Learn with Fun - 1

1 . Decimal Numbers !
A Decimal Number is a number that contains a Decimal Point


 Place Value
To understand decimal numbers you must first know about Place Value.

When we write numbers, the position (or "place") of each number is important.

In the number 327:

the "7" is in the Units position, meaning just 7 (or 7 "1"s),
the "2" is in the Tens position meaning 2 tens (or twenty),
and the "3" is in the Hundreds position, meaning 3 hundreds.






As we move left, each position is 10 times bigger!
  From Units, to Tens, to Hundreds
... and ...

As we move right, each position is 10 times smaller

From Hundreds, to Tens, to Units

But what if we continue past Units?

What is 10 times smaller than Units?

1/10 ths (Tenths) are!







 But we must first write a decimal point,
so we know exactly where the Units position is:



"three hundred twenty seven and four tenths"

but we usually just say "three hundred twenty seven point four"


Decimal Point -
The decimal point is the most important part of a Decimal Number. It is exactly to the right of the Units position. Without it, we would be lost ... and not know what each position meant.

Now we can continue with smaller and smaller values, from tenths, to hundredths, and so on, like in this example:

 



2.  Fractions -


A fraction is a part of a whole

Slice a pizza, and you will have fractions:

                                               

1/2	1/4	3/8
(One-Half)	(One-Quarter)	(Three-Eighths)

The top number tells how many slices you have
The bottom number tells how many slices the pizza was cut into.

Numerator / Denominator

We call the top number the Numerator, it is the number of parts you have.

We call the bottom number the Denominator, it is the number of parts the whole is divided into.

Numerator

Denominator

You just have to remember those names! (If you forget just think "Down"-ominator)

Equivalent Fractions

Some fractions may look different, but are really the same, for example: 

4/8                         =           2/4                         =                              1/2

(Four-Eighths)           Two-Quarters                =                          One-Half)

  =              =                            

It is usually best to show an answer using the simplest fraction ( 1/2 in this case ). That is called Simplifying, or Reducing the Fraction.

i) Adding Fractions

You can add fractions easily if the bottom number (the denominator) is the same:

1/4 + 1/4 = 2/4 = 1/2

(One-Quarter)  + (One-Quarter)  = (Two-Quarters)  = (One-Half)

When denominator is different - 

3/8 + 1/4 = ?

You must somehow make the denominators the same.

In this case it is easy, because we know that 1/4 is the same as 2/8 :

3/8 + 2/8 = 5/8

ii) Subtracting Fractions -

There are 3 simple steps to subtract fractions

Step 1. Make sure the bottom numbers (the denominators) are the same

Step 2. Subtract the top numbers (the numerators). Put the answer over the same denominator.

Step 3. Simplify the fraction.

Example - (For same denominators )

   3/4 -1/ 4 = ?

Step 1. The bottom numbers are already the same. Go straight to step 2.

Step 2. Subtract the top numbers and put the answer over the same denominator: 

    3/4 - 1/4 = (3-1)/4  = 2/4 or 1/2

When denominators are different -

1/2 - 1/6 = ?

To make the bottom numbers the same, multiply the top and bottom of the first fraction (1/2) by 3 like this:

 (1*3)/(2*3) = 3/6

Now, it becomes -

 3/6 - 1/6 = (3-1)/6 = 2/6 = 1/3 

We will learn about  -

Multiplying Fractions

Dividing Fractions  in part 2.

Logics of M3

M3 -  1) Mean 2) Median 3) Mode

1. Mean -   The mean is just the average of the numbers.

It is easy to calculate: add up all the numbers, then divide by how many numbers there are.

 In other words it is the sum divided by the count.


Positive numbers -
 Example 1: What is the Mean of these numbers?
      6, 11, 7
 Add the numbers: 6 + 11 + 7 = 24
 Divide by how many numbers (there are 3 numbers): 24 / 3 = 8
 The Mean is 8


Why Does This Work?
It is because 6, 11 and 7 added together is the same as 3 lots of 8:

Negative Numbers

How do you handle negative numbers? Adding a negative number is the same as subtracting the number (without the negative). For example 3 + (-2) = 3-2 = 1.

Knowing this, let us try an example:

Example 3: Find the mean of these numbers:

3, -7, 5, 13, -2

The sum of these numbers is 3 - 7 + 5 + 13 - 2 = 12

There are 5 numbers.

The mean is equal to 12 ÷ 5 = 2.4

The mean of the above numbers is 2.4 .

2. Median -  The middle number (in a sorted list of numbers). 

To find the Median, place the numbers you are given in value order and find the middle number.

Example: find the Median of {13, 23, 11, 16, 15, 10, 26}. 

Put them in order: {10, 11, 13, 15, 16, 23, 26}

The middle number is 15, so the median is 15. 

Try from urself -

 17 , 26 , 13, 24 , 02

Put them in order & try to find the median 

3. Mode -

To find the mode, or modal value, first put the numbers in order, then count how many of each number.

Example:

3, 7, 5, 13, 20, 23, 39, 23, 40, 23, 14, 12, 56, 23, 29

In order these numbers are:

3, 5, 7, 12, 13, 14, 20, 23, 23, 23, 23, 29, 39, 40, 56

This makes it easy to see which numbers appear most often.

In this case the mode is 23.

More Than One Mode -

You can have more than one mode.

Example: {1, 3, 3, 3, 4, 4, 6, 6, 6, 9}

3 appears three times, as does 6.

So there are two modes: at 3 and 6

Having two modes is called "bimodal".

Having more than two modes is called "multimodal".

Grouping -

When all values appear the same number of times the idea of a mode is not useful. But you could group them to see if one group has more than the others. 

Example: {4, 7, 11, 16, 20, 22, 25, 26, 33}

Each value occurs once, so let us try to group them.

We can try groups of 10:

0-9: 2 values (4 and 7)

10-19: 2 values (11 and 16)

20-29: 4 values (20, 22, 25 and 26)

30-39: 1 value (33)

In groups of 10, the "20s" appear most often, so we could choose 25 as the mode.

You could use different groupings and get a different answer!

Basic Operations of Mathematics

In basic mathematics there are many ways of saying the same thing:


Symbol        Words Used
+          Addition, Add, Sum, Plus, Increase, Total
-          Subtraction, Subtract, Minus, Less, Difference, Decrease, Take Away, Deduct
×          Multiplication, Multiply, Product, By, Times, Lots Of
÷          Division, Divide, Quotient, Goes Into, How Many Times


Description -

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

  The numbers to be added together are called the "Addends":




2.  Subtraction is ...
... taking one number away from another.



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.



3.   Multiplication is ...
.. (in its simplest form) repeated addition.

Here we see that 6+6+6 (three 6s) make 18

It could also be said that 3+3+3+3+3+3 (six 3s) make 18


But you can also multiply by fractions or decimals, which goes beyond the simple idea of repeated addition:

Example: 3.5 × 5 = 17.5
which is 3.5 lots of 5, or 5 lots of 3.5





4.  Division is ...
... splitting into equal parts or groups. It is the result of "fair sharing".

Division has its own special words to remember.

Let's take the simple problem of dividing 22 by 5. The answer is 4, with 2 left over. Here we illustrate the important words:







Which is the same as:

Basic Parts of Computer

We shall discuss about some basic parts of Computer -



system unit
monitor
keyboard
mouse
floppy disk drive
flash memory reader
CD or DVD drive
hard disk drive
printer
USB Memory stick
audio ports
joystick port
keyboard port
mouse port
network connection
parallel or printer port
power supply
RAM
serial ports
USB port
video port
laptop
external harddrive
scanner
ear phones
speakers

Description on some above points are :-

1. system unit (CPU-Central Processing Unit) -

 This is the box that contains the computer's main working components. It may rest on the floor or be on a desk.





2.  Monitor

Looks like a tv screen. The computer displays information to you on this screen



3 . Keyboard -
The most familiar input device is the keyboard. Users type the text directly into the computer. There are a number of layouts of the keyboard. In a QWERTY layout the keys are arranged in the same order as that of a type writer. This is called QWERTY because the keys Q-W-E-R-T-Y occur on the left top row of the keyboard. The keys in this type of keyboard can be grouped into following five types:
1. Function keys – F1 to F12 are programmable keys used as short cut keys to perform certain functions
2. QWERTY keys – alphanumeric keys arranged in same order as that of type writers.
3. Special purpose keys – Tab, Caps lock, Shift, Ctrl, Alt, Esc, Backspace, Enter, Print Scrn, Scroll Lock and Pause/Break are special purpose keys.
4. Numeric pad keys – separate section in the keyboard used for entering numeric data.
5. Cursor control keys- these are used to navigate the cursor on the monitor.
Dvorak keyboards were introduced to improve typing efficiency with simpler layout. However it has yet to overcome the popularity of QWERTY keyboards. Concept keyboard layout has flat board containing a grid of switches. An overlay image is placed on top of the grid to indicate what will be done on pressing different areas of the keyboard. Such keyboards are useful for children who may find QWERTY keyboard quite complicated to use. Other variation in the keyboards is based on the language variations. For example, the US and UK keyboards are quite similar but are very different from the French keyboard.




4. Mouse

Along with the keyboard, the mouse is the main way of telling your computer what you want it to do. It looks a bit like a real mouse because of its shape


 

5.   Printer


The printer is there to get paper copies of stuff that you or family members want or something that interests you from online. Make sure you put more paper in the printer so you won't ran out of paper.

6. Network connection

The network connetion is like the phone jack. You can get internet by plugging the cord in the modem and computer, but first you ought to call the cable or the telephone company to connect the internet.

7. Scanner


Takes a visual picture of a picture or a document on papper and digitaly stores it on a computer.