1. The problem asks to fill in the blank in the sentence: "By the ________ property of equality, we may multiply or divide both sides of an equation by any nonzero number without changing the solution of the equation." 2. The property described is the one that allows multiplication or division on both sides of an equation without changing its solution. 3. This property is known as the **multiplication property of equality**. 4. Therefore, the correct word to fill in the blank is **multiplication**. Final answer: multiplication