List of Topics

SfC Home > Arithmetic > Algebra >


Key words: Algebra, purpose, solving, equations, mathematics, math, maths, mathematical relationship, substitute, equation, manipulate, unknown quantities, Ron Kurtus, School for Champions. Copyright © Restrictions

Purpose of Algebra is to Solve Equations

by Ron Kurtus (revised 7 June 2015)

There are numerous mathematical relationships that have been established in science, finance and other areas. Examples include the relationship between force and acceleration, conversion of centimeters to inches, and determining the payments on a loan with a given interest rate.

The purpose of Algebra is to make it easy to state the relationship by using letters to represent entities as a form of shorthand. The relationship is then called an equation. Algebra then allows you to substitute values for entities in order to determine the value of other items.

Finally, you can manipulate the equations to solve for the various items or unknown quantities.

Questions you may have include:

  • How are letters used to state a relationship?
  • How are values substituted?
  • How are equations manipulated?

This lesson will answer those questions.

Stating relationship with letters

The best way to explain how a relationship can be stated with letters is to provide some examples.

Changing inches to centimeters

The relationship for changing meters to centimeters to is to multiple the number of meters by 100 to get the number of centimeters.

Suppose we represent meters with the letter m and centimeters with the letter c. Then we have the equation:

c = 100 × m

The letters m and c are called variables in the equation, since they can vary depending on what value you give them.

Note: Often, you will see the multiplication sign as * instead of ×, as a way to avoid confusion with x. This is mostly seen in web pages and on some calculators.

Example of loan payments

The amount of interest you pay on a loan is equal to the interest rate times the money owed.


  • I = amount of interest
  • r = interest rate
  • m = money owed

Thus, the equation is:

I = r × m

The letters I, r and m are called variables in the equation, since they can vary depending on what value you give them.

Substituting values

Given a relationship, you can substitute values to solve the equation.

Since we have the equation c = 100 × m, you can substitute m = 2 meters to find the corresponding number of centimeters.

c= 100 × 2

c = 200 centimeters

Likewise, since you have the equation I = r × m, and if r = 5% = 0.05 and m = $1000, you can substitute those values into the equation to get:

I = 0.05 × $1000 = $50

Manipulating equations

The equation for converting centimeters into meters can be manipulated to get another equation that converts meters into centimeters by simply dividing both sides of the equal sign by 100.

c = 100 × m

m = c ÷ 100 = c/100

Likewise, the equation for interest can be manipulated to be the equation for rate or the equation for money owed:

I = r × m

r = I/m

m = I/r


The primary purpose of Algebra is to allow you to substitute letters for the names of items in a relationship, thus creating an equation. Then you can substitute in values to solve for an item. You can manipulate the equation to put it in terms of one of the variables.

Simplify your life

Resources and references

Ron Kurtus' Credentials


Algebra Resources


Top-rated books on Algebra

Questions and comments

Do you have any questions, comments, or opinions on this subject? If so, send an email with your feedback. I will try to get back to you as soon as possible.


Click on a button to bookmark or share this page through Twitter, Facebook, email, or other services:


Students and researchers

The Web address of this page is:

Please include it as a link on your website or as a reference in your report, document, or thesis.

Where are you now?

School for Champions

Algebra topics

Purpose of Algebra is to Solve Equations

Algebra topics


Exponents and roots



Quadratic equations

Also see

Let's make the world a better place

Be the best that you can be.

Use your knowledge and skills to help others succeed.

Don't be wasteful; protect our environment.

You CAN influence the world.

Live Your Life as a Champion:

Take care of your health

Seek knowledge and gain skills

Do excellent work

Be valuable to others

Have utmost character

Be a Champion!

The School for Champions helps you become the type of person who can be called a Champion.