[Math] Multiplication convention rules

arithmetic

Student was asked to convert the following statement into multiplication format
$$7+7+7+7+7+7$$
She wrote the answer as $7\times 6=42$ and was marked wrong as the teacher expected $6\times 7=42$.

Is there any rule that can clarify the answer format?

The same with converting a multiplication sum into adding $6\times 3$

she wrote $3+3+3+3+3+3$ and once again was marked as wrong. Teacher expected $6+6+6=18$

Best Answer

Just for the sake of concreteness, suppose we are counting apples. Many educators prefer to consistently interpret $m \times n$ as "$m$ groups of $n$ apples". In your example, $$7 + 7 + 7 + 7 + 7 + 7 = 6 \times 7$$ because it is 6 groups with 7 apples in each group. Similarly, $$6 + 6 + 6 + 6 + 6 + 6 + 6 = 7 \times 6$$ because it is 7 groups with 6 apples in each group. The fact that these both count the same number of apples overall is known as the commutative property of multiplication and should not be taken for granted (many other mathematical operations do not commute).

If this is what the teacher had in mind, then indeed $$ 6 \times 3 = 3 + 3 + 3 + 3 + 3 + 3, $$ so perhaps the he/she is mistakenly inconsistent in grading the second example.

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