Simply Mathematical: Basic Algebra Rules for Beginners

math problems on graph paper with pencil

Algebra adds up. It is confusing at first. Letters suddenly appear in your equations, and numbers start having little subtraction signs next to them. 

But don’t panic. Algebra has a set of rules that you can learn in no time. You will be solving equations soon enough. 

Here is a brief guide to basic algebra rules. 

Algebra Terms

There are a few key terms that you should be familiar with. 

Arithmetic is basic math. You add, subtract, multiply, and divide in arithmetic. When you write 2 + 3 = 5, you are performing arithmetic. 

Terms are numbers or combinations of numbers. In 2 + 3 = 5, 2, 3, and 5 are all terms. 

Variables are letters that substitute for unknown numbers. In 2 + x = 5, x is the variable. A variable can be any letter in the alphabet, but x, y, and z are the most common. 

Parentheses prioritize terms. You should perform arithmetic on terms included within parentheses first. In 2 + (2 – 1), you should perform 2 – 1 first. 

Properties of Algebra

Arithmetic and algebra have several properties. You have probably used them already, but you should know their exact definitions. 

The symmetry of equations means that the terms on one side of the equal sign can appear on the opposite side. 2 + 3 = 5 is equivalent to 5 = 2 + 3. 

The commutative property means that terms can be reversed when adding or multiplying them. 2 + 3 is equivalent to 3 + 2. 2 * 3 equals 3 * 2. 

The associative property means that parentheses can be moved when adding or multiplying. 2 + (3 – 1) is equivalent to (2 + 3) – 1. 

Basic Algebra Rules for Negatives

We think of subtraction as taking one number away from another number. In 3 – 2, we are taking 2 away from 3, leaving 1. However, we can also think of subtraction as adding a negative number to another number: 3 + -2. 

Thinking of subtraction as adding a negative number allows us to use the properties of algebra. We can move terms around for convenience. We can write -2 + 3 and produce the same result. This is important when dealing with variables.

Multiplying or dividing two negative terms will always produce a positive term: -2 * -2 = 4.  

Multiplying or dividing a negative term and a positive term always produces a negative term: – 2 / 2 = -1. 

Like Terms

Like terms have the same variables. 2x and 3x are like terms, while 2x and 3y are not like terms. 2 and 3 are like terms, as they have the same variable, which is nothing. 

To perform algebra on like terms, you add or subtract the numbers attached to the variables. In 2x – 2y + 3x + 3y, you can use the commutative property to move the like terms so they are next to each other: 2x + 3x + -2y + 3y. Then, you add the numbers together, resulting in 5x + y. 

Like terms can be tricky. There are experienced tutors out there who can help you. Here, you can speak to an experienced algebra tutor. 

Consult With the Experts

Basic algebra rules are basic, once you get their quirks down. Study the terms and properties that work in basic algebra. Then, apply the lessons you have learned in arithmetic to like terms.

Keep practicing until you produce accurate answers on a regular basis. Consult with experts if you are feeling stuck.

Want more? Then read more of our science and math articles.

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