# Purpose of Algebra

by Ron Kurtus (updated 18 January 2022)

The purpose of Algebra is to make it easy to state a mathematical relationship and its equation by using letters of the alphabet or other symbols to represent entities as a form of shorthand. Algebra then allows you to substitute values in order to solve the equations for the unknown quantities.

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. These relationships are stated as equations.

Algebra allows you to use letters of the alphabet or other symbols to represent objects and numbers. This makes it more convenient

You can state a physical equation by using letters to represent the elements of the equation. For example, force equals mass times acceleration.

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

Algebra allows you to use letters of the alphabet to represent objects, number, or expressions. Numbers can be constants or variables.

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

### Example of loan payments

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

I = r * m

where:

• I = amount of interest
• r = interest rate
• m = money owed
• * is the multiplication sign

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.

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

### Gravity equation

In Physics, the gravity equation is:

F = m*g

where

• F is the force pulling an object toward the ground
• m is the mass of the object
• g is the acceleration due to gravity

g is a constant, since its value does not change, while F and m are variables.

## 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

## Solving 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

## Summary

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.

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