parenthesis are often omitted in print, e.g. use sin(2x) instead of sin 2x.
- Add parentheses around integrands, e.g.
  
  $\int(x^2+2)\,dx$ vs $\int x^2+2 \,dx$ .
  
  The parentheses should not include the differential.

If you have experience with Mathematica and have specific tips about how best to use MathType to work with it, we would love to hear from you. Please send questions, comments and suggestions to interop@dessci.com.

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