[UnP V 1.0]

Here's the link to our main unproject page, which will be about percents.

[BG.V 1.1]

---|contents|----

__top__

-algebra

__bottom__(under first breakline)

-percent

__Algebra__

Algebra is basically finding the unknown number in an expression or an equation. This unknown number is also known as the **"variable".**

Ex. 2n=8

This means that -{2 times a number equals 8.}- The -{n]- is the variable.

Also, since it has a definite answer, in this case 8, it is called an **"equation".**

An equation only has **one answer.**

An **"expression"** is an algebraic expression that can have **many answers.**

It shows a pattern, and can be referred to as the "rule" of a chart, diagram, etc.

Ex. n+6 means shows the pattern of a number increased by 6.

For instance, this chart shows that numbers in the 'y' column are made from taking the corresponding figure number -{x}- and multiplying by 2.

Now look at this chart.

What are the next 3 numbers in 'y'?

To find these, we need to find a **common expression that applies to at least 3** of the y numbers...even though there's only 3 of them. First let's look at the first one.

1 and 6. We can look at this as 1+5=6. Let's try this with the second term.

2 and 7. If we add 5 to 2 we get 7. So we have 1 more to go. 3+5=8, so we can say that the rule is x+5.

__-{Solving addition or subtraction equations]-__

Let's start with an easy one for an example....

n+3=7

Okay, so the first step is to **isolate the variable**, and you do this by **canceling** out the integer (3 in this case).

You c**ancel it by doing the opposite**, and since both sides have to be equal, we get...

n+3**-3**=7**-3**

This works out to n=4, so n is 4.

Then to make sure our answer is right, we verify.

n+3=7

We then replace n with our answer of 4.

(4)+3=7

Since 4+3 = 7, we conclude that 7=7.

If it's subtraction, you'd add to cancel out the integer.

So if it were n-3=7..

n-3**+3**=7**+3**

n=10

Another way to see this process is through 'alge-tiles'. Here's the first example in algetiles.

__-{Solving multiplication or divison equations}-__

When you have multiplcation or division, the same steps come into play, inlcuding the cancelling. **You use multiplication to cancel division and vice versa.**

Let's see, how about... 3n=18

(when you multiply, put the number you're multiplying by before the variable)

So we start with 3n=18, we cancel that by dividing each side by 3, because 3/3 = 1.

3**/3** n=18**/3**

So we'd end up with 1n=6, simplified to n=6.

And again we verify:

3n=18

3(6)=18

18=18.

And as for a division question...

n/2=10

The first thing we now have to do is cancel out that -{/2}- and we do this by multiplying it by two, and the other side as well.

n(/2**x2**)=10**x2**

And we end with n=20. Once more, we verify..

n/2=10

(20)/2=10

10=10.

__ -{Two Step Equations}-__

Solving these are pretty simple, you still isolate the variable by cancelling the integers.

Let's say we have 3n+1=25.

We first subtract: 3n+1**-1**=25**-1**, which gives us 3n=24.

Then we cancel out the 3: 3n/3=24/3 which is n=8.

Don't forget to verify:

3n+1=25

3(8)+1=25

24+1=25

25=25.

Now let's try n/5-6=6.

We first cancel the integer.

n/5-6**+6**=6**+6**, which is n/5=12

So now we cancel the /5

n/5**x5**=12**x5** which turns to n=60.

Verify:

n/5-6=6

(60)5-6=6

12-6=6

6=6

Here's a little practice question...

If the length of a rectangle is 2.5 times the width, and the perimeter is 60cm, what is the length and width?

First we should say that Length is l and Width is w.

Then we know that:

Length = 7w-2

Width = ? (variable)

Perimeter = 60.

We can draw several things for this..

__ -{Links}-__

-algebra on wikipedia

-more information

-more examples

**Percent-**

A percent is a part or parts out of 100. It can be converted into fractions, decimals and ratios. It may go over 100%. This indicates that there is more than one whole.

----|Remember|----

-to find any percent of any number, divide any number by 100 then multiply by whatever % you want to find.

say the number is 50 and I wanted to find 42% of 50.

----|How to convert into..|----

--|Fractions|--

-take your percent(40) and put 100 as your denominator. simplify.

--|Decimals|--

-percent(40) divided by 100.

--|Ratios|--

-take your percent(40)and subtract it from 100. your percent will be the first part of the ratio.

-whatever is left of 100 is your second part.

----|word problem!|----

-Bob has 30 apples he needs to sell. He wants to sell at least 70% of the apples by the end of the day. How many apples would Bob need to sell?

1. 30/100. --0.3

2. 0.3(70) --21

__-Bob needs to sell at least 21 apples by the end of the day.__

----|Links|----

-% at a glance

-% on wikipedia

-the 2 types of problems

-examples

<========>

Version Information

[BG=bg info changes]

[UnP=unproject link changes]

[BG.V 0.1] added banner, algebra up to addition and subtraction equations

[BG.V 0.2] percent background information added, further updates still to come..

[BG.V 0.3] added charts, chart examples

[BG.V 1.0]added two step, multi and divi, finished basic background info

[BG.V 1.1]percent section overhauled, links, table of contents added

[UnP.V 1.0] added link to unproject

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