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# Algebra of Objects

by Ron Kurtus (revised 18 January 2022)

In * Algebra*, an alphabetical letter can represent an

*, number, or group of numbers. When the letter represents an object, algebraic rules are limited.*

**object**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:

- What happens when dealing with a single object?
- What happens when dealing with several objects?
- What happens when multiplying or dividing objects?

This lesson will answer those questions.

## Dealing with one type of object

When you are considering one type of object, you can add the numbers together and subtract then (as long as the result is positive).

### Adding 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.

### Subtracting

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

But you cannot have a negative object. The result of **4a − 6a** is not equal to **−2a**, since a negative apple is meaningless.

### Multiply or divide by number

You can multiply or divide an object by a number.

For example **5** pairs of apples would be: **5 * 2a = 10a**.

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

## Dealing with different objects

If "**a**" represents an apple and "**b**" represents a banana, adding and subtracting is limited to the object type. But you can group the objects.

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 objects together

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

## 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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objects.htm**

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## Algebra of Objects