Examples of extensive properties include mass and volume. In contrast, an extensive property is one that does depend on sample size. It is a bulk property, which means it is a physical property that is not dependent on the size or mass of a sample. This, along with the multiplicative property of equality, is one of the most commonly used properties for solving equations. An intensive property is a property of matter that does not change as the amount of matter changes. Multiplication : Multiplication is the repeated addition of the same number denoted with the symbol x. The formal name for the property of equality that allows one to add the same quantity to both sides of an equation. Multiple : The multiple of a number is the product of that number and any other whole number.
Note: textbooks vary somewhat in the names they give these properties you'll need to refer to the examples in your book to know the exact format you should use. Monomial : An algebraic expression made up of one term. And you can plug in for variables, so if x = 3, then 4 x = 12, because 4 x = 4(3): this is the "substitution" property. Two numbers are either equal to each other or unequal this is the "trichotomy" law (so called because there are three cases for two given numbers, a b). You can "cut out the middleman", so to speak if x = y and y = z, then you can say that x = z: this is the "transitive" (moving across) property. Also, it doesn't matter which order the equality is in if x = y, then y = x: this is the "symmetric" (they match) property. Anything equals itself: this is the "reflexive" (reflecting onto itself) property. This is the "zero-product property".Īnd there are some properties that you use to solve word problems, especially where substitution is required. The only way you can multiply two things and end up with zero is if one (or both) of those two things was zero to start with. The basic fact that you need for solving many equations, especially quadratics, is that, if p× q = 0, then must have either p = 0 or else q = 0.
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