Four Rules of Algebra
Algebra is a branch of mathematics that focuses on solving unknown values which are represented by letters. Instead of working with real numbers like in regular math, here you purely work with unknowns and work them like a puzzle to try to find your final solution. You could have them in linear equations, inequalities, functions, and graphs. They are introduced to children as early as the ninth grade, to help them get accustomed to it early enough. Its level progresses as that child graduates from year to year, and depending on the major they take on campus, they may or may not continue working with Algebra.
Just like any other component, there has to be a set of rules to govern how an item is used to produce accurate results. Without these rules, then there would be no telling which is the correct way to approach certain tasks. There are different laws of Algebra, each set to approach different problems in their unique way. They are mainly grouped into four which include Commutative Law, Associative Law, Distributive Law, and Cancellation Law. If you decide to approach an algebraic equation without following any of these set rules, then you will get false results from your calculation. This will have people questioning you whether you really went to school to study or to pass time with the rest of the students.
Commutative Law is divided into two categories. We look at equations that require you to add figures, while others require you to multiply. In a case where you are required to multiply, assuming that ‘a’ with ‘b’ are your algebraic expressions of choice, then this rule dictates that the sum of both ‘a’ and ‘b’ are the same, no matter their position in an equation. On one side we could have ‘a’ leading that equation, while on the other we’ve got ‘b’ leading, but their sum will be the same.
When looking at those that require you to find the product, the same applies. No matter the position of these expressions in an equation, their solution will always be equal. The only difference could come in when on one side we’ve got a sign that is not present on the other, this would warrant different results. When this happens, then this rule is not applicable in such a scenario.
Associative Law is also grouped into categories that focus on addition or multiplication, depending on the equation presented before you. Unlike Commutative Law, this focuses on equations with more than two variables. Taking ‘c’, ‘d’, and ‘e’ as our variables, we can compute their addition satisfying that rule in question. For an expression with more than one variable, the sum of the first letter together with that of the last two would be the same as the sum of the first two letters together with the last one. No matter their arrangement, your result will always be the same.
In an expression that requires you to multiply, a case where order does not matter would still fit. Wherever you place these letters, in whichever order you place them, as long as their signs are the same, then the result will also be the same all through. Even when you group them into two, with one being left outside to multiply with after, your answer will still be equal.
Distributive Law focuses on a combination of both addition and multiplication operations. You will have your unknowns grouped into pairs, from where you will add their products. When using three unknowns, then one will appear in both brackets to satisfy the expression. This representation is equivalent to when you have the sum of two of the letters, which you later multiply with the third unknown.
Cancellation Law is divided into addition and multiplication applications, depending on the nature of your expression. When working with three variables, the rule states that the sum of any two of these unknowns is equal to the sum of one of the initial unknowns with the third variable. This is possible if two different letters represent the same value. If you’re applying this rule in multiplication, then the product of any two variables is equal to that of one in the initial expression with the third value. This is satisfied when where any two values are the same, and the third is equal to zero.