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ArithmeticResult—Wolfram Documentation

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• The arithmetic comparison method considers two mathematical expressions to be equivalent if they match without doing any arithmetic operations, e.g. 1 + 1  2.
• Answers are considered correct when the only differences are ordering of terms inside orderless operations like addition and multiplication.
• The values of the key and answer can both be specified as held expressions Hold[expr] to prevent evaluation. Even when the values are held, reordering transformations are performed to determine equivalence during assessment. It is recommended to always hold the answer.
• To require the order of terms in orderless operations to match the order of the answer key, use the "OrderlessMatch" setting: AssessmentFunction[key,<|"ComparisonMethod""ArithmeticResult","OrderlessMatch"False|>].
• Values in "ArithmeticResult" answer keys are patterns and support Blank expressions.
• The following table shows a comparison of "ArithmeticResult" with other comparison methods for a typical answer key of 2x+8 and several possible submitted answers:

Create an AssessmentFunction for an arithmetic question:

Non-computed addition is considered inequivalent and incorrect:

Reordered terms are considered equivalent and correct:

Create a simple addition question without holding the answer key:

The original question is not accepted as an answer:

The computed result is correct:

Create a radical simplification question:

Require addition terms to have the same order as the answer key:

Try different answers:

Create an assessment function for an addition pattern with the order specified:

Answers must match the pattern, including the order of terms:

With the "HeldExpression" comparison method, this is not possible. Using Hold in the answer key does not support patterns:

Using HoldPattern supports pattern matching but allows reordering:

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