recursal/Fanatic-Fandom huggingface dataset:
Dionsn Dusaw

Dionsn Dusaw

Dionsn Dusaw is one of three Force Sensitive clones created from Sith Lord Zakras's soul, he serves the Grey Jedi as a Maenowan and has a side Job as a smuggler.

During his childhood he was forced to become a weapon of the Sith but eventually escaped along with his clone brother Kenji Dusaw, leaving their other brother Perdix Dusaw behind.

As a teenager Dio and Kenji eventually ended up on the planet Volik,after fleeing from an early state Galactic Empire. Kenji eventually left the planet a few years after arriving on it, Dio stayed to become a Grey Jedi.

After becoming a Koawan, Dio bought an old Stock XS Light Freighter to pursue his smuggling side job.
Mylene Dubois

## Family Information

### Family

Beauregard Dubois (Father), Renee Dubois (Mother), Cerise Dubois (Sister), Charlie Dubois (Sister), Ambrose Dubois (Brother), Bastien Dubois (Uncle), Bernadette Dubois (Niece), Questa Dubois (Aunt), Etienne Dubois (Uncle)

## Physical Description

### Supernatural Type

* Fianna Kinfolk
* Autumn Sidhe Kinain

## Merits and Flaws

### Merits

* Enchanting Voice
* Animal Magnetism

### Flaws

* Nightmares
* Low Self Image
Commutative, Associative and Distributive Laws

*Wow! What a mouthful of words! But the ideas are simple.*

## Commutative Laws

The "Commutative Laws" say we can **swap numbers** over and still get the same answer ...

... when we **add**:

a + b**=**b + a

### Example:

... or when we **multiply**:

a × b**=**b × a

### Commutative Percentages!

Because a × b**=**b × a it is also true that a% of b**=**b% of a

### Example: 8% of 50 = 50% of 8, which is 4

Why **"commutative**" ... ?

Because the numbers can travel back and forth like a **commuter**.

## Associative Laws

The "Associative Laws" say that it doesn't matter how we group the numbers (i.e. which we calculate first) ...

... when we **add**:

(a + b) + c**=**a + (b + c)

... or when we **multiply**:

(a × b) × c**=**a × (b × c)

### Uses:

Sometimes it is easier to add or multiply in a different order:

### What is 19 + 36 + 4?

19 + 36 + 4  =  19 + **(36 + 4)**
=  19 + **40** = 59

Or to rearrange a little:

### What is 2 × 16 × 5?

2 × 16 × 5**=  (2 × 5)** × 16
=  10**× 16 = 160**

## Distributive Law

The "Distributive Law" is the BEST one of all, but needs careful attention.

This is what it lets us do:

3 lots of **(2+4)** is the same as **3 lots of 2** plus **3 lots of 4**

So, the **3×** can be "distributed" across the **2+4**, into **3×2** and **3×4**

And we write it like this:

a × (b + c)  =  a × b  +  a × c

Try the calculations yourself:

* 3 × (**2 + 4**)  =  3 × **6**  =  18
* 3×2 + 3×4  =  6 + 12  =  18

Either way gets the same answer.

* multiply a number by a **group of numbers added together**, or
* do each **multiply** separately then **add** them

### Uses:

Sometimes it is easier to break up a difficult multiplication:

### Example: What is 6 × 204 ?

6 × 204  =  6×200 + 6×4
=  1.200 + 24
=  1.224

Or to combine:

### Example: What is 16 × 6 + 16 × 4?

16 × 6 + 16 × 4  =  16 × **(6+4)**
= 16 × **10**
=  160

We can use it in subtraction too:

### Example: 26×3 - 24×3

26×3 - 24×3 = **(26 - 24)** × 3
=  2 × 3
=  6

We could use it for a long list of additions, too:

### Example: 6×7 + 2×7 + 3×7 + 5×7 + 4×7

**6**×7 + **2**×7 + **3**×7 + **5**×7 + **4**×7
= **(6+2+3+5+4)** × 7
= **20** × 7
= **140**

## And those are the Laws . . .

                  . . . but don't go too far!

The Commutative Law does **not** work for subtraction or division:

### Example:

* 12 / 3 = **4**, but
* 3 / 12 = **¼**

 The Associative Law does **not** work for subtraction or division:

### Example:

* (9 – 4) – 3 = 5 – 3 = **2**, but
* 9 – (4 – 3) = 9 – 1 = **8**

 The Distributive Law does **not** work for division:

### Example:

* 24 / (4 + 8) = 24 / 12 = **2**, but
* 24 / 4 + 24 / 8 = 6 + 3 = **9**
Decimal Numbers !

*A Decimal Number is a number that contains a Decimal Point*

### What is a Decimal Number?

* Place Value
* Introduction to Decimals
* Decimals, Fractions and Percentages
* Decimals, Fractions and Percentages On the Number Line
* Zoomable Number Line

### Putting Decimal Numbers in Order

* Ordering Numbers
* Ordering Decimal Numbers

### How to add, subtract, multiply and divide decimals

* Adding Decimals
* Subtracting Decimals
* Multiplying Decimals
* Dividing Decimals

### Big and Small Decimal Numbers

* Powers of 10
* Metric Numbers
* Rounding Numbers
* Scientific Notation

### How to convert decimals **to fractions** and vice versa

* Converting Decimals to Fractions
* Decimal to Fraction Converter
* Converting Fractions to Decimals

### How to convert decimals **to percents** and vice versa

* Converting Decimals to Percentages
* Converting Percentages to Decimals
Composing Numbers

3

## Composing

So 349 is **composed** of 3 hundreds, 4 tens and 9 ones, in other words:

300 + 40 + 9  ⇒  349
"Composing"

## Decomposing

Decomposing is when we break the number apart:

349  ⇒  300 + 40 + 9
"Decomposing"

## Standard and Expanded Form

Some people call the two different forms "Standard" and "Expanded":

 Standard Form

## Decimal Numbers

We can also compose and decompose decimal numbers:

37,2  ⇒  30 + 7 + 0,2
"Decomposing"

4 + 0,7 + 0,08  ⇒  4,78
"Composing"
Money

## Handling Money

* Money Master (a Coin Game)
* Make the Amount (a Coin Game)
* Currencies of the World
* Unit Price and Unit Price Game

* Counting Coins Activity
* Grass for the Garden Activity

## Interest

* Introduction to Interest
* Compound Interest
* Compound Interest Calculator
* Compound Interest Derivation
* Compound Interest: Periodic Compounding
* Annuities

## Making Money

* Introduction to Investing
* What To Do With Your Money
* Personal Budget
* Pay (Wages, Salary)
* Present Value
* Net Present Value
* Internal Rate of Return
* Investment Graph
Number Names to 100 Table

one

 eleven

 twenty-
one
two
three
four
five
six
seven
eight
nine

 thirty-
one
two
three
four
five
six
seven
eight
nine

 forty-
one
two
three
four
five
six
seven
eight
nine

 fifty-
one
two
three
four
five
six
seven
eight
nine

 sixty-
one
two
three
four
five
six
seven
eight
nine

 seventy-
one
two
three
four
five
six
seven
eight
nine

 eighty-
one
two
three
four
five
six
seven
eight
nine

 ninety-
one
two
three
four
five
six
seven
eight
nine
hundred

## The Pattern for 20 to 99

 twenty

to these:

 -one

*Note that **forty** does not have a **u** but **four** does!*
Cardinal, Ordinal and Nominal Numbers

*Cardinal: how many*
Ordinal: position

Nominal: name

## Cardinal Numbers

A Cardinal Number says how many of something there are, such as one, two, three, four, five.

A Cardinal Number answers the question "How Many?"

Example: here are **five** coins:

It does **not** have fractions or decimals, it is only used for counting.

How to remember: "Cardinal is Counting"

## Ordinal Numbers

An Ordinal Number tells us the position of something in a list.

**1st, 2nd, 3rd, 4th, 5th** and so on (seeCardinal and Ordinal Numbers Chart for more.)

### Example: In this picture the girl is **2nd**:

And the two pups are **3rd** and **4th**.

How to remember: "Ordinal says what Order things are in".

## Nominal Numbers

A Nominal Number is a number used only as a name, or to identify something (not as an actual value or position)

### Examples:

* the number on the back of a player: "8"
* a zip code: "91210"
* a model number: "380"

How to remember: "Nominal is a Name".

## Example With Everything

In this photo there are **6** cars. Car Number **"99"** (with the yellow roof) is in **1st** position:

* **6** is a Cardinal Number (it tells how many)
* **1st** is an Ordinal Number (it tells position)
* **"99"** is a Nominal Number (it is basically just a name for the car)
Dividing by Zero

Just kidding.

In truth:

Dividing by Zero is **undefined**.

## Dividing

To see why, let us look at what is meant by "division":

Division is splitting into equal parts or groups.

It is the result of "fair sharing".

Example: there are 12 chocolates, and 3 friends want to share them, how do they divide the chocolates?

So they get 4 each: 12/3 = 4

## Dividing by Zero

Now, let us try dividing the 12 chocolates among **zero** people, how much does each person get?

**Does that question even make sense?** No, of course it doesn't.

We can't share among zero people, and we can't divide by 0.

## Another Good Reason

After dividing, can we multiply to get back again?

But multiplying by 0 gives 0, so that won't work.

Once again, dividing by zero gives us difficulties!

## Imagine We Could Divide by Zero

Okay, let us **imagine**we**can** divide by zero, and see what happens.

That means that things like 1/0 and 0/0 would behave like normal numbers.

### Try Multiplying By Zero

So let us try using our new "numbers".

For example, we know that zero times any number is zero:

Example: 0×1 = 0, 0×2 = 0, etc

So that should also be true for 1/0:

0 × (1/0) = **0**

But we could also rearrange it a little like this:

0 × (1/0) = (0/0) × 1 = **1**

(Careful! I am **not** saying this is correct! We are **assuming**that we **can** divide by zero, so 0/0 should work the same as 5/5, which is 1).

Arrggh! If we multiply 1/0 by zero we could get 0 *or* 1.

In fact we can't have both possibilites, so we **cannot** define 1/0 to be a number.

So it is **undefined**.

## So what is 0/0 ?

0/0 is like asking "how many 0s in 0?"

Are there no zeros in zero at all? Or perhaps there is exactly one zero in zero? Or many zeros?

So 0/0 is **indeterminate** (it could be any value).

## In conclusion:

When we try to divide by zero, things stop making sense

That is all.
Calculator Fun

Use your own calculator, or the Full Precision Calculator for many more digits.

Many of these seem like magic, but there is always a reason ... see if you can discover it!

## Seven

Try this in a calculator: **1/7**

We get 0,142857142857...

**2/7** gets 0,285714285714...

**3/7** gets 0,428571428571...

In each case it is the same digits "142857" repeating over and over again, justy starting at a different spot.

## Nine

Try this in a calculator: **1/9**

We get 0,11111111...

**2/9** gets 0,22222222...

**8/9** gets 0,88888888...

**9/9** gets ?

## Nines Squared

Now try **1/9^2** (1 divided by 9 squared which equals **1/81**)

We get 0,0123456790123...

All the digits from 0 to 9 repeat over and over again, but '8' is missing!

Now try **1/99^2** (1 divided by 99 squared which equals **1/9801**)

We get 0,0001020304050607080910111213141516171819 etc

Do you see the decimals are 00.01,02.03,... (but '98' is actually missing)

Now try **1/999^2** (=**1/998001**)

We get 0,000001002003004005006007008009010011012 etc

the decimals are 000.001.002.003,... (but '998' is actually missing)

## Eighty Nine

1/89 = 0,01123595505617977528089887640449438202247191*0112...*

The first few digits (0,1,1,2,3,5) are the Fibonacci sequence

In a way they **all** are, except multiple digit numbers (13, 21, etc) **overlap**, like this:

## Ends With Seven Magic

Type in a random 3 digit number twice

E×ample: start with 638, so enter **638638**

Now divide by 11: 638638 / 11 = 58058

Now divide by 13: 58058 / 13 = 4466

Then divide by the original number: 4466 / 638 = 7

You will **always end with 7**

## Ends With Seventy Three Magic

Type in a random 4 digit number twice

E×ample: start with 6385m so enter **63856385**

Now divide by 137: 63856385 / 137 = 466105

Then divide by the original number: 466105 / 6385 = 73

You will **always end with 73**

## Guess the Number

Ask someone to choose a number between 1 and 9

Have them multiply their number by 12345679 (no 8 OK) and they will have a big number like 86419753. Now ask them to give you the calculator.

You then multply that number by 9 (let them see you only press a few buttons), and you will see a number like 777777777, which means their chosen number was 7

## Guess The Numbers

Get a friend to choose two numbers between 1 and 9

Get them to multiply one of them by 5, then add 7, then multiply all of that by 2

Now get them to add their other number, and announce the result.

You can now subtract 14 and the two digit number remaining is the two original numbers next to each other

Example: 4 and 9

They calculate: 4 x 5 = 20, + 7 = 27, x 2 = 54, + 9 = 63.

You subtract 14 from that and get 49. You can the say "your original numbers were 4 and 9".

## Calculator Words

Do the calculation then rotate the display 180°:

* 206 × 3 BIG
* 454 × 17 BILL
* 13 × 26 BEE
* 1 − 0,98 ZOO
* 101 × 8 BOB
* 1 − 0,2266 HELLO
* 333 + 204 LES
* 101 × 7 LOL
* 499 × 155 SHELL
* 115469 × 5 SHELLS
* 819 × 7 EELS
* 5555 + 82 LEGS
* 0,0113 × 7 IGLOO
* 73 × 106 BELL
* 0,18 + 0,19 LEO
* 68 × 81 BOSS
* 1102 × 7HILL
* 5001 × 7LOOSE
* 27689 × 2BLESS
* 1262 × 28GEESE
* 10238 × 37 GOBBLE
Counting to 1.000 and Beyond

## 1 to 20

 one

 eleven

Join these:

 twenty

to these:

 -one

*Note that **forty** does not have a **u** but **four** does!*

## 100 to 999

Write how many hundreds ("one hundred", "two hundred", etc), then the rest of the number as above.

In UK English use "hundred **and**".

## 1,000 to 999,999

Write how many thousands ("one thousand", "two thousand", etc), then the rest of the number as above.

## Millions and More

Write how many millions then the rest of the number like above.

### Examples:

 1,006,101
 191,232,891
 999,999,999

Use the same method for:

## Commas

When writing the number put **commas every three digits** like this:

1,006,101

When writing **words** some people use commas, some don't. Which do you prefer?

* one million six thousand one hundred one
* one million, six thousand, one hundred one
Calculus

The word Calculus comes from Latin meaning "small stone",
Because it is like understanding something by looking at small pieces.

**Differential Calculus** cuts something into small pieces to find how it changes.

**Integral Calculus** joins (integrates) the small pieces together to find how much there is.

Read Introduction to Calculus or *"how fast **right now**?"*

## Limits

Limits are all about approaching. Sometimes you can't work something out directly, but you **can** see what it should be as you get closer and closer!

* Introduction to Limits
* Limits and Infinity
* Evaluating Limits
* Limits (Formal Definition)

* Continuous Functions

## Derivatives (Differential Calculus)

The Derivative is the "rate of change" or slope of a function.

* Introduction to Derivatives
* Slope of a Function at a Point (Interactive)
* Derivatives as dy/dx
* Derivative Plotter (Interactive)
* Derivative Rules
* Power Rule
* Second Derivative and Second Derivative Animation
* Partial Derivatives
* Differentiable
* Finding Maxima and Minima using Derivatives
* Concave Upwards and Downwards and Inflection Points
* Implicit Differentiation
* Taylor Series (uses derivatives)

## Integration (Integral Calculus)

Integration can be used to find areas, volumes, central points and many useful things.

* Introduction to Integration
* Integration Rules
* Integration by Parts
* Integration by Substitution
* Definite Integrals
* Arc Length
* Integral Approximations
* Integral Approximations Calculator and Graph
* Solids of Revolution by Disks and Washers
* Solids of Revolution by Shells
* Fourier Series and Fourier Series Grapher

## Differential Equations

In our world things change, and **describing how they change** often ends up as a Differential Equation: an equation with a **function** and one or more of its **derivatives**:

* Introduction to Differential Equations
* Differential Equations Solution Guide
* Separation of Variables
* First Order Linear Differential Equations
* Homogeneous Differential Equations (Homogeneous Functions)
* The Bernoulli Differential Equation

Second Order Differential Equations:

* Second Order Differential Equations
* The Method of Variation of Parameters
* The Method of Undetermined Coefficients
Hexadecimals

A Hexadecimal Number is based on the number **16**

## 16 Different Values

There are **16** Hexadecimal digits. They are the same as the decimal digits up to 9, but then there are the letters A, B, C, D, E and F in place of the decimal numbers 10 to 15:

So a single Hexadecimal digit can show 16 different values instead of the normal 10.

## Counting

Choose "Hexadecimal" below and watch it count:

Base:

Hexadecimal

Decimal

Binary

0

268435456 = **167**

0

16777216 = **166**

0

1048576 = **165**

0

65536 = **164**

0

4096 = **163**

0

256 = **162**

0

16 = **161**

0

1 = **160**

© 2018 MathsIsFun.com v0,82

After the "Ones" position is filled up (after **F**) the ones start back at **0**, and we add **1** to the next position on the left (to show 1 lot of 16).

And after *that* position reaches **F**, we do the same thing, and so on.

As we move left, every number place is **16 times bigger**.

### Example: What is the decimal value of the hexadecimal number "D1CE"

= 53.248 + 256 + 192 + 14
= 53.710 in Decimal

*(Test it in the Binary to Decimal to Hexadecimal Converter.)*

## The Point !

### Example: 2E6.A3

This is **2×16×16 + 14×16 + 6 + 10/16 + 3/(16×16)**
=742,63671875 in Decimal
Read below to find out why

Numbers can be placed to the left or right of the point, to show values greater than one or less than one:

As we move further right, every number place is **16 times smaller** (one sixteenth as big).

## More Examples

### **Example 1:**What is 4B5 (Hexadecimal)?

* The "4" is in the "16×16" position, so that means 4 ×16×16
* The "B" (11) is in the "16" position, so that means 11 ×16
* The "5" is in the "1" position so that means 5.
* Answer: 4B5 = 4×16×16 + 11×16 + 5 (=1205) in Decimal

### **Example** 2: What is 2,3 (Hexadecimal)?

* On the left side is "2", that is the whole number part.
* The 3 is in the "sixteenths" position, meaning "3 sixteenths", or 3/16
* So, 2,3 is "2 and 3 sixteenths" (=2,1875 in Decimal)

## The Word "Hexadecimal"

The word "Hexadecimal" means "based on 16" (From Greek *hexa: "six"* and Latin *decima*: *"a tenth part"*).
Division

12 Chocolates Divided by 3

Answer: 12 divided by 3 is 4. They get 4 each.

## Symbols

÷  /

We use the **÷** symbol, or sometimes the **/** symbol to mean divide:

12 / 3 = 4

Let's use both symbols here so we get used to them.

## More Examples

Here are some more examples:

Example

12 ÷ 2   =   6

12 divided by 2 equals 6

© 2015 MathsIsFun.com v 0,81

## Opposite of Multiplying

Division is the **opposite of multiplying**. When we know a multiplication fact we can find a division fact:

Example: 3 × 5 = 15, so 15 / 5 = 3.

Also 15 / 3 = 5.

Why? Well, think of the numbers in rows and columns like in this illustration:

So there are **four related facts**:

* 3 × 5 = 15
* 5 × 3 = 15
* 15 / 3 = 5
* 15 / 5 = 3

Knowing your Multiplication Tables can help you with division!

### Example: What is 28 ÷ 7 ?

Searching around the multiplication table we find that 28 is 4 × 7, so 28 divided by 7 must be 4.

Answer: 28 ÷ 7 = 4

## Names

There are special names for each number in a division:

dividend ÷ divisor = quotient

### Example: in 12 ÷ 3 = 4:

* 12 is the dividend
* 3 is the divisor
* 4 is the quotient

## But Sometimes It Does Not Work Perfectly!

Sometimes we cannot divide things up exactly ... there may be something left over.

### **Example:** There are **7** bones to share with **2** pups.

But 7 cannot be divided exactly into 2 groups,
so each pup gets 3 bones,
but there will be **1 left over**:

We call that the **Remainder**.
Subtraction

## Subtraction is ...

... taking one number away from another.

then **subtract 2**,

we are left with 3 apples.
5 − 2 = 3

## Try It Yourself

Click on the pears

8 − 0 = 8

© 2015 MathsIsFun.com v0,92

## Train Yourself

You get good at subtraction with practice...

... so use Math Trainer - Subtraction to train yourself!

You can also "look up" answers for simple subtraction using this table:

## Names

Other names used in subtraction are **Minus, Less, Difference, Decrease, Take Away, Deduct.**

The names of the numbers in a subtraction fact are:

**Minuend − Subtrahend = Difference**

**Minuend**: The number that is to be subtracted from.

**Subtrahend**: The number that is to be subtracted.

**Difference**: The result of subtracting one number from another.

## Subtracting Larger Numbers

To subtract numbers with **more than one digit** (such as "42-25") use any of these methods, ***choose the one you prefer***:
Percentages (%)

**1%** of this line is shaded green: it is very small isn't it?

(25% of this box is green)

## Examples:

5% of **80** is *5***100** × 80 = 4

When 100% =

then:

75% = 60

Use the slider and try some different numbers
(What is 40% of 80? What is 10% of 200? What is 90% of 10?)

So **75%** really means *75***100**

And **100%** is *100***100**, or exactly **1**(100% of any number is just the number, unchanged)

And **200%** is *200***100**, or exactly **2**(200% of any number is twice the number)

### A **Percent** can also be expressed as a ***Decimal*** or a***Fraction***

Read more about this at Decimals, Fractions and Percentages.

## Some Worked Examples

### Example: Calculate 25% of 80

25% = *25***100**

And  *25***100** × 80 = **20**

So 25% of 80 is **20**

### Example: 15% of 200 apples are bad. How many apples are bad?

15% = *15***100**

**30** apples are bad

### Example: if only 10 of the 200 apples are bad, what percent is that?

As a fraction, *10***200** = 0,05

As a percentage it is: *10***200** x 100 = 5%

**5%** of those apples are bad

=== Example: A Skateboard is reduced 25% in price in a sale.

The old price was $120.

Find the new price. ===
First, find 25% of $120:

25% = *25***100**

And  *25***100** × $120 = **$30**

25% of $120 is $30

So the **reduction** is $30

Take the reduction from the original price

$120 − $30 = $90

The Price of the Skateboard in the sale is **$90**

## Calculation Trick

This little rule can make some calculations easier:

x% of y = y% of x

### Example: 8% of 50

**8% of 50** is the same as **50% of 8**

And 50% of 8 is 4

So 8% of 50 is also **4**

## The Word

"Percent" comes from the latin *Per Centum*. The latin word *Centum* means 100, for example a Century is 100 years.

## Percent vs Percentage

My Dictionary says "Percentage" is the "result obtained by multiplying a quantity by a percent". So 10 **percent** of 50 apples is 5 apples: the 5 apples is the **percentage**.

But in practice people use both words the same way.
Addition

bringing two or more numbers (or things) together to make a new total.

to 1 ball
## Try it

Write this down, with the answer, using **numerals**:

You should get:   4 + 3 = 7

## Swapping Places

Swapping the position of the numbers we are adding still gets the same result!

More Examples:

5 + 1 = 1 + 5 = 6

7 + 11 = 11 + 7 = 18

4 + 100 = 100 + 4 = 104

==

Addition Table ==
We can also "look up" answers for simple addition using the Addition Table (but it is really best to learn to remember the answers).

### Example: Find 3 + 5

• find the row starting with "3"

• move along to be under the column "5"

• and there is the number "8", so **3 + 5 = 8**

## Larger Numbers: Use Addition in Columns

26
+\_
64
\_\_
1

## Names

Other names for Addition are **Sum, Plus, Increase, Total**

And the numbers to be added together are called the "**Addends**":
Roman Numerals

Ancient Romans used a special method of showing numbers

Examples: They wrote **V** instead of **5**
And wrote **IX**instead of **9**

*Read on to learn about Roman Numerals or go straight to the Roman Numeral Conversion Tool*.

## The Roman Symbols

Romans Numerals are based on the following symbols:

## Forming Numbers - The Rules

When a symbol appears **after a larger** (or equal) symbol it is **added**

* Example: VI = V + I = 5 + 1 = 6
* Example: LXX = L + X + X = 50 + 10 + 10 = 70

But if the symbol appears **before a larger** symbol it is **subtracted**

* Example: IV = V − I = 5 − 1 = 4
* Example: IX = X − I = 10 − 1 = 9

To Remember: **A**fter Larger is **A**dded

Don't use the same symbol more than three times in a row (but IIII is sometimes used for 4, particularly on clocks)

## How to Convert to Roman Numerals

Break the number into Thousands, Hundreds, Tens and Ones, and write down each in turn.

### Example: Convert 1984 to Roman Numerals.

Break 1984 into 1000, 900, 80 and 4, then do each conversion

* 1000 = M
* 900 = CM
* 80 = LXXX
* 4 = IV

1000 + 900 + 80 + 4 = 1984, so **1984 = MCMLXXXIV**

## How To Remember

Think "MeDiCaL XaVIer".
It has the roman numerals in descending order from 1000 to 1.

I, for one, like Roman numerals!

## Really Big Numbers

Numbers greater than 1.000 are formed by placing a dash over the symbol, meaning "times 1.000", but these are not commonly used:
Ordering Decimals

*"Could I have a 3,65 and an 0,8, please ... ?"*
NO, not THAT type of ordering. I mean **putting them in order** ...

Ordering decimals can be tricky. Because often we look at 0,42 and 0,402 and say that 0,402 must be bigger because there are more digits. But no!

We can use this method to see which decimals are bigger:

* Set up a table with the **decimal point in the same place** for each number.
* Put in each number.
* Fill in the **empty squares with zeros**.
* Compare using the **first column** on the left
* If the digits are equal move to the **next column** to the right until one number wins.

## Example: Put the following decimals in ascending order:

In a table they look like this:

Point
 1
 1

### Fill in the empty squares with zeros:

Point
 1
 1
 0

### Compare using the first column (Ones)

Two of them are "1"s and the other is a "0". Ascending order needs smallest first, and so "0" is the winner:

Answer so far: **0,8**

Now we can remove 0,8 from the list:

Point
 1
 1

### Compare the Tenths

Now there are two numbers with the same "Tenths" value of 5, so move along to the "Hundredths" for the tie-breaker

### Compare the Hundredths

One of those has a 6 in the hundredths, and the other has a 0, so the 0 wins (remember we are looking for the smallest each time). In other words 1,506 is less than 1,56:

Answer so far: **0,8, 1,506**

Remove 1,506 from the list:

Point
 1

Only one number left, it must be the largest:

Answer: **0,8, 1,506, 1,56**

Done!

## Example: Put the following decimals in DESCENDING order:

In a table they look like this:

And we want to go from **highest to lowest** (descending).

### Compare using the first column (Ones):

There is a 1, all the rest are 0. Descending order needs largest first, so 1,2 must be the highest. (Write it down in your answer and cross it off the table).

Answer so far: **1,2**

### Compare the Tenths.

The 8 is highest, so 0,85 is next in value.

Answer so far: **1,2, 0,85**

Now there are two numbers with the same "Tenths" value of 4, so move along to the "Hundredths" for the tie-breaker

One number has a 2 in the hundredths, and the other has a 0, so the 2 wins. So 0,42 is bigger than 0,402:

Answer so far: **1,2, 0,85, 0,42, 0,402**

Only 0,375 left, so the answer is:

**Answer: 1,2, 0,85, 0,42, 0,402, 0,375**
Skip Counting

"Skip Counting" is counting by a number that is**not 1**

### Example: We Skip Count by 2 like this:

2, 4, 6, 8, 10, 12, 14, 16, 18, 20, ...

* count many things quickly
* learn your multiplication tables

## Skip Counting by 10s

Skip Counting by 10s is the easiest.

It is like normal counting (1,2,3,...) except there is an extra "0":

10, 20, 30, 40, 50, 60, 70, 80, 90, 100, ...

* Practice: Skip Counting by 10s to 100
* Practice: Skip Counting by 10s to 300

## Skip Count by 2

https://www.mathsisfun.com/numbers/skip-counting.html

## Try It Yourself

https://www.mathsisfun.com/numbers/skip-counting.html

## Now Get Some Practice!

Now you can practice by "Filling Out the Missing Numbers":

* First try: Skip Counting by 2s to 20
* And then: Skip Counting by 2s to 100

## Skip Counting by 5s

Skip Counting by 5s has a nice pattern:

5, 10, 15, 20, 25, 30, 35, 40, 45, 50, ...

That pattern should make it easy for you!

OK, let us get some practice:

* Start with: Skip Counting by 5s to 50
* And then try: Skip Counting by 5s to 100

## Skip Counting by 3s and 4s

Skip Counting by 3s is:

3, 6, 9, 12, 15, 18, 21, 24, 27, 30, ...

* Practice: Skip Counting by 3s to 36
* And: Skip Counting by 3s to 90

Skip Counting by 4s is:

4, 8, 12, 16, 20, 24, 28, 32, 36, 40, ...

* Practice: Skip Counting by 4s to 48
* And: Skip Counting by 4s to 120

## Skip Count on the Number Line

Also try skip counting on the number line
Abculas's Math Wiki

**Welcome to the Mathpedia!**
We're a collaborative community website that anyone, including you, can build and expand. Wikis like this one depend on readers getting involved and adding content. Click the "ADD NEW PAGE" or "EDIT" button at the top of any page to get started!

*Community Founders*: Write a good and paragraph-length description here about your topic. Let your readers know what your topic is about and add some general information about it. Then you should visit the admin dashboard for more tips.

Addition

Subtraction

Multiplication

Long Multiplication

Division

Long Division

## Important articles

PlaceholderA page about your topicPlaceholderA Main CharacterPlaceholderThe First EpisodePlaceholderAn Important LocationPlaceholderA Key EventPlaceholderA Crucial Item

*Need help building out this community?*

* Getting Started
* How to Contribute
* Managing your new community
* Guides
* All Help articles

You can also be part of the larger Fandom family of communities. Visit Fandom's Community Central!
Alonya MacAlpin

## Family Information

### Family

Viktor Strauss (Father), Isla MacAlpin (Mother), Illarion Chernov (Brother), Elena MacAlpin (Sister), Arkadi MacAlpin (Brother), Tavish MacAlpin (Brother), Viktoria MacAlpin (Sister), Laila MacAlpin (Sister), Callum MacAlpin (Brother), Caelan MacAlpin (Brother)

### Partners

* Illarion Chernov
* Elena MacAlpin

### Children

* (with Illarion Chernov)
* (with Illarion Chernov)

## Merits and Flaws

### Merits

* Recognize Garou
* Danger Sense
* Gnosis

### Flaws

* Soft-Hearted
* Twisted Upbringing
* Post Traumatic Stress Disorder
Percentages !

## What a Percentage is

Introduction to Percentages
Decimals, Fractions and Percentages

Decimals, Fractions and Percentages On the Number Line

## How to find the Percentage Difference

Percentage Difference

Percentage Difference vs Percentage Error

Percentage Points

## How to convert Percents to Decimals and vice versa

Convert Percents to Decimals

Convert Decimals to Percents

## How to convert Percents to Fractions and vice versa

Convert Percents to Fractions

Convert Fractions to Percents

https://www.mathsisfun.com/percentage-menu.html
Algebra

Algebra is great fun - you get to solve puzzles!

With computer games you play by running, jumping or finding secret things. Well, with Algebra you play with letters, numbers and symbols, and you also get to find secret things!

## The Basics

* Introduction to Algebra
* Balance when Adding and Subtracting(animation)
* Introduction to Algebra - Multiplication
* Order of Operations - BODMAS, or PEMDAS
* Substitution
* Equations and Formulas
* Inequalities and Solving Inequalities
* Basic Algebra Definitions

## Exponents

* What is an Exponent?
* Negative Exponents
* Reciprocal in Algebra
* Square Roots, Cube Roots, and nth Roots
* Surds
* Simplifying Square Roots
* Fractional Exponents
* Laws of Exponents
* Using Exponents in Algebra
* Multiply and Divide Variables with Exponents

## Simplifying

* Expanding (removing parentheses)
* Multiplying Negatives
* Associative, Commutative and Distributive Laws
* Cross Multiply
* Proportional
* Directly Proportional and Inversely Proportional
* Fractions in Algebra

## Logarithms

* What Is A Logarithm
* Logarithms Can Have Decimals
* Working with Exponents and Logarithms

## Polynomials

* What is a Polynomial?
* Adding And Subtracting Polynomials
* Multiplying Polynomials
* Polynomial Long Multiplication
* Rational Expressions
* Dividing Polynomials
* Polynomial Long Division
* Conjugate
* Rationalizing The Denominator
* Special Binomial Products

## Linear Equations

* Equation of a Straight Line
* Explore the Straight Line Graph
* Cartesian Coordinates

## Quadratic Equations

* Quadratic Equations
* Quadratic Equation Solver
* Factoring Quadratics and Quadratic Factoring Practice
* Completing the Square

## Solving Word Questions

* Solving Word Questions
* Solving Inequality Word Questions

## Sequences and Series

* Sequences and Series
* Sequences - Finding a Rule
Binary Fingers!

orget about counting to 10 on your fingers ... you can count past 1.000 if you want!

## Right Hand

With just your right hand you can count to 31:

No fingers up is 0

Thumb is 1

Index finger is 2

2 and 1
makes 3

Middle finger is 4

Add your thumb
for 5

4 and
2 makes 6

4 and 2 and 1
makes 7

Fourth finger is 8

* add your thumb (+1) to make 9,
* or add your index finger (+2) to make 10
* or add thumb (+1) and index finger (+2) to make 11
* etc.

makes 26

makes 30

## Why?

So you can count to bigger numbers when you don't have a pencil or paper.

You can also "remember" numbers by holding your fingers in the right way.

Or you can show someone a secret number using just your hand (or hands, see later).

## Your Turn

Practice counting from 0 to 31 on your fingers, just like above.

Do it many times until it becomes easy.

When you can do it well, demonstrate it to your friends!

## Left Hand

Want bigger numbers? Your left hand can help:

Now we can use all 10 fingers to make numbers like these:

makes 34

makes 60

makes 803

And lastly, what happens when all fingers are up?

makes 1.023

So now you can count just past 1.000 using only 10 fingers. Wow.

Practice this over the next few days ... you will gain a new skill and also find binary much easier to understand.
Times Tables Test

# Try out your Multiplication Tables

Learn your Multiplication Table with these quizzes:

 Five Times Tables
 Eight Times Tables
 Eleven Times Tables
 Fourteen Times Tables

## Multiplication Table Instructions

To use the times tables follow this guide:

* Select the times tables you want to try
* Use the drop down boxes and select the one you think is the correct answer
* Once you have completed all the questions press the **OK Done** button
* You then see your results!
* Then do more (*the test is always different!*), or come back here and choose another table
Always End With 1089

=== Add two numbers together and always end with 1089.

Here is How: ===
Pick a three digit number.**The three numbers used must be different**\*. i.e. 123

Reverse that number. 123 becomes 321

Take the smallest three digit number from the largest.
321 − 123 = 198

Take the answer and reverse that number. 198 becomes 891

Add that number to the answer of the subtraction.
891 + 198 = 1089

### The answer will be 1089!

==== So why does it do this?

Find out here ====

### A Little Footnote

But I ended with **198** not **1089** ... !

This happens if you pick a number like 546.

546 goes like this: 645−546=99, then 99+99=198.

BUT if you assume that **099 is a 3 digit number**, you will get:
990−099=891, and 891+198=1089

\*If you don't pick three different numbers then this might happen:
343−343=0, 0+0=0
Measurement

Measurement is finding a number that shows the size or amount of something.

There are two main "Systems of Measurement": **Metric** and **US Standard**.

## Metric

* Introduction to the Metric System (with Maggie!)
* The Metric System of Measurement
* Metric Numbers

## US Standard Units

* Introduction to US Standard Units (with Maggie!)

We can measure many different things, but mostly we measure **Length, Area, Volume, Mass and Time**.

## Length

* Metric Length
* US Standard Length
* Activity: Discover Lengths

## Area

* Metric Area
* US Standard Area
* Area of Circle, Triangle, Square, Rectangle, Parallelogram, Trapezium, Ellipse and Sector
* Activity: Area of a Garden

## Volume

* Metric Volume
* US Standard Volume
* Measuring Cups
* Activity: Discover Capacity

## Mass (Weight)

* Metric Mass
* US Standard Mass
* Weight or Mass?
* Apparent Weight
* Activity: Discover Mass

## Time and Date

* Clocks - Digital and Analog
* Analog and Digital Clocks Animation
* Date and Time Clock (24 hour and AM/PM)
* Stopwatches
* Adding and Subtracting Time
* Day of the Week you were Born

* Introduction to Days, Weeks, Months and Years
* Days
* Weeks
* Months
* Years
* Seasons
* Days Between Two Dates
* 12 Month Calendar

* AD and BC
* Leap Years
* Earth's Orbit and Daylight
* Sun Clock
* World Time Zones

* The Time - Converting AM/PM to 24 Hour Clock
* Time Worksheets

## Conversions

How do you change from one measurement to another? If you know how long something is in meters, but need to know feet? Or square inches to square meters? You need to know how to do Conversions!

* Conversion of Length (a simple intro to conversion)
* Conversion of Area
* Conversion of Volume
* How to Convert Imperial to Metric
* How to Convert Metric to Imperial
* Metric US/Imperial Conversion Charts
* Unit Conversion Method
* Unit Converter

## Temperature

How hot or cold is it going to be today? Is 40° Celsius nice weather? How about 40° Fahrenheit?

* Interactive Thermometer
* Conversion of Temperature - Celsius to Fahrenheit

## Speed

* Metric Speed/Velocity
* US Standard Speed/Velocity
* Speed and Velocity

* Acceleration

## Direction

* Compass: North, South, East and West
* Direction Game
* Mazes

## Units

* The "Unit" in Measurement
* Unit Price and Unit Price Game
* Cooking Measurements

## Accuracy and Precision

* Accuracy and Precision
* Errors in Measurement
Long Multiplication

**Long Multiplication** is a special method for multiplying larger numbers.

It is a way to multiply numbers larger than 10 that **only needs your knowledge of the ten times Multiplication Table**.

Let us say we want to multiply

612 × 24

* First we multiply **612 × 4** (=2.448),
* then we multiply **612 × 20** (=12.240),
* and last we add them together (2.448 + 12.240 = 14.688).

But we can do better!

When we multiply **612 × 20** we only need to multiply **612 × 2**and **place the result one column over** (so it is the same as multiplying by 20).

We just have to be careful about**lining up the columns**. Here is how to do it (press the play button):

## More Than Two Digits

The same idea works when multiplying by more than two digit numbers. We just have to move over more spaces:
Abacus

An abacus has beads that slide on rods. It can be used to count, add, subtract, multiply and more.

The most common abacus is split into two basic rows:

* the top row for the "5"s, and
* the bottom row for the "ones".

There are two beads in the top row, and five beads in the bottom one.

For example, 7 can be made by using one bead on the top row, and 2 beads from the bottom row, because 5 + 2 = 7

Have a play with this one:

Every column represents a different digit, such as Units, Tens, Hundreds, etc.

The abacus has been around for thousands of years, and is still used in some parts of the world. Sometimes blind people will use an abacus, because they can feel the numbers easily.

Expert abacus users can sometimes do calculations faster than on a calculator, and can even use them to find the square root of whole numbers.

https://www.mathsisfun.com/numbers/abacus.html
Pi (π)

Draw a circle with a **diameter**(all the way across the circle) of **1**

Then the **circumference** (all the way around the circle) is **3,14159265...** a number known as **Pi**

**Pi** is often written using the greek symbol π

The definition of π is:

*The**Circumference***
divided by the**Diameter**

of a Circle.

To help you remember what π is ... just draw this diagram.

## Finding Pi Yourself

Draw a circle, or use something circular like a plate.

Measure around the edge (the **circumference**):

I got **82 cm**

Measure across the circle (the **diameter**):

I got **26 cm**

Divide:

82 cm / 26 cm = 3,1538...

That is pretty close to π. Maybe if I measured more accurately?

## Using Pi

We can use π to find a Circumference when we know the Diameter

Circumference = π × Diameter

### Example: You walk around a circle which has a diameter of 100 m, how far have you walked?

Distance walked= Circumference

= π × 100 m

= 314,159... m

= **314 m** (to the nearest m)

Also we can use π to find a Diameter when we know the Circumference

Diameter = Circumference / π

### Example: Sam measured 94 mm around the outside of a pipe ... what is its Diameter?

Diameter= Circumference / π

= 94 mm / π

= 29,92... mm

= **30 mm** (to the nearest mm)

## Radius

The radius is half of the diameter, so we can also say:

For a circle with a **radius** of **1**

The distance *half way around* the circle is **π = 3,14159265...**

## Digits

π is approximately equal to:

**3,14159265358979323846…**

The digits go on and on with no pattern.

π has been calculated to over two quadrillion decimal places and still there is **no pattern** to the digits

## Approximation

A quick and easy approximation for π is 22/7

22/7 = **3,1428571...**

But as you can see, 22/7 is **not exactly right**. In fact π is not equal to the ratio of any two numbers, which makes it an irrational number.

A really good approximation, better than 1 part in 10 million, is:

355/113 = **3,1415929...**
*(think "113355", slash the middle "113/355", then flip "355/113")*

## Remembering The Digits

I usually just remember "3,14159", but you can also count the letters of:

*"May I have a large container of butter today"*
3 1 4 1 5 9 2 6 5

## To 100 Decimal Places

Here is π with the first 100 decimal places:

4197169399375105820974944592307816
4062862089986280348253421170679...

### Calculating Pi Yourself

There are many special methods used to calculate π and here is one you can try yourself: it is called the **Nilakantha series** (after an Indian mathematician who lived in the years 1444–1544).

It goes on for ever and has this pattern:

3 + *4***2×3×4** − *4***4×5×6** + *4***6×7×8** − *4***8×9×10** + ...

(Notice the + and − pattern, and also the pattern of numbers below the lines.)

It gives these results:

 2
 3
 4
 ...

Get a calculator (or use a spreadsheet) and see if you can get better results.

### Pi Day

Pi Day is celebrated on March 14. March is the 3rd month, so it looks like 3/14
Long Division with Remainders

When we are given a long division to do it will not always work out to a whole number.

Sometimes there are numbers left over. These are called **remainders**.

Taking an example similar to that on the Long Division page it becomes more clear:

*(If you feel happy with the process on the Long Division page you can skip the first bit.)*
Order of Operations BODMAS

### Operations

**"Operations"** mean things like add, subtract, multiply, divide, squaring, etc. If it isn't a number it is probably an operation.

But, when you see something like...

7 + (6 × 52 + 3)

... what part should you calculate first?

Start at the left and go to the right?
Or go from right to left?

*Warning: Calculate them in the wrong order, and you can get a wrong answer !*

So, long ago people agreed to follow rules when doing calculations, and they are:

## Order of Operations

Do things in Brackets First

Exponents (Powers, Roots) before Multiply, Divide, Add or Subtract

Multiply or Divide before you Add or Subtract

Otherwise just go left to right

## How Do I Remember It All ... ? BODMAS !

 **AS** | **A**ddition and **S**ubtraction (left-to-right)

Divide and Multiply rank equally (and go left to right).

Add and Subtract rank equally (and go left to right)

So do it this way:

After you have done "B" and "O", just go from left to right doing any "D" ***or*** "M" as you find them.

Then go from left to right doing any "A" ***or*** "S" as you find them.

*Note: the only strange name is "Orders". "Exponents" is used in Canada, and so you might prefer "BEDMAS". There is also "Indices" which makes it "BIDMAS". In the US they say "Parentheses" instead of Brackets, so it is "PEMDAS"*

## Examples

### Example: How do you work out **3 + 6 × 2** ?

**M**ultiplication before **A**ddition:

First **6 × 2 = 12**, then **3 + 12 = 15**

### Example: How do you work out **(3 + 6) × 2** ?

**B**rackets first:

First **(3 + 6) = 9**, then **9 × 2 = 18**

### Example: How do you work out **12 / 6 × 3 / 2** ?

**M**ultiplication and **D**ivision rank equally, so just go left to right:

First **12 / 6 = 2**, then **2 × 3 = 6**, then **6 / 2 = 3**

A practical example:

### Example: Sam threw a ball straight up at 20 meters per second, how far did it go in 2 seconds?

Sam uses this special formula that includes gravity:

height = velocity × time − (1/2) × 9,8 × time2

Sam puts in the velocity of 20 meters per second and time of 2 seconds:

height = 20 × 2 − (1/2) × 9,8 × 22

Now for the calculations!

Start with:20 × 2 − (1/2) × 9,8 × 22

Brackets first:20 × 2 − 0,5 × 9,8 × 22

Then Orders (22=4):20 × 2 − 0,5 × 9,8 × 4

Then the Multiplies:40 − 19,6

Subtract and DONE !**20,4**

**The ball reaches 20,4 meters after 2 seconds**

## Exponents of Exponents ...

What about this example?

432

Exponents are special: **they go top-down** (do the exponent at the top first). So we calculate this way:

So 432 = 4(32), not (43)2

***And finally, what about the example from the beginning?***

Start with:7 + (6 × 52 + 3)

*Brackets* first and then *"Orders"*:7 + (6 × 25 + 3)

Then *Multiply*:7 + (150 + 3)

Then *Add*:7 + (153)

*Brackets* completed:7 + 153

Last operation is an *Add*:**160**
Place Value

*We write numbers using only ten symbols (called Digits).*
Where we place them is important.

## The Ten Digits

The Digits we use today are called "Hindu-Arabic Numerals":

0   1   2   3   4   5   6   7   8   9

We can use these on their own to count up to 9:

But what happens after 9?

## Ten Or More ...

When we have more than 9 items, we start **another column** - the "tens" column - and we write down how many "tens" we have, followed by how many "ones" (also called "units").

So we write:

### Example: this is how we write down **twelve**:

 1

The Number "12"

It says we have **1 Ten** and **2 Ones**, which makes 12.

This can also be written as 1 × 10 + 2 × 1.

### Example: "35" means 3 Tens and 5 Ones, which is also 3 × 10 + 5 × 1

 3

The Number "35"

## Zero

What if we have 1 Ten, but no Ones? We show "no Ones" by **putting a zero** there:

 1

The Number "10"

We have to put a Zero in the Ones place or "10" looks like "1".

## A Hundred Or More ...

When we have more than 99 items, we start **another** column - the "hundreds" column. Now we need to show how many Hundreds, Tens and Ones:

 1

The Number 143

That shows we have 1 Hundred, 4 Tens and 3 Ones:

This can also be written as 1 × 100 + 4 × 10 + 3 × 1.

### Example: "369" means 3 Hundreds, 6 Tens and 9 Ones

Which is also 3 × 100 + 6 × 10 + 9 × 1

We also use a Zero when there are no Tens:

### Example: "104" means 1 Hundred, **Zero** Tens and 4 Ones.

 1

The Number 104

## And So On ...

Each time we want to show a bigger number we just add one column **to the left** and we know it is always **10 times bigger** than than the column on its right.

each new column on the left is ten times bigger

So, where we PLACE a digit is important!

## Names for Each Column

These are the names of each column:

*(For bigger amounts, see Metric Numbers)*

### Example: The number eleven thousand, three hundred and twenty seven in a place value table:

 1

The Number 11.327