Because multiplying is the inverse of dividing
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Because multiplication and division are inverse operations. And the reciprocal of a number is its multiplicative inverse.
Addition is the inverse operation of subtraction and multiplication is the inverse operation of division. The word inverse means "opposite".
Because division and multiplication are mutually inverse operations.
Inverse Operations: Divison undoes multiplication. Addition undoes subtraction. Subtraction undoes addition. Multiplication undoes division.