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Algebra of Objects

by Ron Kurtus (revised 24 October 2016)

In Algebra, an alphabetical letter can represent an object, number, or group of numbers. When the letter represents an object, algebraic rules are limited.

You can add, subtract, multiply, or divide an object by a number. You are limited in adding or subtracting different objects. You cannot multiply or divide different objects together.

Questions you may have include:

This lesson will answer those questions.



Dealing with one object

Let the letter "a" represent an apple. Then 2a represents two apples. Likewise, 2a + 3a represents two apples plus three apples. The sum equals five apples.

You can also subtract apples: 6a − 4a = 2a.

But you cannot have a negative object. The result of 4a − 6a is not −2a, that is meaningless.

You can multiply or divide an object by a number: 5 * 2a = 10a.

You can have a fraction of an apple: ½a is one half an apple.

Dealing with two or more objects

If "a" represents an apple and "b" represents a banana, adding and subtracting is limited to the object type.

For example: 3a + 2b − 2a + b equals or results in a + 3b. You can only add or subtract the same type of object.

You can multiply or divide several objects by a number: 5(2a +3b) = 10a + 15b.

Multiplying or dividing objects together

You cannot multiply or divide objects by each other. 2a * 3a is meaningless, since apple times apple has no real value.

Summary

When an alphabetical letter represents an object, algebraic rules are limited. You can add, subtract, multiply, or divide an object by a number. You are limited in adding or subtracting different objects. You cannot multiply or divide different objects together.


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