Algebra Toy Explanation

Why algebra?

Algebra mixes lots of sums up into the same thing so you can do them all at the same time.

We are never changing the equations themselves, we are just pushing them round so they look different.


What is a term?

The thing that helped me a lot when learning algebra is to think of equations as blocks of "terms"

A "term" is made up of four bits.. like this -2a2

1) A Sign : -2a2

Postitive or negetive

Clicking on two terms will combine them.

Combine a positive and a negetive... they'll cancel eachother out.

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a

-

a

2) A Factor : -2a2

Tells you how many of the variable there are.

Click on the terms to combine them.

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a

+

a

+

a

3) A Variable: -2a2

This is a number you don't know what it is yet. For the moment you have put a letter in there till you do know what it is.

The varible is the most important bit of the term when you are trying to combine them. You can only combine terms that have the same variable.

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2

a

+

b

+

4

a

4) A Power : -2a2

The power says that there are "a" groups of "a". It is a short way of writing a x a.

When you are looking to combine terms, the power must match as well as the variable.

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2

a2

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b2

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4

a

+

b2


Multiplying

If you want to multiply some stuff in an equation you have to be sure that you multiply all the terms you should be.

So that we remember to do this we group all the terms together in a bracket and put the term we are multiplying everything by directly outside the bracket.

Basics

To simplify the bracket just click on the term outside the bracket and a term inside the bracket

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2

+

5

a

-

4

b

Multiplying Variables

Multiplying is not the same as combining. You can multiply terms that don't have the same variable.

When you do this the result will have a new variable. If the varaibles are the same the power will go up. If they are different the new variable will be a combination of both of the original variables.

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2

a

+

5

a

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4

-

4

d


Dividing

Basics

The basics of division are pretty much the same as multiplication. Division will show up as a fraction.

The term we are dividing by is on the bottom of the fraction (the denominator). Click on the denominator then a term on top to do the simplification.

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4

a

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2

When to divide

As I said at the beginning, we are trying to make the equation look better, dividing can help this a lot.

If we can see that all of the terms have a factor in common, we can make it look simplier by dividing by thay number

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4

a

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6

b

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2

c

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2

This goes for variables as well as factors.

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a

+

b

a

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c

a

+

a

Dividing Variables

Helpfully, division isn't as forgiving as multiplication.

If you want to divide by a term with a variable, the term you are dividing by must have that term in it.

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4

d

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4

a

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4

b

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4

a

Getting Rid of a Denominator

Ok, so if we want to get rid of a denominator we must be able to carry out the division.

To do this we need to make the terms on the top have the term on the bottom as a factor --- by multiplying the whole thing by it.

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4

a

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4

d

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4

a

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4

b

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4

a

Go

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+

*

/

1

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9

0

Clear

none

a

b

c

d

1

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9

0

Clear

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2

+

5

a

-

4

+

3

a

=

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4

d

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4

a

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4

b

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4

a

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4

a