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Purpose of Algebra is Solving Equations

by Ron Kurtus (10 Janauary 2008)

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 are:

• How is a relationship stated using letters?
• How are values substituted?
• How are equations manipulated?

This lesson will answer those questions. There is a mini-quiz near the end of the lesson.

Stating relationship with letters

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

Changing centimeters to inches

The relationship for changing centimeters to inches is to multiply the number of centimeters times 2.54 to get the number of inches. This can be reworded as: The number of inches equals 2.54 times the number of centimeters.

Suppose we represent inches with the letter i and centimeters with the letter c. Then we have the equation:

c = 2.54 × i

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

Loan payments

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

Let:

• I = amount of interest (note that this is different than the small i in the previous example)
• 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 = 2.54 × i, you can substitute i = 2 inches to find the corresponding number of centimeters.

c= 2.54 × 2

c = 5.08 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 inches can be manipulated to get another equation that converts inches into centimeters by simply dividing both sides of the equal sign by 2.54.

c = 2.54 × i

i = c ÷ 2.54 = c/2.54

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 an of the variables.

Answers to Readers' Questions

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Resources

The following resources provide information on this subject:

Websites

Algebra Resources

Books

Top-rated Algebra books

Miscellaneous

Mini-quiz to check your understanding

1. What is a big advantage of Algebra?

2. What is another advantage of Algebra?

3. What is the equation F = m × a in terms of a?

If you got all three correct, you are on your way to becoming a Champion in Algebra. If you had problems, you had better look over the material again.

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