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Algebra Basics

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Introduction to Algebra

 

What is Algebra?

The core driving principle behind algebra is to try and give definition to the undefined or in other, more technical words, abstraction.

Algebra is quite similar to Arithmetic, it involves usage of the same four basic operators - Addition, Subtraction, Division and Multiplication. Let’s take an example:

1+2=?

The above example is how Arithmetic works. Like Arithmetic, Algebra revolves around the same four operators but it introduces something new, the element of the unknown. Let’s look at another example:

1+2=x  -----(1)

In Arithmetic, the only unknown is the answer itself. In Algebra, when we don’t know the number yet we use a symbol in its place. That symbol can be anything that you want and is usually a letter from the alphabet. The answers in both the above examples would give you the answer 3, only in Algebra it would be replaced by x which is equal to 3.

1+2=x  -----(2)

This is a basic algebraic equation

3=x OR x=3

Doing basic addition on one side gives you the value of the unknown, in this case x. Finding the value for x is called Solving the equations. The question that pops up in the head, “This was too easy.” In Algebra, the equations are a bit complicated, but the basic principle involved is just the same as above.

x-2=1  -----(3)

If you look closely, Equation (2) and (3) are the same but Equation (3) has been rearranged to make it seem more complex.

A few Basic rules for Algebra:

  • X is a variable. The word variable is a giveaway for easy understanding, break the word and it has “vary” which means different. In simpler terms, X can be used for different numbers in different equations.

x+8=15                    x+4=10

x=7                    x=6 

Two different equations, two different values for x

 

  • In one equation, the variable X can have only one value.

(x+10)(x-5)=(x+20)(x+4)

You see X being repeated in the equation? Bingo! All the X’s represent the same number/value. 

  • If there are 2 variables involved in one equation, then their values will vary according to each other.

x+y=2

Here, x=0, y=2

Or

x=1, y=1

Or

x=2, y=0

As X’s value changed, so did Y’s along with it. The above example also proves that two different variables can have the same value.

 

Sub Topics

Here are a few links that will help you understand the related topic. Also, download free worksheets to practice a few questions.

Download Free Grade 6 Worksheets
An Introduction to Abstraction
Grade6 | Worksheet 1
An Introduction to Abstraction
Grade6 | Worksheet 2
Download Free Grade 8 Worksheets
A Consolidation of the Basics
Grade8 | Worksheet 1
A Consolidation of the Basics
Grade8 | Worksheet 2