The Associative Property says that if you are adding or multiplying a string of terms and some of these terms are grouped inside parentheses, you can change the position of the parentheses without changing the answer or meaning. For example, (2+3)+7 equals 12 and 2+(3+7) also equals 12. You can remember this property by thinking that it does not matter which terms "associate" with each other in the parentheses.
The Commutative Property states that you can change the order of terms being multiplied or added without affecting the answer. For example, 14 x 5 and 5 x 14 both equal 70. Although the associative and commutative properties are both only for multiplication and addition, you can use them for subtraction by changing a "minus" to "plus a negative." For example, 2 - 5 would change to 2 + -5, which the commutative property could then switch to -5 + 2.
There are properties of equality for division, multiplication, addition and subtraction. The properties state that if you perform one of the operations to both sides of an equation, the equality statement remains true. These properties are the most important ones for equation solving because they let you eliminate numbers from around the variable and determine its value. For example, the Addition Property of Equality lets you subtract 7 from both sides of X + 7 = 12 to determine that X = 5.
According to the Identity Property of Multiplication, you can multiply any number by the number one and its identity will stay the same. When solving equations, you can multiply both sides by special forms of one and keep the sides equal to each other. On the other hand, the Identity Property of Addition states that when zero is added to a number or variable, it does not change the value. For example, 3X + 0 simplifies to 3X.
Another property essential to equation solving is the Substitution Property, which allows you to perform operations and replace the original numbers with the answer. For example, with 8 + 7 - 6X = 13, you can add the 8 and 7 and replace them with 15 to get 15 - 6X = 13.
The Distributive Property states that if you are multiplying one term with other terms that are added or subtracted inside parentheses, multiply the term outside the parentheses by each term inside, and then add together the results to get the same answer you would if you performed the addition first. For example, solve 3(4 + 9) by rewriting it as 3(13) or as 12 + 27 and you will get 39 either way. The Distributive Property is useful for rearranging equations into forms that are solvable.