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# What is the "zero property" of multiplication?

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The zero property of multiplication states that if a times b equals zero, then either a or b (or both) must equal zero. It is also called the zero product property.

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Multiplying any number by zero gives a product of zero. Therefore, if the product of two numbers is zero, one or both of those numbers must be zero. This property may seem self-evident, but it can be very useful for many mathematical processes, such as solving quadratic equations. It is important to note that the reverse process, dividing by zero, is not possible in normal mathematics. This why the denominator of a fraction can never equal zero.

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## Related Questions

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The distributive property is an algebraic rule that states that a multiplied by the sum of b and c is equal to a times b added to a times c. The actual formula is written as a(b + c) = ab + ac.

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The equation y = ln(x) states that y is equal to the natural logarithm of x. The natural logarithm is defined as the area under the curve of y = 1/t between t = 1 and t = x.

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In certain applications of mathematics, particularly in business math and economics, the law of variable proportions states that the marginal product of a factor, when increased by itself, will eventually start to decline. In other words, increasing a single factor of production, such as labor or equipment, without increasing other related factors will lead to an increase in marginal product followed by an inevitable decrease.