How to do Algebra

Algebra is an important subject in high school and even in college. Many people do not really consider it as their favorite subject because of the complexities of algebraic equations that must be solved. However, it is important to learn how to do algebra to graduate from school or to solve basic everyday algebraic problems. To do algebra, you must first know the different axioms in algebra as well as the order of operations. They are basic algebraic principles that you can apply in any problem you would solve. 

 

What is Algebra?

Algebra is a branch of mathematics that uses symbols and letters in formulas and equations. These symbols and letters are also called variables that represent numbers or quantities. In school systems, algebra is considered a higher level of mathematics and is usually taught in secondary schools. Algebra follows several important axioms or guiding principles, as well as the order of operations.

What Are the Different Axioms of Algebra?

Algebra has five basic axioms or principles, which are the reflexive, symmetric, transitive, additive, and multiplicative axioms. The reflexive axiom states that any number is equal to itself. For example, "a" equals "a," or "1" equals "1." The symmetric axiom states that expressions around the equal sign are symmetrical to each other, such that if "x" equals "y," then "y" equals "x." An expression is a group of terms; a term may be a single variable, or a single number called a constant, or a variable multiplied by a number called a coefficient. The transitive axiom is best expressed as, if "x" equals "y" and "y" equals "z," then "x" equals "z." For the additive axiom, if there are two sets of quantities that are equal and both are added with equal number or quantity, they will remain to be equal. For example, if "a" equals "b" and "x" equals "y," then "a" plus "x" equals "b" plus "y." Lastly, the multiplicative axiom can be expressed as, if a equals "b" and "x" equals "y," then, "ax" equals "by."

What is the Order of Operations in Algebra?

The order of operations in algebra refers to the order on which mathematical operations should be computed first when solving problems that involve two or more mathematical operations. The first operations to solve are those within a set of parentheses or other grouping symbols such as brackets. If there are grouping symbols within grouping symbols, work on the innermost group of expression first. When doing any operation, do it in order from left to right, and following the rule of "multiplication then division, followed by addition and subtraction."

How to Do Algebra?

By applying the different axioms and order of operations in algebra, it is easier to know how to do algebra. In algebra, there are algebraic equations where one or more terms are often represented by a letter that is not known. For example: "1" plus "x" equals "5," where "x" is the unknown figure. To solve this, you can apply the additive axiom to come up with a solution: "1" plus "x" minus "1" equals "5" minus "1," which will eliminate "1" and give you the solution of "x" equals "4." You can check your answer by substituting "4" for the "x" in the original equation: "1" plus "4" equals "5." This same principle applies when subtracting, multiplying, and dividing integers in algebra. However, two or more axioms may apply as the equation becomes more complex.

If you like to know how to do algebra, it is important that you familiarize yourself first with some of the basic principles that govern this branch of mathematics. You have to fully understand the axioms in algebra and know the order of operations. In basic algebra, you will be solving for an unknown figure often represented by a letter called variable. After getting the unknown figure, you can check if you got the correct answer by substituting the resulting number to the variable in the