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Distributive property, also known as distributive law, is a fundamental concept in mathematics that applies to both multiplication and division. It is particularly useful in simplifying algebraic expressions and solving equations. The distributive property of multiplication states that for any numbers a, b, and c, the following equation holds true: a * (b + c) = (a * b) + (a * c). This means that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products. For example, 3 * (4 + 5) = (3 * 4) + (3 * 5), which simplifies to 3 * 9 = 12 + 15, and further to 27.

The distributive property of division is less commonly taught but equally important. It states that for any numbers a, b, and c (where c is not zero), the following equation holds true: a / (b + c) = (a / b) + (a / c). However, it's important to note that this property does not apply to division in the same way it does to multiplication. For example, 12 / (3 + 4) does not equal (12 / 3) + (12 / 4). Instead, the distributive property of division is more accurately described as the property of fractions, where a single fraction can be broken down into the sum of two or more fractions with the same denominator.

The distributive property is widely used in various mathematical disciplines, including algebra, calculus, and number theory. It is a key tool for simplifying complex expressions, solving equations, and proving mathematical theorems. Understanding and applying the distributive property is essential for anyone studying or working in mathematics.