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# krisandmichaelunproject

last edited by 15 years, 9 months ago [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.

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 cancel 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.

(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(/2x2)=10x2

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/5x5=12x5 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.. -algebra on wikipedia

-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|--

--|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.

-% at a glance

-% on wikipedia

-the 2 types of problems

-examples <========>

Version Information

[BG=bg info changes]

[BG.V 0.3] added charts, chart examples

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