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.