What is Algebra? What do we use it for?

This is always a big question when a student begins to take their first algebra course. Algebra encompasses relationships, the use of symbols, modeling, and the study of mathematical change. The first formal algebra course that most students enroll is Algebra I. Usually begins in the ninth grade, although several students are starting to take it in the eighth grade.

Some students say that I can not do algebra because I do not understand it. The problem with this statement is that you have been working on algebra problems every since kindergarten. The word algebra is not used, but the ideas are used. You have used elements of algebra when solving problems and when you solve word problems.

Here is an example: in grades three through five you investigate the properties of whole numbers. You learn to multiply 18 times 14 mentally. First you multiply 18 times 10 and then multiply 18 times 4, and then you add the two products. This is called the distributive property of multiplication over addition. This is algebra and algebraic reasoning.

Algebra is a major component of math that is used to unify mathematic concepts. Algebra is built on experiences with numbers and operations, along with geometry and data analysis. Some students think that algebra is like learning another language. This is true to a small extent, algebra is a simple language used to solve problems that can not be solved by numbers alone. It models real-world situations by using symbols, such as the letters x, y, and z to represent numbers.

The vocabulary of algebra is similar to basic arithmetic such as adding, subtracting, multiplying, and dividing. PEMDAS is still used to solve algebra problems, because order of operations is strictly followed in algebra.

There are several terms that describe algebraic operations. These include:

• Algebraic Expressions: is more of a phrase. It uses variables, constants, and operating symbols such as plus and multiplication. Since it is only a phrase it does not have an equal sign. For example: 5x - 2y + 3yz + 10. The variables x, y, and z need to be defined with numbers and then the expression can be solved.
• Variables: are letters that represent numbers that are sometimes known and sometimes not. The letters called variables because they can represent any number. The typical letters used are x, y, and z.
• Coefficients: are the number parts of a variable, for example: 5y where 5 is the coefficient. If there is only a letter, such as "x" the coefficient is 1.
• Constants: these are the terms in the algebraic expression that only contains numbers, for example: 5y + 4 where 4 is the constant because it does change and 5y changes because of the variable "y."
• Real Numbers: are a set of real world numbers such as: amounts, distances, age, time, temperature, etc. A real number can be a whole number, fraction, or decimal. In addition these numbers can be rational or irrational.
• Rational Numbers: rational comes from the word ratio and can always be written as a ratio or quotient of two integers. For example: 1/2 is the ratio of 1 to 2.
• Irrational Numbers: can not be expressed as a quotient of two integers. Pi is an example of an irrational number because the decimal numbers are non-repeating and non-terminating.

We use algebra everyday of our lives. Examples of ways that we use algebra are finding the distance, perimeter of an area, volume, determining the cost of something, renting something, time relationships, pricing options for something you want to buy, and more.